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--- Page 2 ---
Non-Equilibrium Air Plasmas at Atmospheric
Pressure
--- Page 3 ---
Series in Plasma Physics
Series Editors: Steve Cowley, Imperial College, UK
Peter Stott, CEA Cadarache, France
Hans Wilhelmsson,
Chalmers University of Technology, Sweden
Other books in the series
Magnetohydrodynamic Waves in Geospace
ADM Walker
Plasma Waves, second edition
D G Swanson
Microscopic Dynamics of Plasmas and Chaos
Y Elskens and D Escande
Plasma and Fluid Turbulence: Theory and Modelling
A Yoshizawa, S-I Hoh and K Hoh
The Interaction of High-Power Lasers with Plasmas
S Eliezer
Introduction to Dusty Plasma Physics
P K Shukla and A A Mamun
The Theory of Photon Acceleration
J T Mendon~a
Laser Aided Diagnostics of Plasmas and Gases
K Muraoka and M Maeda
Reaction-Diffusion Problems in the Physics of Hot Plasmas
H Wilhelmsson and E Lazzaro
The Plasma Boundary of Magnetic Fusion Devices
PC Stangeby
Non-Linear Instabilities in Plasmas and Hydrodynamics
S S Moiseev, V N Oraevsky and V G Pungin
Collective Modes in Inhomogeneous Plasmas
J Weiland
Transport and Structural Formation in Plasmas
K Hoh, S-I Hoh and A Fukuyama
Tokamak Plasmas: A Complex Physical System
B B Kadomstev
Electromagnetic Instabilities in Inhomogeneous Plasma
A B Mikhailovskii
--- Page 4 ---
Series in Plasma Physics
Non-Equilibrium Air Plasmas
at Atmospheric Pressure
K H Becker
Stevens Institute of Technology, Hoboken, NJ, USA
U Kogelschatz
ABB Corporate Research, Baden, Switzerland (retired)
K H Schoenbach
Old Dominion University, Norfolk, V A, USA
and
R J Barker
US Air Force Office of Scientific Research, Arlington, V A, USA
loP
Institute of Physics Publishing
Bristol and Philadelphia
--- Page 5 ---
© lOP Publishing Ltd 2005
All rights reserved. No part of this publication may be reproduced, stored in
a retrieval system or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior per-
mission of the publisher. Multiple copying is permitted in accordance with
the terms of licences issued by the Copyright Licensing Agency under the
terms of its agreement with Universities UK (UUK).
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN 0 7503 0962 8
Library of Congress Cataloging-in-Publication Data are available
Commissioning Editor: John Navas
Editorial Assistant: Leah Fielding
Production Editor: Simon Laurenson
Production Control: Sarah Plenty
Cover Design: Victoria Le Billon
Marketing: Louise Higham and Ben Thomas
Published by Institute of Physics Publishing, wholly owned by The Institute
of Physics, London
Institute of Physics Publishing, Dirac House, Temple Back, Bristol BSI 6BE, UK
US Office: Institute of Physics Publishing, The Public Ledger Building, Suite
929, 150 South Independence Mall West, Philadelphia, PA 19106, USA
Printed in the UK
--- Page 6 ---
Contents
Foreword
ix
1 Introduction and Overview
1
1.1
Motivation
2
1.2
Parameter Space of Interest
4
1.3
Naturally-occurring Air Plasmas
7
1.4
Sources of Additional Information
9
1.5
Organization of this Book
12
2 History of Non-Equilibrium Air Discharges
17
2.1
Introduction
17
2.2
Historical Roots of Electrical Gas Discharges
17
2.3
Historical Progression of Generating Techniques for Hot
and Cold Plasmas
19
2.3.1
Generation of hot plasmas
19
2.3.2 Generation of cold plasmas
21
2.3.3 Properties of non-equilibrium air plasmas
24
2.4
Electrical Breakdown in Dense Gases
29
2.4.1
Discharge classification and Townsend breakdown
29
2.4.2 Streamer breakdown
35
2.4.3
Pulsed air breakdown and runaway electrons
38
2.5
Corona Discharges
41
2.5.1
Phenomenology of corona discharges
41
2.5.2 Negative dc corona discharges
47
2.5.3
Positive dc corona discharges
54
2.5.4 AC corona discharges
60
2.5.5 Pulsed streamer corona discharges
63
2.6
Fundamentals of Dielectric-Barrier Discharges
68
2.6.1
Early investigations
68
2.6.2 Electrode configurations and discharge properties
70
2.6.3
Overall discharge parameters
70
v
--- Page 7 ---
vi
Contents
3 Kinetic Description of Plasmas
76
3.1
Particles and Distributions
76
3.2
Forces, Collisions, and Reactions
90
3.3
The Kinetic Equation
105
3.4
Evaluation and Simplification of the Kinetic Equation
117
4 Air Plasma Chemistry
124
4.1
Introduction
124
4.2
Air Plasma Chemistry Involving Neutral Species
127
4.2.1
Introduction
127
4.2.2 Neutral chemistry in atmospheric-pressure air
plasmas
128
4.2.3 Summary of the important reactions for the
neutral air plasma chemistry
130
4.3
Ion-Molecule Reactions in Air Plasmas at Elevated
Temperatures
136
4.3.1
Introduction
136
4.3.2 Internal energy definitions
138
4.3.3 Ion-molecule reactions
140
4.3.4 Summary
153
4.4
Non-Equilibrium Air Plasma Chemistry
154
4.4.1
Introduction
154
4.4.2 Translational and vibrational energy dependence
of the rates of chemical processes
156
4.4.3 Advances in elucidating chemical reactivity at very
high vibrational excitation
161
4.5
Recombination in Atmospheric-Pressure Air Plasmas
168
4.5.1
Theory
169
4.5.2 ot +e-
170
4.5.3 NO+ + e-
171
4.5.4 Nt +e-
173
4.5.5
H30 +(H2O)n
174
4.5.6 High pressure recombination
175
5 Modeling
183
5.1
Introduction
183
5.2
Computational Methods for Multi-dimensional
Nonequilibrium Air Plasmas
185
5.2.1
Introduction
185
5.2.2 Basic assumptions
186
5.2.3 The conservation equations
186
5.2.4 Equations of state
189
5.2.5 Electrodynamic equations
189
5.2.6 Transport properties
190
--- Page 8 ---
Contents
vii
5.2.7 Chemical kinetics
193
5.2.8 Numerical method
193
5.2.9 Simulation results
195
5.2.10 Conclusions
198
5.3
DC Glow Discharges in Atmospheric Pressure Air
199
5.3.1
Introduction
199
5.3.2 Two-temperature kinetic simulations
200
5.3.3 Predicted electric discharge characteristics
211
5.3.4 Experimental dc glow discharges in atmospheric
pressure air plasmas
218
5.3.5 Electrical characteristics and power requirements
of dc discharges in air
228
5.3.6 Conclusions
231
5.4
Multidimensional Modeling of Trichel Pulses in Negative
Pin-to-Plane Corona in Air
233
5.4.1
Introduction
233
5.4.2 Numerical model
235
5.4.3
Results of numerical simulations
238
5.4.4 Conclusions
244
5.5
Electrical Models of DBDs and Glow Discharges in Small
Geometries
245
5.5.1
Introduction
245
5.5.2 Model of plasma initiation and evolution
246
5.5.3 Dielectric barrier discharges
251
5.5.4 Micro-discharges: discharges in small geometries
258
5.5.5 Conclusions
259
5.6
A Computational Model of Initial Breakdown in
Geometrically Complicated Ssystems
262
5.6.1
Introduction
262
5.6.2 The numerical model
265
5.6.3
Simulation results
269
5.6.4 Discussion
274
6 DC and Low Frequency Air Plasma Sources
276
6.1
Introduction
276
6.2
Barrier Discharges
277
6.2.1
Multifilament barrier discharges
278
6.2.2 Modeling of barrier discharges
280
6.3
Atmospheric Pressure Glow Discharge Plasmas and
Atmospheric Pressure Townsend-like Discharge Plasmas
286
6.3.1
Introduction
286
6.3.2 Realization of an APG discharge plasma
287
6.3.3 Applications of APG discharge and APT discharge
plasmas
291
--- Page 9 ---
Vlll
Contents
6.4
Homogeneous Barrier Discharges
293
6.4.1
DBD-based discharges at atmospheric pressure
294
6.4.2 The resistive barrier discharge (RBD)
299
6.4.3 Diffuse discharges by means of water electrodes
301
6.5
Discharges Generated and Maintained in Spatially
Confined Geometries: Microhollow Cathode (MHC) and
Capillary Plasma Electrode (CPE) Discharges
306
6.5.1
The microhollow cathode discharge
307
6.5.2 The cathode boundary layer discharge
319
6.5.3 The capillary plasma electrode discharge
321
6.5.4 Summary
324
6.6
Corona and Steady State Glow Discharges
328
6.6.1
Introduction
328
6.6.2 Methods to control negative corona parameters
329
6.6.3 DC glow discharge in air flow
334
6.6.4 Transitions between negative corona, glow and
spark discharge forms
338
6.6.5 Pulsed diffuse glow discharges
348
6.7
Operational Characteristics of a Low Temperature AC
Plasma Torch
350
6.7.1
Introduction
350
6.7.2 Torch plasma
351
6.7.3 Power consumption calculation
359
7 High Frequency Air Plasmas
362
7.1
Introduction
362
7.2
Laser Initiated or Sustained, Seeded High-Pressure
Plasmas
364
7.2.1
Introduction
364
7.2.2 Laser-sustained plasmas with CO seedant
365
7.2.3 Ultraviolet Laser Produced TMAE Seed Plasma
379
7.3
Radiofrequency and Microwave Sustained High-Pressure
Plasmas
395
7.3.1
Introduction
395
7.3.2 Review of rf plasma torch experiments
395
7.3.3 Conclusions
406
7.3.3 Laser initiated and rf sustained experiments
407
7.3.4 Methods for spatial localization of a microwave
discharge
413
7.4
Repetitively Pulsed Discharges in Air
419
7.4.1
Introduction
419
7.4.2 Experiments with a single pulse
421
7.4.3 Experiments with 100 kHz repetitive discharge
423
7.4.4 Conclusions
427
--- Page 10 ---
Contents
ix
7.5
Electron-Beam Experiment with Laser Excitation
427
7.5.1
Introduction
427
7.5.2 Electron loss reduction
428
7.5.3 Experimental discharge; electron beam ionizer
429
7.5.4 Results and analysis of discharge operation
431
7.5.5 Summary; appraisal of the technique
440
7.6
Research Challenges and Opportunities
443
8 Plasma Diagnostics
446
8.1
Introduction
446
8.2
Elastic and Inelastic Laser Scattering in Air Plasmas
450
8.2.1
Background and basic theory
450
8.2.2 Practical considerations
462
8.2.3 Measurements of vibrational distribution function
465
8.2.4 Filtered scattering
469
8.2.5 Conclusions
480
8.3
Electron Density Measurements by Millimeter Wave
Interferometry
482
8.3.1
Introduction
482
8.3.2 Electromagnetic wave propagation in plasma
483
8.3.3 Plasma density determination
486
8.4
Electron Density Measurement by Infrared Heterodyne
Interferometry
488
8.4.1 Introduction
488
8.4.2 Index of refraction
490
8.4.3 The infrared heterodyne interferometer
492
8.4.4 Application to atmospheric pressure air
microplasmas
493
8.4.5 Measurement of the electron density in dc plasmas
494
8.4.5 Measurement of the electron density in pulsed
operation
498
8.4.6 Conclusions
500
8.5
Plasma Emission Spectroscopy in Atmospheric Pressure
Air Plasmas
501
8.5.1
Temperature measurement
501
8.5.2 NO A-X and N2 C-B rotational temperature
measurements
506
8.5.3 Nt B-X rotational temperature measurements
508
8.5.4 Measurements of electron number density by optical
emission spectroscopy
508
8.6
Ion Concentration Measurements by Cavity Ring-Down
Spectroscopy
517
8.6.1
Introduction
517
8.6.2 Cavity ring-down spectroscopy
518
--- Page 11 ---
x
Contents
8.6.3
~t measurements
520
8.6.4
~O+ measurements
531
9 Current Applications of Atmospheric Pressure Air Plasmas
537
9.1
Introduction
537
9.2
Electrostatic Precipitation
539
9.2.1
Historical development and current applications
539
9.2.2 Main physical processes involved in electrostatic
precipitation
541
9.2.3 Large industrial electrostatic precipitators
546
9.2.4 Intermittent and pulsed energization
549
9.3
Ozone Generation
551
9.3.1
Introduction: Historical development
551
9.3.2 Ozone properties and ozone applications
553
9.3.3 Ozone formation in electrical discharges
554
9.3.4 Kinetics of ozone and nitrogen oxide formation
555
9.3.5 Technical aspects of large ozone generators
560
9.3.6 Future prospects of industrial ozone generation
563
9.4
Electromagnetic Reflection, Absorption, and Phase Shift
565
9.4.1
Introduction
565
9.4.2 Electromagnetic theory
566
9.4.3 Air plasma characteristics
569
9.4.4 Plasma power
571
9.4.5 Applications
572
9.5
Plasma Torch for Enhancing Hydrocarbon-Air
Combustion in the Scramjet Engine
574
9.5.1
Introduction
574
9.5.2 Plasma for combustion enhancement
577
9.5.3 Plasma torch for the application
580
9.6
The Plasma Mitigation of the Shock Waves in
Supersonic/Hypersonic Flights
587
9.6.1
Introduction
587
9.6.2 Methods for flow control
588
9.6.3 Plasma spikes for the mitigation of shock waves:
experiments and results
589
9.7
Surface Treatment
597
9.7.1
Introduction
597
9.7.2 Experimen tal
599
9.7.3 Cleaning
601
9.7.4 Oxidation
605
9.7.5 Functionalization
607
9.7.6 Etching
613
9.7.7 Deposition
615
9.7.8 Conclusions
617
--- Page 12 ---
Contents
Xl
9.8
Chemical Decontamination
9.8.1
Introduction
621
621
622
625
630
9.8.2 de-NOx process
9.8.3 Non-thermal plasmas for de-NOx
9.8.4 Parametric investigation for de-NOx
9.8.5 Pilot plant and on-site tests
9.8.6 Effects of gas mixtures
9.8.7 Environmentally harmful gas treatments
9.8.8 Conclusion
632
632
636
639
9.9
Biological Decontamination by Non-equilibrium
Atmospheric Pressure Plasmas
643
9.9.1
N on-equilibrium, high pressure plasma generators
643
9.9.2 Inactivation kinetics
645
9.9.3 Analysis of the inactivation factors
648
9.9.4 Conclusions
653
9.10 Medical Applications of Atmospheric Plasmas
655
9.10.1 A bio-compatible plasma source
655
9.10.2 In vivo treatment using electric and plasma methods
657
9.10.3 Plasma needle and its properties
663
9.10.4 Plasma interactions with living objects
666
Appendix
673
Index
679
Note:
A summary of references to Air Plasmas compiled by R Vidmar is available
on the Web at:
http://bookmark.iop.org/bookpge.htm?&isbn = 0750309628
--- Page 14 ---
Foreword
Air plasmas (lightning and aurora) and flames were probably the first plasmas
to be studied. Until reliable vacuum pumps were developed, these complicated
plasmas were the subject of mostly empirical studies. Up to the 1940s, studies
were often made with what was a relatively poor vacuum. In the 1920s and
1930s the favorite discharge was the mercury vapor discharge because of
the ubiquitous mercury diffusion pump, McLeod gauge and the interest in
developing large rectifiers and the fluorescent lamp. Langmuir greatly
advanced the understanding of many plasma phenomena using simple
mercury vapor discharges. When vacuum techniques improved, most of the
attention was on the rare gases or, at most, binary mixtures of these gases.
After 1946, there was an initial interest in the real gas effects in air flows
over blunt bodies moving at hypersonic speeds. At Mach numbers greater
than about 12, modest dissociation and ionization effects already occur and
air can no longer be considered as a mixture of just nitrogen, oxygen, and
argon. At Mach numbers around 20, the gas temperature behind a normal
shock for a blunt body reaches values higher than 6500 K and the effects of
dissociation, ionization, radiation and recombination on heat transfer and
radio wave communication become dramatic. The quality of the work
performed at that time was very impressive and includes two of the now
classical reports from F. R. Gilmore of the Rand Corporation, 'Equilibrium
Composition and Thermodynamic Properties of Air to 24000K' and his
often cited potential energy diagrams in 'Potential Energy Curves for N2,
NO, O2 and Corresponding Ions' published in 1955 and 1964, respectively.
There were excellent reports from several laboratories treating the problems
of re-entry mostly using local thermodynamic equilibrium approaches. After
the initial surge of interest, the aeronomy studies continued apace. However,
it took some years for the non-equilibrium plasma tools to mature.
Plasmas generated and maintained at atmospheric pressure enjoyed a
renaissance in the 1980s, mostly driven by applications such as high power
lasers, opening switches, novel plasma processing applications and sputter-
ing, EM absorbers and reflectors, remediation of gaseous pollutants, medical
Xlll
--- Page 15 ---
xiv
Foreword
sterilization and biological decontamination and excimer lamps and other
non-coherent vacuum-ultraviolet (VUV) light sources. Atmospheric-
pressure plasmas in air are of particular importance as they do not require a
vacuum enclosure and/or additional feed gases. This edited volume brings to
the community the state-of-the-art in atmospheric-pressure air plasma
research and its technological applications. Advances in atmospheric-pressure
plasma source development, air plasma diagnostics and characterization, air
plasma chemistry at atmospheric pressure, modeling and computational
techniques as applied to atmospheric-pressure air plasmas, and an assessment
of the status and prospects of atmospheric-pressure air plasma applications are
addressed by a diverse group of experts in the field from all over the world.
While the book emphasizes atmospheric-pressure plasmas in air, many
results presented will also be applicable, perhaps with modifications, to
atmospheric-pressure plasmas in other gases and gas mixtures. This book
is primarily directed to researchers and engineers in the field of plasmas
and gas discharges, but it is also suitable as a pedagogical review of the
areas for graduate and professional certificate courses. The extensive section
on applications (in various states of technological maturity) makes this book
also attractive for practitioners in many fields of application where technol-
ogies based on atmospheric-pressure air plasmas are emerging.
Alan Garscadden
February 2004
[Dr Alan Garscadden is the Chief Scientist of the Propulsion Directorate at the Air Force
Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio, USA. He has
worked extensively in the areas of plasmas, optical and mass spectroscopy, laser kinetics
and diagnostics, and propulsion and power technologies. He has authored or co-authored
160 publications in professional journals and he has given numerous invited talks at
international conferences on topics relating to gas discharge and plasma physics and
their applications. Among Dr Garscadden's many credentials are the Will Allis Prize of
the American Physical Society (2001) and the Presidential Meritorious Award. He is a
Fellow of the APS, IEEE, AIAA, and the Institute of Physics (UK).]
--- Page 16 ---
Chapter 1
Introduction and Overview
R J Barker
Interest continues to grow worldwide in practical applications of weakly
ionized, low-temperature, sea-level air plasmas. This book is written for
scientists, engineers, practitioners, and graduate students who seek a detailed
understanding of 'cold' (non-equilibrium) atmospheric-pressure air plasmas;
and their generation, sustainment, characterization, modeling, and practical
application. Non-thermal, ambient temperature and pressure volumes of
natural air plasmas avoid the restrictions imposed by costly, cumbersome
vacuum chambers and by destructively high temperatures. At the same
time, however, they vastly complicate the plasma physics and chemistry
involved. This edited volume provides the technically savvy reader with
the fundamental knowledge necessary to understand the science and the
application of these non-equilibrium air plasmas at atmospheric pressure.
This first chapter sets the stage for all that follows and should be
read carefully in order to maximize one's appreciation for the following
chapters. It begins by explaining why this topic is important to researchers
in the fields of defense, medicine, electronics, materials science, environ-
mental health, and aviation. Equally important, it explains why this book
is an excellent information source for this topic. After that, the second
section carefully describes what portion of air plasma parameter space is
treated in this book. This is crucial for determining the range of applicability
of the information provided herein. Section 1.3 then digresses briefly to
provide the reader with a natural reference frame from which to better
view the subsequent discussions of man-made air plasmas; namely it
describes where and how nature generates large volumes of plasma in air.
Section 1.4 presents the wealth of sources, both in publications as well as
in conferences, from which a reader may gain further details of and updates
to the air plasma information contained in this volume.
This first chapter ends with a complete chapter-by-chapter overview of
this entire edited volume. The logic underlying the flow of the book is
--- Page 17 ---
2
Introduction and Overview
discussed and brief synopses of the material covered in each of the remaining
chapters are presented. A reader can use section 1.5 to identify which
chapters contain the most important information relating to his/her specific
area of air plasma interest.
1.1
Motivation
One of the most important yet often underutilized questions facing any
technical author is, 'Who should read this book and why?' This proper
delineation of a book's target audience is crucial toward determining the
ultimate 'usefulness' of the book. The two major characteristics of concern
regarding the audience are (1) its educational level and (2) its technical
interests.
At the earliest stage in the preparation of this book, the editors agreed
that all material will be written under the assumption that it will be read
by a scientist and/or engineer/practitioner who has completed at least a
Master of Science or Engineering degree. The reader should have a famil-
iarity with basic electromagnetics as well as concepts governing chemical
rate equations. Completion of at least a basic course in plasma physics
and/or plasma chemistry would be beneficial but not mandatory. This
volume may be appropriate for classroom adoption as a graduate level
text for a special-topics seminar course in high-pressure plasmas or for
supplemental reading in a graduate level course on Gas Discharge Physics
or Plasma Processing or for a continuing education or short course text.
Nevertheless, it was not intentionally designed to be used as a textbook.
(For example, it lacks end-of-chapter homework problems.) At the same
time, its intended usefulness is specifically not limited to university air
plasma researchers but rather broadly targeted to also include industrial
and military applications and design engineers. For these reasons, not only
are underlying theories discussed but also practical laboratory techniques
are explained, with care being taken at the end to show how all can have
important real-world applications.
This book was written to serve as a comprehensive source of detailed
information for readers with a wide variety of technical interests. To begin
with, this would make valuable reading for anyone in the fields of plasma
physics and/or plasma chemistry. It covers parameter ranges of growing
importance to the industrial community but which are normally omitted
from traditional university plasma courses. However, the value of this
volume is by no means limited to the plasma communities. On the contrary,
pains were taken throughout to ensure its understanding by all scientific and
engineering communities that have interests in atmospheric pressure 'cold'
air plasmas for a growing list of applications. The technical fields involved
include but are not limited to the following:
--- Page 18 ---
Motivation
3
1. Microwave propagation. Volumes of lightly ionized air can act as
extremely efficient and broadband absorbers of microwave radiation.
The free electrons present act to collisionally convert the electromagnetic
energy into thermal energy in the ambient gas (Vidmar 1990).
2. Sterilization/decontamination. Weakly ionized air is an extremely efficient
killer of micro-organisms, including bacteria and even spores (Laroussi
et al 2002, Birmingham and Hammerstrom 2000, Roth et al 2001,
Montie et al 2000). This seems to be driven by the plasma chemistry of
the ions and excited neutral species rather than any short-lived free
electron population.
3. Pollution control. Air ionization systems are used to deposit electrical
charge on particulate pollutants and then efficiently extract such particles
from the airflow via oppositely-charged electrodes (White 1963, Parker
1997). More recent work has shown promise for using air plasma
chemistry to neutralize chemical pollutants as well (Nishida et aI2001).
4. Surface materials processing. A brief exposure of certain types of materials
to a volume of ionized air can significantly modify the surface properties
of the material. For example, the water-repellent surfaces of certain
plastics have been made wettable (Tsai et aI1997).
5. Aerodynamics. There is evidence that thin, weakly-ionized volumes of air
flowing along airfoils can be electronically steered, thereby offering the
possibility of achieving some level of flight control without hydraulic
mechanical actuator servers (Roth 2003, Van Dyken et al 2004). There
have also been claims of plasma-based supersonic shock-front mitigation
although this remains controversial (Kuo et aI2000).
6. High-speed combustion. The 'flame-out' of jet engines in high-speed flight
can be a disconcerting event even for experienced pilots. Furthermore, as
military aircraft designers push toward hypersonic speeds, possibly driven
by ramjet technology, they must be concerned even more about uniform
combustion ignition and sustained 'flame holding'. Plasma-based
combustors are being successfully tested and employed for such an
application (Kuo and Bivo1aru 2004, Liu et al 2004).
7. Lightning discharge control. Violent lightning strikes cause millions of
dollars worth of damage every year to commercial power distribution
systems. The sometimes extended power outages that can result cause
even more millions of dollars worth of loss to industrial and private
customers. It would be useful to create methodologies for the pre-
planned establishment of air plasma channels through the atmosphere
to harmlessly drain thunderstorm charge accumulations in a safe
manner before lightning-strike conditions can even be achieved in
sensitive locales.
Those applications will be discussed in chapter 9. Additional possible future
air plasma applications will also be addressed there.
--- Page 19 ---
4
Introduction and Overview
While there are other books available for scientists and engineers
interested in the examination and application of air plasmas, this is the
only book that combines the following three elements in its focus.
1. Natural air is treated herein, not only simple laboratory mixtures of
oxygen and nitrogen.
2. Results center on one-atmosphere-pressure air.
3. The emphasis is on non-equilibrium, 'cold' air plasmas rather than their
thermally equilibrated counterparts.
The combination of the above three characteristics make this book a unique
technical resource and a valuable reference work to newcomers and experi-
enced air plasma researchers alike. Of course, subject matter alone cannot
ensure the value of this or of any book. The other crucial factor that
makes this book an important work is the stature and recognized expertise
of its international team of contributing authors. The authors are leaders
in their respective fields, intimately familiar with the state-of-the-art as well
as with likely future trends.
1.2 Parameter Space of Interest
Conducting plasma experiments on gases sealed in a chamber gives one the
powerful advantage of controlling, or at least the ability to control, the
precise pressure and chemical composition of those gases. For that reason,
most of the empirical studies discussed in this book will deal with such
chambered gases. A scientist seeks to understand complex phenomena by
collecting data points for systems with as many knowns and as few variables
as possible. In that way, solid data can form the solid foundation for complex
predictions.
Such considerations highlight the ambitious goal of this book to focus
on non-equilibrium atmospheric pressure air plasmas. What is sought here
is an understanding of non-thermal plasma formation in 'open' air. One is
here interested in creating a population of free electrons in whatever ambient
air happens to be present in one's laboratory (or work-site). Since this labora-
tory may be situated in the humid, sea-level environment of Hamburg,
Germany, as likely as in the high (1.52 km above sea level), dry environment
of Albuquerque, New Mexico, USA, it is important to specify the known
range of chemical constituents and pressures that may be encountered.
Being mindful of such differences can prepare one for observed variations
in air plasma results from place to place on the globe and even from
season to season.
Although the deviations of ground level from sea level may seem large,
nevertheless, every point on the surface of earth lies well within the lowest
(and thinnest) layer of the atmosphere, namely the troposphere (see figure
--- Page 20 ---
Parameter Space of Interest
5
TROPOSPHERE
Altitude
km
miles
200+--if---
120+
120-+_ 74
85-+_53
60-+-37
50
31
15 --if--- 9
o
Figure 1.1. Profile of the earth's atmosphere from sea level to low earth orbit (LEO).
1.1). At any point on the earth's surface, the ambient dry air is composed of
the following independent gases at approximately the respective volume
percentages: nitrogen (N2, 78.09%), oxygen (02, 20.95%), argon (Ar,
0.93%), carbon dioxide (C02 , 0.03%), neon (Ne, 0.0018%), helium (He,
0.00053%), and krypton (Kr, 0.0001 %). There are slight variations to
those numbers from location to location, and of course experimental
errors can creep into any such measurements. In addition to the gases
listed above, relatively minute amounts of hydrogen and xenon are perma-
nent constituents of air. Finally, trace amounts of radioactive isotopes,
--- Page 21 ---
6
Introduction and Overview
nitrogen oxides, and ozone may also be found in a given sample of dry
surface air. By far the most variable constituent of surface air is water
vapor. When one departs from the use of dry air, then one is subject to the
ambient humidity of a given locale. Aside from obvious humidity variations
due to the proximity of large bodies of water, there are measurable annual
averages based on latitude that show a clear dependence on average air
temperature. As an illustration, it is instructive to compare such annual
averages as follows that show the relative volume percentages of N2/02/
Ar/H20/C02 for the equator, 50oN, and 700 N respectively: 75.99/20.44/
0.92/2.63/0.02, 77.32/20.80/0.94/0.92/0.02, and 77.87/20.94/0.94/0.22/0.03.
In a common misconception, it is often assumed that the concentration of
the heavier molecules decreases with increasing altitude due to gravity. It
would seem reasonable that lighter molecules would preferentially migrate
upward. In reality, however, the powerful dynamics of solar heating cause
such extensive mixing that relative molecular concentrations remain virtually
unchanged from ground level up to about 20 km. The only large deviations
occur in the relative concentration of water vapor since it depends critically
on the local ambient temperature and that average temperature decreases
with increasing altitude (Humphreys 1964).
Thus, the chemical composition of the air treated in this book is left to
nature and, luckily, behaves quite well except for the few percent variations
due to ambient water vapor. The question of gas temperature is one more
closely controlled by the individual experimentalist and here there was
indeed some divergence among this book's contributing authors. Funda-
mentally, there was unanimous agreement on the focus of non-equilibrium
plasmas. The goal remained to discuss techniques for generating a much
larger population of free electrons in air than could result from the
simple brute-force heating of the background air. The rationale for that
goal is twofold; first, thermal ionization implies minimum efficiency of
plasma generation due to the 'wasted' heating of the background gas,
and, second, the thousands of degrees of temperature necessary to achieve
even a modest 1012 free electrons per cm3 in a thermal plasma would be
clearly destructive to many of the proposed beneficiaries of the previously
listed air plasma treatments. At the same time, there is no ionization
technique that can completely avoid any heating of the background
gas. Thus, a truly 'cold' plasma in which the background air remains
fixed at room temperature is not realistic for the practical applications
that motivate this book. Therefore, it can best be stated that this book
deals with 'warm' plasmas in which background air temperatures of
several hundred Kelvin above 'room temperature' are considered quite
acceptable.
The paragraph above touches on a subject that cannot be passed over so
lightly, namely that of power consumption necessary for the generation of
ambient air plasmas. This point is crucial for anyone seeking to apply air
--- Page 22 ---
Naturally-occurring Air Plasmas
7
plasmas to real-world applications since this is the issue that drives the cost of
the application. Over the past decades, several attractive technologies have
been sidelined simply because they required the sustainment of electron
densities on the order of 1013 per cm3 and that required hundreds of mega-
watts of electrical power per cubic meter. To some, this simply excluded
the consideration of ambient air plasmas for a range of applications. To
others, however, this signaled a challenge to explore hybrid ionization tech-
niques that avoided the brute-force re-ionization of molecules on electron
recombination timescales. The pioneering efforts of those forward-thinking
researchers is captured herein. Luckily, a vast majority of air plasma applica-
tions require only very modest free electron populations to achieve. Those
applications, and their required technologies for realization are likewise
covered herein.
1.3 Naturally-occurring Air Plasmas
A more accurate title for this book would be 'Artificial Non-equilibrium Air
Plasmas at Atmospheric Pressure'. This books treats only non-thermal air
plasmas that result from other-than-natural causes. From that perspective,
it is worth a brief digression here to examine what types of plasmas (in the
broadest sense) can be found in Nature. Sometimes a researcher can gain
insights by first observing what Nature has wrought.
To begin with, sea-level air abhors free electrons. As will be discussed
later in this book, at room temperatures three-body recombination of
electrons with molecular oxygen limits electron lifetimes to only about
16 ns. The situation becomes friendlier for free electrons as one increases
one's altitude in the atmosphere and, thereby encounters ever-decreasing
air pressure. For example, at 30000 and 60000 ft the free electron lifetime
increases to 119 ns and 1.83 J.1S respectively. Above about 60 km above
sea level, one enters the ionosphere, where the copious flux of extreme
ultraviolet (EUV) solar photons and, to a lesser extent, collisions with
energetic particles (mostly electrons) that penetrate the atmosphere easily
maintains free electron densities on the order of 102 to 107 cm-3 in the
rarified background (Schunk and Nagy 2000). The dominant ion species
balancing that electron charge consists primarily of H+ and He + above
1000 km, 0+ from 300 to 500 km and molecular ions (NO+, ot, and Nt)
below 200 km (NASA 2004). There exist some excellent reviews of the domi-
nant ionospheric ionization processes (Hudson 1971, Stolarski and Johnson
1972) as well as complete lists of the major plasma chemistry reactions at
work (Torr 1979). It should be noted, however, that there are numerous
reactions that result in minor chemical constituents that are not well
understood. Some of these involve metastable atomic states, negative
ions, ionization by photoelectrons, energetic neutrals, and the vibrational
--- Page 23 ---
8
Introduction and Overview
states of molecules. Readers interested in the photo-ionization of air would
be well advised to first familiarize themselves with such ionospheric
chemistry.
When Nature seeks to generate high free-electron densities in the lower
atmosphere, she resorts to thermal plasma generation via lightning
discharges. The physics of natural lightning is fascinating and certainly
worthy of its own text. Unfortunately, scientific details must generally be
gleaned from sections of meteorology texts (Moran et at 1996). Never-
theless, readers interested in atmospheric 'arcs and sparks' would do well
to examine such natural phenomena before embarking on a quest for
laboratory imitations. Simply stated, a lightning discharge may be best
described as 'a complex propagating gas breakdown process' (Jursa
1985). It is believed to be triggered when large amounts of space charge
accumulate in small volumes in clouds and thus create locally intense
electric fields of several hundred kV 1m. The lightning channel progressively
extends below the cloud base (in cloud-to-ground lightning) in what is
termed a 'stepped leader'. In this process, each 'leader' breaks down the
air in a sequence of (approximately) 50m 'steps'. It is interesting to note
that each step forms in only about 1 j.1S but there is an average of a 50 j.1S
delay before the next step is formed. This ever-growing stepped leader
continues extending toward the ground until the huge voltage (about
108 V) between its head and the earth's surface (or conducting projection
from that surface) exceeds the air breakdown threshold. At that moment,
there occurs a very rapid equalization of the charge in the channel at the
amazing speed of about one-third the speed of light. It is this so-called
'return stroke' from the ground that is responsible for the most intense
and rapid heating and expansion of a significant volume of air, thus produ-
cing the characteristic bright flash and loud thunder associated with a bolt
of lightning. Typically, subsequent lightning strokes will follow the existing
partially ionized channel. Overall, a given ground lightning 'event' lasts
only 0.1-1.0s with 0.5s being a typical value. Most such events neutralize
tens of coulombs of charge. Such individual events typically consist of
three or four individual strokes, each lasting about 1 ms and separated by
40-100ms.
Before ending this section, one may venture into murkier researches of
science by considering the possible natural occurrence of 'ball lightning'. For
newcomers to the air plasma arena, a caution must be voiced. While
numerous claims of ball lightning sightings have been reported in the
scientific and popular press, no reproducible laboratory experiments for
the recreation of such phenomena (except for tiny manifestations) have
been published. This fact unfortunately has relegated this to the status of
'borderline' science. It is instructive to note that the most comprehensive,
recent text on this subject is largely anecdotal in nature (Stenhoff 1999).
Still it is reasonable to deduce that there is some type of unexplained,
--- Page 24 ---
Sources of Additional Information
9
plasma-related atmospheric phenomenon that underlies the 'ball lightning'
sightings. One may hope that someday the proper scientific tools are brought
to bear so that a true understanding may follow.
1.4 Sources of Additional Information
No book could hope to capture all of the technical details of so complex a
subject as non-equilibrium atmospheric pressure air plasmas. This book
rather serves as a comprehensive guide to the current state of knowledge
regarding these phenomena. It surveys the rich history and details today's
capabilities and opportunities regarding these plasmas and thus constitutes
an ideal starting point for the non-equilibrium high pressure air plasma
professional who has at his/her disposal a comprehensive library of reference
works. In this section, suggestions are made regarding specific books and
journals that would be most useful for such reference purposes. In addition,
mention is made of particular professional meetings that may be most
rewarding for pursuing specific topical areas. It is a certainty that not
every relevant book, journal, and conference will be mentioned here.
However, as one examines those that are referenced here, one can then
branch out, as always, to explore the references that they reference. This is
a natural process.
In order to understand many of the concepts covered in this book, a
reader must have a firm foundation in electromagnetic theory and plasma
physics. There are many excellent, comprehensive texts covering these
subjects (Jackson 1998, Pollack and Stump 2002, Griffiths 1998, Chen
1984, Dendy 1995, Boyd and Sanderson 2003). The choice of 'favorite'
texts will vary from scientist to scientist.
On the specific subject of non-equilibrium atmospheric pressure air
plasmas, two other books stand out as excellent companion works to this
book. The first is one co-edited by one of this book's editors (K.H.S.) and
concentrates on non-equilibrium low temperature plasmas but not in air
(Hippler et aI2001). That collection of papers deals with any and all species
oflightly ionized, low temperature gases, although atmospheric applications
are discussed in several of the papers. It has a strong bias toward industrial
plasma processing and lighting applications. It spends little time on theory
and modeling fundamentals but does give a good discussion of relevant
diagnostic techniques that complements presentations in this book on that
subject. It also gives good experimental details but mainly on industrial
plasma reactor concerns.
A second excellent possible companion to this work is one that,
instead of dealing directly with air, deals only with various mixtures of
air's principal molecular constituents, namely oxygen, nitrogen, and
major oxides of nitrogen (Capitelli et al 2000). That monograph focuses
--- Page 25 ---
10
Introduction and Overview
on theoretical (computational) analyses of basic kinetic theory and detailed
investigation of kinetic processes of lightly ionized, low temperature, non-
equilibrium plasmas in N2, 02, and their mixtures. It examines self-
consistent solutions of the electron Boltzmann equation coupled to a
system of vibrational and electronic state master equations, including
dissociation and ionization reactions in conjunction with electrodynamics.
The main target applications there are gas discharges and natural (e.g.
ionospheric or spacecraft re-entry) plasmas, although sea-level applications
are also discussed. It looks at ionization degrees ranging from 10-7 to
10-3 and mean electron energies from 0.1 to 10eV. In effect, the book
serves as an excellent 'how-to' book for a theoretician interested in under-
standing air plasma phenomena. Experimental data are cited, but only to
benchmark theoretical treatments. In addition, there are several other
books that concentrate on the fundamental physics and the applications
of non-equilibrium gas discharge plasmas and mention in passing
atmospheric-pressure plasmas (Raizer et al 1995, Roth 1995, Batenin et al
1994, Lieberman and Lichtenberg 1994, Chapman 1980, Mitchner and
Kruger 1973).
Also worthy of note are several texts that explore specific subtopics
covered herein. For those readers particularly interested in computer
modeling and simulation of plasma phenomena, there are two primary
reference texts, the first by Birdsall and Langdon (1991) and the second by
Hockney and Eastwood (1988). For experimentalists most concerned with
the difficult task of taking accurate data in complex plasma systems, an
excellent reference may be found in Hutchinson's classic diagnostics text
(Hutchinson 2002). Finally, readers focused on rapid plasma applications
may benefit from referring to the second volume of Roth's industrial
plasma text (Roth 2001).
In order to reap the many benefits of interacting with scientists and
engineers with similar air plasma interests, there are a number of professional
organizations a reader should consider joining. This is an excellent way for
individuals who are new to the field to make necessary personal technical
contacts with individuals already active in the field. An approximate ordering
of these professional organizations in roughly decreasing order of air plasma
involvement is as follows:
1. The Institute of Electrical and Electronics Engineers (IEEE) Nuclear and
Plasma Sciences Society (NPSS).
2. The Institute of Physics (lOP), United Kingdom.
3. The American Vacuum Society (AVS) and its industrial affiliates.
4. American Institute of Aeronautics and Astronautics (AIAA).
5. The American Physical Society (APS) through the Division of Plasma
Physics, the Division of Atomic, Molecular, and Optical Physics, and
the Division of Chemical Physics.
--- Page 26 ---
Sources of Additional Information
11
6. The European Physical Society (EPS) through its Division of Atomics,
Molecular, and Optical Physics and its Division of Plasma Physics.
7. Institute of Electrical Engineering (lEE), United Kingdom.
8. Corresponding societies in Japan and Korea.
For the same reasons given above, researchers and engineers who wish to be
active in the field of air plasmas would be wise to participate in those tech-
nical meetings that at least have technical sessions devoted to this topical
area. Again in approximately decreasing order of air plasma participants
such meetings may be listed as follows:
1. The Gaseous Electronics Conference, GEC (annual).
2. The International Conference on Phenomena in Ionized Gases, ICPIG
(bi-annual).
3. The IEEE International Conference on Plasma Science, ICOPS (annual).
4. The International Symposium on High Pressure Low Temperature
Plasma Chemistry (also known as the 'Hakone Conference', named
after the city of Hakone in Japan where the first meeting was held in
1987) is a bi-annual series of conferences devoted exclusively to high-
pressure discharge plasmas and their applications.
5. The Eurosectional Conference on Atomic and Molecular Processes in
Ionized Gases, ESCAMPIG, which is a bi-annual European conference
on fundamental processes in ionized gases.
6. The AIAA Conference in Reno, Nevada, USA (every January) (only the
'Weakly Ionized Gas (WIG)' sessions are of interest there).
7. 'ElectroMed', International Symposium on Non-thermal Medical/
Biological Treatments Using Electromagnetic Fields and Ionized Gases
(bi-annual).
8. The APS annual meetings of the Division of Plasma Physics and the
Division of Atomic, Molecular, and Optical Physics.
Finally, researchers in the field of non-equilibrium, atmospheric pressure air
plasmas should consider publications in any of the following professional
journals:
1. Plasma Sources, Science, and Technology (lOP).
2. IEEE Transactions on Plasma Science.
3. Plasma Chemistry and Plasma Processing (Kluwer Academic/Plenum
Publishers).
4. Journal of Physics D: Applied Physics (lOP).
5. Plasma Processes and Polymers (Wiley-VCH).
6. Physics of Plasmas (AlP).
7. Physical Review Letters and Physical Review (AlP).
8. Applied Physics Letters/Journal of Applied Physics (AlP).
9. Review of Scientific Instruments (AlP).
10. Contributions to Plasma Physics (Wiley).
--- Page 27 ---
12
Introduction and Overview
1.5 Organization of this Book
This volume has been assembled using three cooperative levels of authorship
consisting of Authors, Chapter Masters, and Editors. The Authors, as listed
in the front of this book, are those who have written significant sections of
one or more chapters. The Chapter Masters acted not only as Authors but
were also responsible for the content of their specific chapters. In cooperation
with the Editors, they established the detailed outlines of their respective
chapters and determined which sections to write themselves and which
sections to solicit from other expert authors. These Chapter Masters had
the responsibility to modify contributed text in order to smooth the internal
flow of the sections and to ensure consistency within their chapters. They
worked with the Editors and with the other Chapter Masters to resolve
issues of overlap and repetition. Finally, the Editors, in addition to their
service as Authors and Chapter Masters for specific portions of this book,
shared the responsibility of reviewing the entire volume. To ensure a coherent
book with synergistic chapters, they iterated numerous changes with Authors
and worked toward a common terminology throughout and a reduction of
differences in writing styles between the various chapters.
There are three major groupings of chapters within this book. The first
grouping consists of chapters 1-5 and is fundamentally introductory in
nature. After the subject matter is delineated in this chapter, chapter 2
proceeds to present the rich history of this field. Chapters 3 and 4 then
proceed to provide the reader with all necessary theoretical foundations in
both plasma physics and plasma chemistry respectively. This first grouping
ends with chapter 5 which shows how the theoretical formulations of the
previous two chapters are integrated into computer simulations to better
understand and eventually predict observed air plasma phenomena. The
next grouping, this one consisting of three chapters, takes the reader into
the plasma laboratory itself to examine actual air plasma experiments,
including the demanding experimental diagnostics necessary to truly under-
stand the ionized phenomena under study. The final chapter, chapter 9, is a
group unto itself. It looks to the future, discussing first the remaining
scientific challenges presented by these plasmas and then looking closely at
the array of attractive practical applications for which they can be employed.
In the remainder of this section, each chapter is examined one by one. The
responsible Chapter Master as well as all the individual contributing Authors
of each chapter are listed in their respective chapter's heading.
Chapter 2, 'History of Non-Equilibrium Air Discharges', presents
the historical progression and development of cold-plasma generation tech-
niques. First, the discovery and study of dielectric barrier discharges is
covered, followed by corona discharges and pulsed air discharges. Electrical
breakdown and spark formation, as well as much of the fundamentals of
corona discharges and high pressure glow discharges, are all treated
--- Page 28 ---
Organization of this Book
13
herein. The evolution of the concept of non-equilibrium plasma conditions is
traced.
Chapter 3, 'Kinetic Description of Plasmas', not only captures the key
points of the classic textbook by Mitchner and Kruger (1973), but also focuses
on those elements crucial to the specific understanding of sea-level air plasmas.
The characteristics of weakly ionized and weakly coupled plasmas are
presented including the concepts of multi-body elastic and inelastic collisions,
an explanation of total and differential collision cross sections and rate
constants, surface interactions and other 'collision-like' processes, as well as
characteristic lengths and time-scales. A complete kinetic description of
electrons is presented, including the concepts of phase space and velocity
distribution functions, the general form of kinetic equations, collision terms
and their general properties, a comparison with the fluid-dynamic picture,
and the impossibility of general analytic and numerical solutions.
Chapter 4, 'Air Plasma Chemistry', reviews relevant collision processes
including electron, ion-molecule, three-body, and step-wise collisions. The
key reactions and types of reactions governing air plasma chemistry are
highlighted. Ion-molecule reactions at elevated temperatures are discussed,
highlighting the inadequacy of using rate constants obtained over a limited
temperature range at high temperatures where vibrational excitation is
important. The chapter then turns to non-equilibrium ion chemistry with
considerations of the vibrational energy dependence of ion-molecule reac-
tions, collision-induced dissociation reactions, scaling approaches, and
state-resolved experiments and results. The state-of-the-art in electron-ion
recombination science is then explained, with emphasis on product distribu-
tion and energy dependencies as well as recent key measurements.
Chapter 5, 'Modeling', illustrates how the theoretical formulations of
plasma physics and plasma chemistry that were presented in chapters 3 and
4 have been successfully incorporated into computational models. The chapter
begins with a general discussion of the technical challenges one encounters
when undertaking air plasma modeling. It then presents a successful effort
dealing with non-equilibrium air discharges using a numerical technique
based on finite-volume computational fluid dynamics. Then the modeling of
the electrical properties of different plasma-based devices is discussed, begin-
ning with dc glow discharges in atmospheric pressure air. This is followed in
turn by models for a negative corona in pin-to-plane configurations, dielectric
barrier discharges, and a surface-discharge-type plasma display panel. By
examining the techniques employed for the range of successful models
presented, a reader can gain valuable insight regarding solutions applicable
to their particular area of interest.
Chapter 6, 'DC and Low Frequency Air Plasma Sources', begins with a
discussion of plasma sources that are often termed 'self-sustained plasmas',
but that term was not used here to avoid confusion on the part of those
outside the plasma discharge community. Among the topics covered are
--- Page 29 ---
14
Introduction and Overview
filamentary breakdown in dielectric barrier discharges, homogeneous and
regularly-patterned barrier discharges, overall discharge parameters of
barrier discharges, hollow and micro-hollow cathode discharges, recently
discovered cathode boundary layer discharges (CBDs), discharges with
micro-structured electrodes (MSEs), capillary plasma electrode discharges
(CPEDs), positive and negative corona discharges, pulsed streamer coronas,
pulsed diffuse discharges, glow discharges, and ac torch discharges with
pronounced non-equilibrium properties.
Chapter 7, 'High Frequency Air Plasmas', gives an overview of the
various 'external' means used to generate an air plasma including lasers, flash-
tubes, rf and microwave, pulsed power, and electron beams. A dominant
theme in this chapter is the ability to ionize air 'at a distance' away from
any driving electrodes, unlike the methodologies described in the previous
chapter. The air plasma technologies presented in this chapter begin with
those using the highest available frequencies, namely those using photons as
the driving ionization source. Two classes of photo-ionization technique are
presented, the first using lasers and the second using ultraviolet flashlamps.
Both of those techniques require the addition of photo-ionization seedants.
The next section turns to rf-sustained discharges, including a microwave
torch, rf-sustainment of a laser-initiated plasma, and creation of a localized
plasma defined by the intersection of two microwave beams. Repetitively
pulsed discharges are then discussed in the fourth section, followed by a section
detailing a successful electron-beam ionization experiment using laser excita-
tion. The final section in this chapter summarizes specific research challenges
and opportunities associated with various of these techniques.
Chapter 8, 'Plasma Diagnostics', discusses the scientific challenges
associated with trying to apply proven low-pressure plasma measurement
techniques to the far more complex realm of collisionally dominated
atmospheric pressure plasmas. Some techniques can be carried over but
others cannot, depending also upon the desired resolution. The treatment
of individual techniques begins in the second section with elastic and inelastic
laser scattering in air plasmas. The next two sections look at electron density
measurements, the first using millimeter-wave interferometry and the second
using infrared (lR) heterodyne interferometry. From there, the chapter turns
to diagnostics employing plasma emission spectroscopy. The chapter
concludes with a section detailing the powerful cavity ring-down spectro-
scopic diagnostic for measuring ion concentrations.
Chapter 9, 'Current Applications of Atmospheric Pressure Air Plasmas',
presents a series of the most compelling established and emerging applica-
tions for air plasma technology. These include the subjects of electrostatic
precipitation, ozone generation, microwave reflection and absorption,
aerodynamic applications, plasma-aided combustion, surface treatment,
chemical decontamination, biological decontamination, and medical appli-
cations. Common for most of these applications is the unique ability of
--- Page 30 ---
References
15
non-equilibrium air plasma to generate high concentrations of reactive
species, without the need for elevated gas temperatures.
Acknowledgments
This chapter represents a (hopefully) faithful summary of the contributed
thoughts and motivations of all the editors and authors who have collabo-
rated in the creation of this volume. Particular assistance was provided by
the author's co-editors along with the generous patience of our Editor-in-
Chief, Professor Kurt Becker.
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of Plasmas 10(5) 2117-2126
Roth J R, Chen Z, Sherman D M, Karakaya F, Tsai P P-Y, Kelly-Wintenberg K and
Montie T C 2001 'Increasing the surface energy and sterilization of nonwoven
fabrics by exposure to a one atmosphere uniform glow discharge plasma
(OAUGDP), International Nonwovens J. 10(3) 34-47
Schunk R Wand Nagy A F 2000 Ionospheres: Physics, Plasma Physics, and Chemistry
(Cambridge: Cambridge University Press)
Stenhoff M 1999 Ball Lightning (New York: Kluwer Academic/Plenum Publishers)
Stolarski R S and Johnson N P 1972 'Photoionization and photoabsorption cross sections
for ionospheric calculations' J. Atmos. Terr. Phys. 34 1691
Torr D G 1979 'Ionospheric chemistry' Rev. Geophys. Space Phys. 17 510-521
Tsai P, Wadsworth L and Roth J R 1997 'Surface modification of fabrics using a one-
atmosphere glow discharge plasma to improve fabric wettability' Textile Research
J. 5(65) 359-369
Vidmar R J 1990 'On the use of atmospheric pressure plasmas as electromagnetic reflectors
and absorbers' IEEE Trans. Plasma Science 18(4) 733-741
White H J 1963 Industrial Electrostatic Precipitation (Reading, MA: Addison Wesley)
--- Page 32 ---
Chapter 2
History of Non-Equilibrium Air Discharges
U Kogelschatz, Yu S Akishev and A P Napartovich
2.1
Introduction
Chapter 2 provides a short review of the historical development of non-
equilibrium discharges with a tendency to focus on air plasmas at atmospheric
pressure. The main physical mechanisms of breakdown and classifications of
various discharges are discussed. The principal discharge configurations are
presented and their main properties and applications are discussed. The
fundamentals of corona discharges (Akishev, Napartovich) and dielectric-
barrier discharges are presented. More detailed information and recent
developments are treated in chapter 6.
2.2 Historical Roots of Electrical Gas Discharges
Until the beginning of the 18th century air like any other gas was believed to be
an ideal electrical insulator. The fact that air can pass electrical charges was
first established by Coulomb, who could show that two oppositely charged
metal spheres gradually lost their charges (Coulomb 1785). In carefully
designed experiments he could conclusively demonstrate that this loss of elec-
trical charge was due to leakage through the surrounding air and not through
imperfect insulation. In the middle of the 18th century Benjamin Franklin had
shown experimentally that a laboratory spark and lightning were of common
nature. Around 1800 V. V. Petrov in St. Petersburg and Humphry Davy in
Britain started to investigate arc discharges in air. Davy suggested the name
arc because the extremely bright discharge column is normally bent due to
the buoyancy of hot air. Arcs can get very hot and were normally started by
separating two carbon electrodes connected to a voltage supply. Powerful
batteries were required to supply enough current to maintain the arc. In
17
--- Page 33 ---
18
History of Non-Equilibrium Air Discharges
addition to these hot arc discharges, cold glow discharges were investigated.
Major investigations on the passage of electricity through various gases and
on fundamental properties of gas discharges were performed by Faraday
(1839, 1844, 1855), Hittorf (1869), Crookes (1879), Stoletow (1890),
Thompson (1903), and Townsend (1915), to name only the most important
ones. Faraday was probably the first to realize that an ionized gas had
unique properties and carefully documented his observations in three volumes
of Experimental Researches in Electricity (1839, 1844, 1855).
Many experiments were carried out at reduced pressure. This had the
advantage that only moderate voltages were required to start the discharge
and that the whole discharge vessel could be filled with discharge plasma.
The progress in gas discharge physics depended heavily on the development
of vacuum pumps and the availability of adequate voltage sources. Of
equal importance were the skills of a good glass blower. Faraday could
already evacuate tubes to about 1 torr and apply voltages up to 1000 V. He
introduced the concept of ions as carriers of electricity (in electrolytes) and
distinguished between cathode and anode, even between cations moving to
the cathode and anions passing to the anode. Crookes emphasized that a
gas discharge actually constitutes a fourth state of the matter. The term
plasma was coined much later, by Langmuir and Tonks, in 1928. Today
the word plasma is mainly used to describe a quasi-neutral collection of
free-moving electrons and ions.
More refined experiments with rarefied gases started at the beginning of
the 20th century. For a long time the transport of electricity through gases
had been treated like the flow of charges in electrolytes. Only about 1900,
mainly due to the work of Wilson (1901) and Townsend (1904), it was estab-
lished that conductivity in electrical gas discharges was due to ionization of
gas atoms or molecules by collisions with electrons. In most gas discharges
the current is mainly carried by electrons.
From the very beginning it was obvious that cold glow discharge
plasmas had different properties than the hot arc discharges. For a long
time it was believed that glow discharges which are characterized by hot elec-
trons and essentially cold heavy particles (atoms, molecules, ions) could exist
only at low pressure. It is one of the purposes of this book to describe recent
developments showing that non-equilibrium plasma conditions with electron
energies substantially higher than those of heavy particles, and properties
resembling those of low pressure glow discharges, can exist also at much
higher pressure, for example in atmospheric pressure air.
References
Crookes W 1879 Phil Trans. Pt. 1 135-164
Coulomb M 1785 Mem. Acad. Royale des Sci. de Paris 612-638
--- Page 34 ---
Historical Progression of Generating Techniques
19
Faraday M 1839 Experimental Researches in Electricity vol. I (London: Taylor and
Francis)
Faraday M 1844 Experimental Researches in Electricity vol. II (London: Taylor and
Francis)
Faraday M 1855 Experimental Researches in Electricity vol. III (London: Taylor and
Francis)
HittorfW 1869 Pogg. Ann. 136 1-31 and 197-235
Stoletow M A 1890 J. de Phys. 9468-472
Thompson J J 1903 Conduction of Electricity through Gases (Cambridge: Cambridge
University Press)
Townsend J S 1915 Electricity in Gases (Oxford: Clarendon Press)
Townsend J S and Hurst H E 1904 Phil. Mag. 8 738-753
Wilson C T R 1901 Proc. Phys. Soc. London 68 151-161
2.3 Historical Progression of Generating Techniques for Hot
and Cold Plasmas
From the early days of gas discharge physics it was apparent that, after igni-
tion of the discharge, entirely different plasma states can be established in the
same medium. One representative was the hot arc discharge, typically oper-
ated in air at atmospheric pressure, approaching conditions of local thermo-
dynamic equilibrium (LTE). This thermodynamic state is characterized by
the property that all particle concentrations are only a function of the
temperature. In short, these plasmas are also referred to as thermal plasmas.
Cold plasmas, on the other hand, are characterized by the property that the
energy is selectively fed to the electrons leading to electron temperatures that
can be considerably higher than the temperature of the heavy particles in the
plasma. These non-equilibrium or non-LTE plasmas exhibit typical plasma
properties such as electrical conductivity, light emission and chemical activity
already at moderate gas temperatures, even at room temperature. Both hot
and cold plasmas have found important and far-reaching technical applica-
tions. In the following sections the historical development of the discharge
configurations used to produce hot or cold plasmas is briefly discussed
with special emphasis on the properties of air plasmas.
2.3.1
Generation of hot plasmas
Typical examples of thermal plasmas are plasmas produced in high-intensity
arcs, plasma torches or radio frequency (rf) discharges at or above atmos-
pheric pressure. Figure 2.3.1 shows three simple configurations used to
produce arcs or plasma jets in atmospheric pressure air.
The electrodes are either water-cooled metal parts or simply graphite
rods. Typical currents range from 10 to 1000 A, typical temperatures from
--- Page 35 ---
20
History of Non-Equilibrium Air Discharges
Electric Arcs
'-~:==Z&
/'
/'
/'
/
+
Electrodes
Figure 2.3.1. Principal arc configurations.
+
Plasma Jet
Anode Plate
with Hole
+
5000 to 50000 K. In most arcs the degree of ionization lies between 1 and
100%. The high temperature of the arc column can be utilized for light
emission as well as for melting materials and for initiating chemical reactions.
The plasma plume extending several centimeters from the orifice in the anode
plate in the lower part of figure 2.3.1 represents a neutral plasma with zero
net current. When specially shaped nozzles are used, supersonic expansion
into a low-pressure environment can produce pronounced non-equilibrium
plasma conditions.
Around 1808 Humphry Davy invented the carbon-arc lamp, using an
arc between two carbon electrodes, which later found applications in
movie projection lamps, in searchlights and as a radiation standard for
spectroscopy. Davy used arcs for melting (1815) and investigated the effects
of magnetic fields on arcs (1821). But it wasn't until 1878 that Sir Charles
William Siemens in Britain built and patented arc furnaces for steel
making using direct-arc and indirect-arc principles. In France this tech-
nology was investigated by Moissan (1892, 1897) and by Herou1t. Much of
the early work on electric arcs is summarized in the monograph of Ayrton
(1902). In 1901 Marconi used an electric arc for radio transmission across
the Atlantic, and around 1910 already 120 arc furnaces of the Sch6nherr
and Birkeland-Eyde design were installed in Southern Norway for nitrogen
fixation. In this electric-arc process, proposed by Birkeland and Eyde in
1903, nitrogen and oxygen in air were combined to form nitrogen oxides,
nitric acid, and finally artificial fertilizer (Norge salpeter, i.e. calcium nitrate).
By 1917 the plant had been extended to use up to 250 MW of cheap hydro
power. Arc welding was first demonstrated around 1910, and in its various
forms is now responsible for the bulk of fusion welds.
SchOnherr (1909) was the first to use a forced gas flow to stabilize long
carbon arcs. Today various kinds of flow and vortex arc stabilization tech-
niques are used in plasma torches. Many technological developments are
--- Page 36 ---
Historical Progression of Generating Techniques
21
1.00 r--I""--r--..,.-::::::=-;:~=-..,.-~
0.75
t 0.50
~
0.25
°6L---"10ie~~1~4~~~18-----2L2----2~6-'-1~~K~~
T (Temperature) -
Figure 2.3.2. Degree of thermoionization in different atmospheric pressure gases (from
Boeck and Pfeiffer (1999) p 130).
described in a book edited by Dresvin (1977), and in reviews by Pfender
(1978) and Pfender et al (1987). The fundamentals and applications of
thermal plasmas are discussed in Boulos et at (1994), in Heberlein and
Voshall (1997) and in Pfender (1999). The most important applications
include circuit breakers, lamps, plasma spraying, welding and cutting, metal-
lurgical processing and waste disposal. Most arcs are approaching the state
of local thermal equilibrium (LTE) and require high temperatures to main-
tain sufficient electrical conductivity by thermal ionization. From figure
2.3.2, showing the degree of ionization as a function of temperature for
different gases including air, it is apparent that temperatures well in excess
of 5000 K are required.
Figure 2.3.3 shows the temperature dependence of particle number
concentrations of an LTE plasma in atmospheric pressure dry air. With
rising temperature the molecules O2 and N2 are dissociated, new molecules
like NO form, the atoms Nand 0 prevail around 8000 K and, at higher
temperatures, the charged the particle species e, N+, and 0+ dominate.
2.3.2 Generation of cold plasmas
Besides thermal plasmas also cold non-equilibrium (non-LTE) plasmas are
of increasing interest. In contrast to thermal plasmas, cold plasmas are
characterized by a high electron temperature Te and a rather low gas
temperature Tg characterizing the heavy particles: atoms, molecules, and
ions (Te » Tg). The thermodynamic properties of the equilibrium and non-
equilibrium states of plasmas were discussed by Drawin (1971). In extreme
cases the electron temperature can reach well above 20000 K while the gas
temperature stays close to room temperature. Such non-equilibrium plasmas
can be produced in various types of low-pressure glow and rf discharges
(figure 2.3.4) as well as in corona, barrier, and hollow cathode discharges at
atmospheric pressure (see sections 2.5 and 2.6 and chapter 6).
--- Page 37 ---
22
History of Non-Equilibrium Air Discharges
-c -
>-t-....
en z
w
&:I
Ill: !
le26~ ______ ~
______ ~
______ ~
______ -, ______ __
D YAIR
PRESSURE: lee kP.
TEMPERATURE, T
)
Figure 2.3.3. Composition of an atmospheric pressure dry air plasma versus temperature
(from P. Fauchais, Summer School, ISPC-16 2003).
The glow discharge at reduced pressure, known since the days of
Faraday, Hittorf and Crookes, has been thoroughly investigated experimen-
tally as well as theoretically. Its main part, the positive column can provide
large volumes of quasi-neutral non-LTE plasma. Glow discharges have
found widespread applications in fluorescent lamps and as a processing
medium for surface modification and plasma enhanced chemical vapor
deposition (PECVD). The inductive rf plasma shown also in figure 2.3.4
was first observed by Hittorf (1884). It provides an elegant way of producing
a plasma not in contact with metal electrodes. Thomson (1927) formulated a
theory and Eckert (1974) published a detailed state of the art. The rf driven,
rf Discharge
Glow Discharge
000 0
0
0 000
! 0
0
0
0
Coil
Figure 2.3.4. Principal configurations of rf discharges and dc glow discharges.
--- Page 38 ---
Historical Progression of Generating Techniques
23
inductively-coupled plasma (ICP) has found a wide range of industrial uses,
including spectroscopic diagnostic tools, plasma torches, and the heating of
fusion plasmas. More recently, ICPs also found important applications in
lamps and as processing tools in the semiconductor industry.
It should be mentioned that arcs can also be operated at reduced
pressure and glow discharges at higher pressure. In addition to dc operation
all types of discharges can be operated at various frequencies or in a pulsed
mode. Special effects can be achieved if additional magnetic fields are used to
influence electron motion: magnetron discharges and electron cyclotron
resonance (ECR) sources.
Since collisions cause a continual exchange of energy between electrons
of mass me and heavy particles of mass mg with a tendency to equilibrate
temperatures it is more difficult to maintain non-equilibrium conditions at
elevated pressure with high collision rates and short mean free paths. For
steady-state discharges the deviation from local thermodynamic equilibrium
can be expressed by the following formula which was derived from an energy
balance (Finkelnburg and Maecker 1956).
Te - Tg
mg (AeeE)2
Te
- 4me GkTe)2·
(2.3.1 )
In this relation Ae is the mean free path of electrons, the term AeeE is the
amount of directed energy an electron picks up along one free path in the
direction of the electric field E and ~kTe is the average thermal energy (e is
the electronic charge, k is the Boltzmann constant). From relation (2.3.1) it
is apparent that large mean free paths (low pressure or density), high electric
fields and low electron energies favor deviations from LTE conditions.
Figure 2.3.5 shows in a semi-schematic diagram how electron and gas
temperatures separate in an electric arc with decreasing pressure (Pfender
1978).
Pronounced non-equilibrium conditions are obtained at reduced
pressure, while in atmospheric pressure arcs columns the deviation from
L TE is on the order of 1 %. At high pressure, non-equilibrium conditions
can be encountered when fast temporal changes occur (ignition and extinc-
tion of a discharge) and in regions of high field or concentration gradients.
In many cases short high voltage pulses are used to preferentially heat elec-
trons. In recent years also dc non-equilibrium air discharges at atmospheric
pressure have been extensively investigated at reduced gas density (Kruger
et al 2002, Yu et al 2002, Laroussi et al 2003). These experiments were
performed at gas temperatures between 700 and 2000 K. Stable diffuse
non-equilibrium air discharges were obtained with electron densities in
excess of 1012 cm -3. This value is roughly six orders of magnitude higher
than the equilibrium value of ne = 3 x 106cm-3 for an LTE air plasma at
2000 K (Yu et al 2002).
--- Page 39 ---
24
History of Non-Equilibrium Air Discharges
,..
:::IC
! 104
:t ...
2 I e
~lO!
102~ __ ~
__ ~
__ ~
__ ~
__ ~
__ ~
__
~
10·" 10·! 10.2 10.1
.0.01
0'
Pf~Wtt {iPO}
Figure 2.3.5. Electron temperature and gas temperature in an arc as a function of pressure
(from Pfender (1978) p 302).
In the literature there exist a number of models treating non-LTE
plasmas. Many of them are based on a fluid approach. In the simplest case
a two-fluid model can be used with two different temperatures, Te and Tg•
The electron kinetics can be treated by determining the electron energy distri-
bution function (EEDF) by means of the Boltzmann equation using, for
example, a two-term approximation. The reaction rate coefficients can be
obtained as functions of the average electron energy, which, in this local
field approximation, is only a function of the reduced electric field E / N.
Knowledge of all relevant electron impact cross sections is an important
requirement.
2.3.3 Properties of non-equilibrium air plasmas
Air is a mixture of many constituents. The CRC Handbook of Chemistry and
Physics (1997 edition) lists the following composition for the sea level dry air
(in vol% at 15°C and 101325 Pa):
Nitrogen
78.084%
Methane
0.0002%
Oxygen
20.9476%
Helium
0.000524%
Argon
0.934%
Krypton
0.000114%
Carbon dioxide
0.031%
Hydrogen
0.00005%
Neon
0.001818%
Xenon
0.0000087%
Electron collision cross sections have been measured and compiled for more
than a century now. The cross sections for the three major air constituents
--- Page 40 ---
..--..
N
E
o
N I
10.0
o
c o
:;:;
o
Q)
!J)
!J)
~
1.0
10,..
U
0.4
Historical Progression of Generating Techniques
25
11'0: - Chang
I1'm: -
- Ramanan
N2
Elastic: D Brennan
• Shyn
·Sohn
-DuBois
....:::-
• Bromberg
/.~.
.. Hermann
/.6 e •
0-0 Srivastava / =
Vibrational:
/
tJ~
-'-Schulz x1.4 /
I '
D Brennan
/
I .
- Tanak~6ectronic: - - Trajmar i \
/
Ionization: A Rapp
I I
/
• Schram
i I
- ./
• Krishnakumar i I
D Goruganthu
I
•
Dissociation: • Cosby
! I,
"Attachment": -
Huetz
I
_100
o 01: -
e nerly
6 Ferch
o Buckmon
• Szmytkowski
--Jost
• Nickel
• Hoffmon
DBloauw
• Karwasz
-Xing
-Garcia
.01
0.1
1
10
100
1000
Electron energy (eV)
Figure 2.3.6. Integral cross sections for electron scattering of N2 (from Zecca et at (1996)
p 94). (Copyright Societa Italiana di Fisica.)
N2, O2 and Ar, taken from a critical review by Zecca et al (1996), are given in
figures 2.3.6-2.3.8.
As a result of such Boltzmann computations figure 2.3.9 shows the
monotonous relation between the mean electron energy and the reduced
..--..
N
E
o
N
I o
c o
:;:; o
Q)
!J)
!J)
!J) o
10,.. u
10.0
1.0
0.2
am: _ .. - Low on
Elastic: .. --. Shyn
-Trajmar
D Sullivan
• Wakiya ;.
.D-Dlga
:
0-0 Daimon
Vibrational:
-'-Shyn
-
Linder
!
Electronic: - Wakiya .I
//
/'
Ionization: //
• Krishnakumar
• Rapp
• Schram
Attachment: -
- Rapp
Dissociation: • Cosby
_J
_100
fl 'I
.01
0.1
10
Electron energy (eV)
• • • • •
•
•
•
•
•
•
••
•
100
1000
Figure 2.3.7. Integral cross sections for electron scattering of O2 (from Zecca et at (1996)
p 115). (Copyright Societa Italiana di Fisica.)
--- Page 41 ---
26
History of Non-Equilibrium Air Discharges
..--..
N
E
o
N
I o
c a
.....,
U
(])
III
III
III a
'-u
10.0
1.0
0.3
(j : 0 Asaf
o • Haddad
• Saha
Ar
I
(jm: --Milloy
\
xlO /
..
\
/
\
I
lastic:
f
I
I
• Williams
I
I
• Srivastava";1
I
• Furst
'\ 1
\
v -
v DuBois \. I
I
\
1
I l
olga
Excitation:
\. I
-- deHeer
\ iI,
-
0 Chutjian
\
I)
lonizotion:
\
v Krishnakumor
\
• Rapp
I
• Nagy
I
.01
0.1
1
10
100
Electron energy (eV)
1000
Figure 2.3.8. Integral cross sections for electron scattering of Ar (from Zecca et al (1996)
p 31). (Copyright Societa Italiana di Fisica.)
electric field. Breakdown in a homogeneous electric field and wide gaps occur
when a reduced field E/N of about lOOTd (1 Td = 10-21 Vm2) is reached.
According to figure 2.3.9 this will produce electrons of mean energy close
to 3 eV, corresponding to an electron temperature of roughly 20000 K. In
narrow discharge gaps, pulsed discharges, and in front of the head of a
propagating streamer these values can be higher.
10
>-
~ 8
~
~
a " i
6
.S
.:iii
iii 4
i
iii e 2
j
III
0
0
100
200
300
400
500
Reduced eleetrie field, EIN (Td)
Figure 2.3.9. Mean electron energy in dry air as a function of the reduced field E/N (from
Chen (2002) p 48).
--- Page 42 ---
Historical Progression of Generating Techniques
27
e + Nz -+ e + N('S) + NI"S.20.2P)
1 0-2 '--........J .......... .l1....~L-..-'-~~(-'da'-S_he~d~li_ne~I.l.....o.~~J
o
2
4
6
8
10
Electron Mean Energy (eV)
Figure 2.3.10. Calculated G-values (number of reactions per 100 eV of input energy) for
dissociation and ionization reactions in dry air, shown as functions of the electron mean
energy in a non-equilibrium discharge plasma (from Penetrante et at (1997) p 253).
Computations in non-equilibrium air plasmas have been carried out for
applications in ozone generation and for pollution control. The efficiency of a
particular electron impact reaction can be expressed in terms of the G-value,
which gives the number of reactions per 100eV of input power. Figure 2.3.10
shows computed values for the dissociation and ionization reactions in
atmospheric pressure dry air.
In the electron energy range encountered in non-equilibrium gas
discharges (typically 3-6eV, in pulsed discharges up to lOeV) oxygen
dissociation is the most efficient reaction (highest G-value). This explains
why non-equilibrium discharges in air invariably lead to the formation of
ozone and nitrogen oxides.
Non-equilibrium plasmas are mainly used to generate chemically reac-
tive species and for their electromagnetic properties. Their applications
include the synthesis of thermally unstable compounds like ozone and the
generation of intermediate free radicals for pollution control. Surface
modification of polymer foils, thin film deposition and plasma etching in
the electronic industry are further applications. Progress in the under-
standing and control of atmospheric pressure non-equilibrium discharges
has led to increased activity in recent years which is manifested in several
monographs and review papers devoted to this special subject (Capitelli
and Bardsley 1990, Eliasson and Kogelschatz 1991, Lelevkin et al 1992,
Penetrante and Schultheis 1993, Manheimer et a11997, Capitelli et a12000,
Kunhardt 2000, Protasevich 2000, van Veldhuizen 2000, Hippler et al
2001, Kruger et aI2002).
--- Page 43 ---
28
History of Non-Equilibrium Air Discharges
References
Ayrton H 1902 The Electric Arc (New York, London: The Electrician Print. Publ. Co.)
Boeck Wand Pfeiffer W 1999 'Conduction and breakdown in gases' in Wiley Encyclopedia
of Electrical and Electronics Engineering (New York: Wiley) vol. 4 p 130
Boulos M I, Fauchais P and Pfender E 1994 Thermal Plasmas: Fundamentals and Applica-
tions (New York: Plenum Press)
Capitelli M and Bardsley J N (eds) 1990 Nonequilibrium Processes in Partially Ionized
Gases (New York: Plenum)
Capitelli M, Ferreira C M, Gordiets B F and Osipov A-I 2000 Plasma Kinetics in Atmos-
pheric Gases (Berlin: Springer)
Chen J 2002 Direct current corona-enhanced chemical reactions, PhD Thesis (Minneapolis:
University of Minnesota) p 48
Dresvin S V (ed) 1977 Physics and Technology of Low-Temperature Plasmas (Ames: Iowa
State University Press)
Drawin H W 1971 'Thermodynamic properties of the equilibrium and nonequilibrium
states of plasmas' in Venugopalan M (ed) Reactions under Plasma Conditions
(New York: Wiley), vol. I pp 53 -238
Eckert H U 1974 High Temp. Sci. 6 99-134
Eliasson Band Kogelschatz U 1991 IEEE Trans. Plasma Sci. 19 1063-1077
Finkelnburg Wand Maecker H 1956 'Elektrische Bogen und thermisches Plasma' in
Flugge S (ed) Encyclopedia of Physics (Berlin: Springer) vol. XXII p 307
Heberlein J V Rand Voshall R E 1997 'Thermal plasma devices' in Trigg G L (ed) Encyclo-
pedia of Applied Physics (New York: Wiley) vol. 21 pp 163-191
Hippler R, Pfau S, Schmidt M and Schoenbach K H (eds) 2001 Low Temperature Plasma
Physics (Weinheim: Wiley-VCH)
HittorfW 1884 Wiedemann Ann. Phys. Chern. 21 90--139
Kruger C H, Laux C 0, Yu L, Pack an D Land Pierot L 2002 Pure Appl. Chern. 74 337-347
Kunhardt E E 2000 IEEE Trans. Plasma Sci. 28 189-200
Laroussi M, Lu X and Malott C M 2003 Plasma Sources Sci. Techno!. 12 53-56
Lelevkin V M, Otorbaev D K and Schram D C 1992 Physics of Non-Equilibrium Plasmas
(Amsterdam: Elsevier)
Manheimer W, Sugiyama L E and Stix T H (eds) 1997 Plasma Science and the Environment
(Woodbury: American Institute of Physics)
Moissan H 1892 C. R. Acad. Sci. Paris 115 1031-1033
Moissan H 1897 Le Four Electrique (Paris: Steinheil)
Penetrante B M and Schultheis S E (eds) 1993 Non-Thermal Plasma Techniquesfor Pollu-
tion Control (Berlin: Springer) Part A and B
Penetrante B M, Hsiao M C, Bardsley J N, Merritt B T, Vogtlin G E, Kuthi A, Burkhart
C P and Bayless J R 1997 Plasma Sources Sci. Technol. 6 251-259
Pfender E 1978 'Electric arcs and arc gas heaters' in Hirsh M Nand Oskam H J (eds)
Gaseous Electronics: Electrical Discharges (New Y ork: Academic) vol. 1 pp 291-398
pfender E 1999 Plasma Chern. Plasma Proc. 19 1-31
Pfender E, Boulos M and Fauchais P 1987 'Methods and principles of plasma generation'
in Feinman J (ed) Plasma Technology in Metallurgical Processing (Warrendale: Iron
and Steel Society) pp 27-47
Protasevich E T 2000 Cold Non-Equilibrium Plasma (Cambridge: Cambridge Int. Sci. Publ.)
SchOnherr 0 1909 Elektrotechn. Zeitschr. 30(16) 365-369 and 397-402
--- Page 44 ---
Electrical Breakdown in Dense Gases
29
Thomson J J 1927 Phil. Mag. Ser. 7,4(25) Supp!. Nov. 1927, 1128-1160
van Veldhuizen E M (ed) 2000 Electrical Discharges for Environmental Purposes: Funda-
mentals and Applications (Commack: Nova Science)
Yu L, Laux C 0, Packan D M and Kruger C H 2002 J. Appl. Phys. 91 2678-2686
Zecca A, Karwasz G P and Brusa R S 1996 Rivista Nuovo Om. 19(3) 1-146
2.4 Electrical Breakdown in Dense Gases
Electrical breakdown in dense gases like air at atmospheric pressure has been
the object of many investigations. In high voltage engineering one of the
major aspects is to avoid breakdown or flashover between adjacent conduc-
tors or between a conductor and ground. The subject of gaseous insulation
has recently been reviewed by Niemeyer (1999). The physical phenomena
occurring in the early phases of breakdown in atmospheric pressure air or
in other compressed gases have many similarities with the ignition phase of
a low pressure gas discharge. They all start with an initial electron growing
into an electron avalanche under the influence of the electric field. In dense
gases, however, the fate of an electron avalanche can be quite different,
depending on the way the voltage is applied to the gas gap. A short overview
of the physical processes involved in breakdown under different conditions
and of the discharge types breakdown can lead to is given in the following
sections.
2.4.1
Discharge classification and Townsend breakdown
Traditionally, many gas discharges have been operated at low or very low
pressure compared to atmospheric conditions. In this context we consider,
for the purpose of this book, atmospheric pressure as high pressure. Also
at this pressure it is useful to characterize the type of discharge similar to
the traditional classification at low pressure (figure 2.4.1). The diagram is a
modified version of a graph from the famous paper by Druyvesteyn and
Penning (1940). It originally related to a discharge in 1 torr Ne, an electrode
area of 10 cm2 and an electrode separation of 50 cm. Nevertheless many
fundamental concepts also apply to a discharge in air at atmospheric
pressure. Since there is always some natural radioactivity resulting in the
production of 10-100 electrons per cm3 per s we can always draw a minute
base current if an electric field is applied. In air at atmospheric pressure
the saturation value of the current density amounts to about 10-18 A cm-2
and is subjected to statistical fluctuations. It can be considerably increased
if x-ray irradiation or ultraviolet illumination of the cathode is used to
produce additional electrons (region A ---> A'). In this region the current
--- Page 45 ---
30
History of Non-Equilibrium Air Discharges
~
B
C
E
V.,.
--1i~
~
I
I i
-
I
; If"
Iii,
1~1
-I
'1~
Ii
i 1
h~!
~F ~
E
F
A
A'
K
'--_..I.- --1- -L --'--
10-16
10.11
10-8
10'"
10-2
10-1
10
---_0 Current Density (A crno2)
Figure 2.4.1. Discharge characterization (based on Druyvesteyn and Penning 1940).
drops to the base current if the external source of electrons is switched off
(non-self-sustained region). Once the breakdown voltage Vbr of the gas
space is reached we get into the self-sustained discharge region, starting
with a Townsend discharge. The range of the Townsend discharge is
characterized by a negligible influence of space charge on the applied external
field. This condition is normally fulfilled in the current density range
j = 10-15_10-6 Acm-2.
According to an empirical relation found by Paschen in 1889 the value
of the breakdown voltage for a given gas (and cathode material) is only a
function of the product pressure p times electrode separation d,
Vbr = f(Pd) , or, as we would formulate it today, V br = f(Nd), where N is
the number density of the gas. The old relation is valid only for a given
temperature, in most cases room temperature, while the second relation is
more universal and does not depend on temperature. Some examples for
Paschen breakdown curves in different gases are given in figure 2.4.2.
Since the isolation properties of atmospheric pressure air are of
fundamental interest in high voltage engineering the Paschen curve of air is
extremely well investigated and documented (figure 2.4.3).
It should be mentioned that humidity has an influence on the break-
down voltage of air. Small admixtures lower the breakdown voltage, which
reaches a minimum at about I % water vapor and then rises again (Protase-
vich 2000, p 69). There is also a pronounced frequency dependence of the
breakdown voltage with a minimum value at about I MHz (Kunhardt 2000).
The Paschen curve can be obtained from the ionization coefficient a of
the gas and the 'Y coefficient quantifying the number of secondary electrons
produced at the cathode per ion of the primary avalanche. The first Town-
send coefficient, the ionization coefficient a, defines the number of electrons
--- Page 46 ---
Electrical Breakdown in Dense Gases
31
102 l-.JL-J--LL.l..-I......Jw..J.l.-.l..-J...J.,;L..l...-.l.-.L.I...L.l--1-.J....J...1.J
10-1
Pressure Spacing Product (Torr cm)
Figure 2.4.2. Paschen breakdown voltages for static breakdown in N2 , air, H2, He, Ne, Ar
(based on Vollrath and Thorner 1967 p 81).
produced in the path of a single electron traveling 1 cm in the direction of the
field E. The second Townsend coefficient 'Y depends on the cathode material
and the gas and includes contributions by positive ions, by photons, by fast
atoms, and by metastable atoms and molecules. Theoretically also volume
processes like photo-ionization of the background gas can produce
Air
Temperature: 2O'C
Hr' L-........................ -'-_-'-' .................. -.-l ......................... _
......................... .l.-..................... '-l-........................ .....J
100l
urI
10
101
Pressure Spacing Product (bar mm)
Figure 2.4.3. Paschen breakdown voltages for static breakdown in air (based on Dakin et at
1974).
--- Page 47 ---
32
History of Non-Equilibrium Air Discharges
secondary electrons to meet the self-sustainment criterion. However,
electrons released at the cathode travel the whole distance to the anode
and produce more ionization than electrons created en route. For this
reason the onset of breakdown is determined by ,-effects at the cathode.
Typical values of, are in the range 10-4 to 10-1. According to Town-
send (1915) current amplification in the homogeneous field can be written as
eQd
1=10
d
(2.4.1)
1 -,(eQ
-
1)
and breakdown is reached when current amplification in a gap tends to
infinity:
(2.4.2)
This Townsend criterion for stationary self-sustainment of the current has
been used ever since as a general criterion for stationary breakdown in homo-
geneous fields.
If the ionization coefficient a is approximated by a relation also
suggested by Townsend
(2.4.3)
where A and B are constants characterizing the gas under investigation. The
breakdown voltage Vbf is given by the simple relation
v =
Bpd
b,.
In(Apd) -lnln[(1 +,)11']
(2.4.4)
For rough calculations in dry air the ionization coefficient a can be approxi-
mated in modern writing as
2: = Ae-BN/ E
N
(2.4.5)
where N is the number density of the molecules, A = 1.4 X 10-20 m2, and
B = 660 Td (1 Td corresponds to 10-21 V m2). This relation approximates
experimental data by Wagner (1971) and Moruzzi and Price (1974) in the
range lOTd < E/N < l50Td (Sigmond 1984). Experimental data for
higher E / N ranges were provided by Raja Rao and Govinda Raju (1971)
and by Maller and Naidu (1976). More sophisticated analytical approxima-
tions for ionization and attachment coefficients covering a wider E / N range
in air can be found in Morrow and Lowke (1997) or Chen and Davidson
(2003).
Using the characteristic values at the minimum of the Paschen curve
(V min and l5 = pd / (Pd)min) equation (2.4.3) can be rewritten as
Vbr
l5
Vmin
l+lnl5'
(2.4.6)
--- Page 48 ---
Electrical Breakdown in Dense Gases
33
so
I
.
. ::p
20 t-
,:"
.. .
10
t'"
l-
..
-
-"
i
5 f- I
-
...
'b
2
.
-
....,
. .,
~ II-
i!
-
!I "
0.5
1 .. .
,
0.2
..
~
1
o
25
SO
75
100
125
to 20
SO 100 200 5001000
E(kVcm·l )
Em (l010 V em:!)
Figure 2.4.4. Ionization coefficient a, attachment coefficient 'fJ and reduced ionization
coefficient 00/ N for dry air (left plots, Les Renardieres Group 1972; right curve from
Raja Rao and Govinda Raju 1971).
a simple formulation of the Paschen law which holds for an extended pd-
range and can be used to get an estimate of the breakdown voltage in a
homogeneous field. For air Vrnin = 230-370 V, depending on the cathode
material, (Pd)rnin ~ 0.6 torr cm. As mentioned before, the original concept
of gas breakdown by successive electron avalanches and a feed-back
mechanism at the cathode was proposed by Townsend in 1915. Later,
more detailed, descriptions can be found in Loeb (1939), Little (1956),
Raether (1964), Hess (1976), Dutton (1978, 1983), Raizer (1986, 1991), and
Boeck and Pfeiffer (1999). A detailed review on the relative contributions
of different "( feedback mechanisms in argon was recently published by
Phelps and Petrovic (1999). An important extension of the simple Townsend
breakdown criterion (2.4.1) for electronegative gases was formulated by
Geballe and Reeves (1953). Introducing the attachment coefficient 'T] the
effective ionization coefficient becomes aeff = a -
'T], and the self-sustainment
condition (2.4.1) becomes
"(a
--[exp(a-'T])d-l] = 1.
(2.4.7)
a-'T]
The ionization and attachment coefficients for room temperature dry air are
plotted in figure 2.4.4. They cross at an Elp value about 25kVcm- 1 bar- 1
corresponding to an E I N value of about 100 Td. At this value the effective
ionization coefficient of air equals zero because electron collisions leading
to ionization are balanced by electron attachment reactions. At higher
fields ionization dominates, at lower fields attachment.
--- Page 49 ---
34
History of Non-Equilibrium Air Discharges
The range of the Townsend discharge (dark discharge) is characterized
by the fact that the current density and the charge density in the plasma is so
low that it has practically no influence on the applied electric field. The degree
of ionization is so small that no appreciable light is emitted. In this regime we
observe an exponential growth of the electron density from the cathode to the
anode, and practically the entire volume is filled with positive ions. A
relatively high voltage is required to meet the self-sustainment condition
(2.4.2). When the current density is increased beyond about 10-5 to
10-6 Acm-2 the Townsend discharge changes to a glow discharge. Now
space charge fields play an important role and the voltage necessary to
sustain the discharge drops to a few hundred volts. A positive space charge
region with high electric fields, the cathode fall region, forms near the
cathode. A positive column of quasi-neutral plasma connects the cathode
region to the anode region. The complicated phenomena occurring in the
transition from a Townsend discharge to a glow discharge have recently
been treated by Sijacic and Ebert (2002).
The theory of the normal glow discharge was formulated by von Engel and
Steenbeck (1934) by applying the Townsend condition for self-sustainment to
the cathode layer. For a wide pressure and current density range the parameters
j / i, VCf and pdcf are constant, where j is the current density, Vcf is the voltage
across the cathode fall region and dcf is the thickness of the cathode fall region.
The values of VCf and pdcf are of the same order of magnitude as those at the
minimum of the Paschen curve. It turns out that the obtained combination
of j / i and VCf corresponds to minimal power dissipation in the cathode
layer (Steenbeck's minimum principle). Typical values for a glow discharge
in air are j/i = 200--570 IlA/(cm torr)2, VCf = 230--370 V, and pdcf = 0.22-
0.52 torrcm, again depending heavily on the cathode material. From these
relations it becomes apparent that glow discharges at atmospheric pressure
can only operate at high current densities with extremely thin cathode layers.
A characteristic feature of the glow discharge is that the two cases of a
normal cathode fall and that of an abnormal cathode fall must be distin-
guished. In the normal glow discharge the current covers only part of the
cathode area, the surface area covered being proportional to the current.
In this case the normal cathode fall voltage is practically independent of
current and pressure. If the current is increased beyond the value required
to cover the whole cathode surface, a region is entered in which the current
density and the cathode fall voltage increase (abnormal glow discharge,
section F --t H in figure 2.4.1, sometimes also referred to as anomalous
glow discharge). The abnormal glow discharge has attracted considerable
attention for technical applications. Due to the positive current voltage
characteristic many of such discharges can be operated in parallel without
requiring individual ballast resistors.
When the current is increased beyond the stage of the abnormal glow
discharge the required voltage drops considerably, to about 10 V, and an
--- Page 50 ---
Electrical Breakdown in Dense Gases
35
arc discharge is established. At atmospheric pressure the plasma in most
arc discharges is approaching local thermodynamic equilibrium (thermal
plasma). Thermal plasmas are outside the scope of this book. It should be
mentioned, however, that in the arc fringes, and especially in fast moving
arcs (gliding arcs), non-equilibrium plasma conditions can also be found
and can be utilized for technical applications (Fridman et al 1999, Mutaf-
Yardimci et al 2000).
2.4.2 Streamer breakdown
As was pointed out by Rogowski (1928), breakdown in wide atmospheric-
pressure air gaps subjected to pulsed voltages proceeds much faster than
can be explained by the mechanism of successive electron avalanches
supported by secondary cathode emission. An essential feature of this Town-
send breakdown mechanism is that the space charge of a single electron
avalanche does not distort the applied homogeneous electric field in the
gap. This limits the number of electrons in the avalanche head to stay
below a critical value Ncr (about 108):
(2.4.8)
When the amplification of the avalanche reaches this critical value before
arriving at the anode, local space charge accumulation leads to a completely
different breakdown mechanism. The concept of this 'Kanalaufbau' or
'streamer breakdown' was developed independently by Raether (1939,
1940), Loeb and Meek (1941) and Meek (1940). Streamer breakdown is a
much faster process and results in a thin conductive plasma channel.
Streamer breakdown can always be provoked by applying a certain over-
voltage to the gap with fast pulsing techniques. The concept of streamer
breakdown is based on the notion that a thin plasma channel can propagate
through the gap by ionizing the gas in front of its charged head due to the
strong electric field induced by the head itself. In air the conditions for Town-
send breakdown or streamer breakdown are well established (figure 2.4.5).
Only close to the boundary line may both types of breakdown occur.
From this curve it is apparent that at larger pd values a relatively modest
overvoltage will result in streamer breakdown. It should also be pointed
out that the often cited criterion originally derived by Raether (1940), that
in air at pd values < 1000 torr cm Townsend breakdown can be expected
and above this value streamer breakdown is not always applicable in this
generality. In dry air the Townsend mechanism must be invoked at low over-
voltages at least to pd values up to 10 000 torr cm (Allen and Phillips 1963).
Following the early observations ofthe Loeb school in California and of
Raether and his students in Hamburg many experimental investigations have
been devoted to the observation of the streamer phase in different gases. The
physical processes involved are discussed in review papers by Marshak
--- Page 51 ---
36
History of Non-Equilibrium Air Discharges
24
..-
~
~ 16
~
~ 1 8
>
0
0
250
850
1450
2050
2650
Pressure Spacing Product (Torr cm)
Figure 2.4.5. Curve separating conditions resulting in air breakdown by the Townsend
mechanism (lower region) and by the streamer mechanism (upper region) (from Korolev
and Mesyats 1998 p 65).
(1961), Lozanskii (1976), Kunhardt (1980), Kunhardt and Byszewski (1980),
Dhali and Williams (1985, 1987) and in various handbook articles (Dutton
1978, 1983) and textbooks (Loeb and Meek 1940, Llewellyn-Jones 1957,
1967, Raether 1964, Meek and Craggs 1978, Kunhardt and Luessen 1983,
Korolev and Mesyats 1998).
The numerical treatment of streamer propagation has become possible
only later, starting with simplified one-dimensional models about 1970.
Among the first computer simulations were those of Dawson and Winn
(1965), Davies et al (1971), Kline and Siambis (1971, 1972), Gallimberti
(1972), and Reininghaus (1973). An analytical approach to streamer propa-
gation was proposed by Lozansky and Firsov (1973). They considered the
streamer to be a conductive body having the shape of an oblong ellipsoid
of revolution, placed in an external field E. For this configuration an
analytical solution exists for the potential distribution around the body. In
such models the streamer propagation velocity is determined by the drift
of electrons in the enhanced field region at the streamer tip. Higher velocities
can be obtained if processes are included that generate electrons in front of
the streamer head or that assume a certain level of background ionization.
There is still considerable debate about the major physical processes involved
in streamer propagation and about the appropriate boundary conditions for
numerical simulations. In air, or other oxygen nitrogen mixtures, photo-
ionization in the gas volume in front of the streamer head is considered an
important process that is included in many numerical simulations. Unfor-
tunately there is only limited experimental evidence of this process (Penney
and Hummert 1970, Zheleznyak et al 1982). Some authors claim that
photo-ionization is a crucial feedback mechanism placing seed electrons
--- Page 52 ---
Electrical Breakdown in Dense Gases
37
1.0
17 ns
I
0.1
0.1
c:
0.7
~ ...
0.50
Ionisation
0.45 \::;I
0.40
<II
D.6
0 a..
OA
'iii
o.a
~ D.2
0.1
23 ns
0.0
0.1 0.0 0.1
0.1 0.0 0.,
0.1 0.0 0.1
0.1 0.0 D.1
Radial Position (em)
Radial Position (em)
Figure 2.4.6. Results of numerical two-dimensional streamer simulations in atmospheric
pressure dry air (Kulikovsky 1998).
ahead of the streamer front in order for the streamer to propagate (Morrow
and Lowke 1995). As a matter of fact, in such models positive (cathode
directed) streamers will not propagate if no photo-ionization and zero
background ionization is assumed. It must be stated, however, that zero
background charge density is not a realistic assumption in atmospheric air.
Negative (anode directed) streamers, on the other hand, can propagate in
numerical simulations without photo-ionization and without background
electrons. Recent two-dimensional simulations of negative streamers starting
from one initial electron obtain streamer propagation and even streamer
branching without these additional assumptions (Arrayas et al 2002,
Rocco et aI2002).
With the advent of faster computers and the availability of better
numerical algorithms to cope with steep gradients and small time steps
numerical two-dimensional simulations of streamer propagation were
greatly improved. Recent developments were reviewed by Babaeva and
Naidis (2000). Figure 2.4.6 shows some details of such simulations performed
by Kulikovsky (1998) on the propagation of a positive streamer in a weak
field in atmospheric pressure dry air. In the left part the electron density
contours of the propagating streamer are plotted for 5, 11, 17, and 23 ns.
The outer contour corresponds to 1011 cm -3, the inner contour to
1013 cm -3. The right part of figure 2.4.4 shows an enlargement of the
region of high ionization rate and space charge density at 17 ns. In these
two plots the region is defined by the contour line corresponding to 10%
of the maximum value. These numerical simulations demonstrate that the
ionization region at the streamer head is extremely thin, about 0.015 cm in
thickness, and that the streamer body reaches appreciable electric con-
ductivity with electron densities in excess of 1013 cm -3. A comparison
shows that the original Raether-Meek streamer criterion and analytical
models based on the propagation of a highly charged sphere predict streamer
--- Page 53 ---
38
History of Non-Equilibrium Air Discharges
properties close to those obtained in two-dimensional simulations
(Kulikovsky 1998). One remark of caution is in place. Most simulations
arrive at field value in the streamer front far in excess of those for which
the approximations used for the ionization coefficient are valid. Since the
ionization efficiency in most gases peaks around 100 e V and then drops
again, this fact should be incorporated.
2.4.3 Pulsed air breakdown and runaway electrons
Rogowski et at (1927) and Buss (1932) reported that pulsed breakdown in
atmospheric pressure air can also occur in two steps (Stufendurchschlag).
Apparently, under certain conditions, an intermediate diffuse discharge
phase can be established before complete breakdown of the gap. This
phenomenon was later investigated in more detail (Chalmers 1971, Water
and Stark 1975), and also in other atmospheric pressure gases. In addition
to air, investigations were performed in nitrogen (Farish and Tedford
1966, Doran 1968, Chalmers 1971, Koppitz 1973), and in hydrogen (Edels
and Gambling 1959, Doran and Meyer 1967, Meyer 1967, Cavenor and
Meyer 1969). Spectroscopic investigations revealed that this transient diffuse
discharge phase can be classified as a glow discharge with pronounced non-
equilibrium plasma properties. The energy balance and the electrical charac-
teristics of pulsed glow discharges have been investigated by Boeuf and
Kunhardt (1986) and by Dhali (1989). At atmospheric pressure the duration
of the pulsed glow discharge is normally restricted to less than 11!s by
instabilities, most likely originating in the cathode layer, that cause constric-
tion or filamentation of the diffuse volume discharge. With the advent of
transversely excited atmospheric (TEA) lasers this transient glow phase in
high pressure gases gained immense practical importance (Rhodes 1979).
Following the early work of Felsenthal and Proud (1965) and Mesyats
and Bychkov (1968) many experimental investigations have been devoted
to nanosecond pulse breakdown in atmospheric pressure air. At certain
over-voltages an intermediate diffuse non-equilibrium volume discharge
phase with an electron density on the order of 1016 cm-3 can be obtained.
The physical phenomena occurring in pulsed breakdown have been treated
in several review articles (Kunhardt 1980, 1983, 1985) and in some mono-
graphs devoted to this special subject (Lozanzkii and Firsov 1975, Bazelian
and Raizer 1998, Korolev and Mesyats 1998). Self-sustained volume
discharges have recently been reviewed by Osipov (2000).
A special situation arises when extremely high electric fields are applied
to a gas gap. Since the cross sections for all electron collisions (elastic,
exciting, ionizing) have a maximum at a certain electron energy, high
enough electric fields must lead to a situation where an electron picks up
more energy between collisions than it loses by collisions with the
background gas. This leads to a runaway situation in which electrons are
--- Page 54 ---
References
39
continuously accelerated. For most gases the ionization cross section peaks
around 100 eV. Wilson (1924) suggested this mechanism as a possible
explanation for the lightning observed in thunderstorms. A rough estimate
of the electric fields required to reach the transition from the streamer
mechanism to continuous acceleration of electrons was formulated by
Babich and Stankevich (1973). The requirement is to get to field values
that correspond to about three times the value for stationary breakdown.
Runaway electrons were also suggested as a conceivable mechanism for
streamer propagation (Kunhardt and Byszewski 1980). A recent monograph
on High-Energy Phenomena in Electric Discharges in Dense Gases (Babich
2003) treats the history of the concept of runaway electrons and the experi-
mental evidence in detail. To establish runaway conditions in atmospheric
pressure air in the laboratory, high voltage pulses of sub-nanosecond rise
time and duration are required (Alekseev et al 2003, Tarasenko et al 2003).
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History of Non-Equilibrium Air Discharges
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--- Page 56 ---
Corona Discharges
41
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Moruzzi J L and Price D A 1974 J. Phys. D: Appl. Phys. 7 1434-1440
Mutaf-Yardimci 0, Savaliev A V, Fridman A A and Kennedy L A 2000 J. Appl. Phys. 87
1632-1641
Niemeyer L 1999 'Gaseous insulation' in Webster J G (ed) Wiley Encyclopedia of Electrical
and Electronics Engineering (New York: Wiley) vol. 8 pp 238-258
Osipov V V 2000 Phys. Usp. 43221-241
Paschen F 1889 Wiedemann Ann. Phys. Chem. 37 69-96
Penney G Wand Hummert G T 1970 J. Appl. Phys. 41 572-577
Phelps A V and Petrovic Z L 1999 Plasma Sources Sci. Technol. 8 R21-R44
Protasevich E T 2000 Cold Non-Equilibrium Plasma (Cambridge: Cambridge International
Science Publishing)
Raether H 1939 Z. Phys. 112464--489 (in German)
Raether H 1940 Naturwissenschaften 28 749-750 (in German)
Raether H 1964 Electron Avalanches and Breakdown in Gases (London: Butterworths)
Raizer Yu P 1986 High Temp. 24 744-754
Raizer Yu P 1991, 1997 Gas Discharge Physics (Berlin: Springer)
Raja Rao C and Govinda Raju G R 1971 J. Phys. D: Appl. Phys. 4494-503
Reininghaus W 1973 J. Phys. D: Appl. Phys. 6 1486-1493
Rhodes Ch K (ed) 1979 1984 Excimer Lasers (New York: Springer)
Rocco A, Ebert U and Hundsdorfer W 2002 Phys. Rev. E 66035102-1 to 035102-4
Rogowski W 1928 Arch. Elektrotech. 2099-106 (in German)
Rogowski W, Flegler E and Tamm R 1927 Arch. Elektrotech. 18479-512 (in German)
Sigmond R S 1984 J. Appl. Phys. 56 1355-1370
Sijacic D D and Ebert U 2002 Phys. Rev. E 66066410
TarasenkoV F, Yakovlenko S I, Orlovskii V M, Tkachev A Nand Shumailov S A 2003
JETP Lett. 77611-615
Townsend J S 1915 Electricity in Gases (Oxford: Clarendon Press)
Vollrath K and Thorner G 1967 Kurzzeitphysik (Wien: Springer) p 81
Wagner K H 1971 Z. Phys. 241 258-270
Water R T and Stark W B 1975 J. Phys. D: Appl. Phys. 8416--426
Wilson C T R 1924 Proc. Cambridge Phil. Soc. 22 534-538
Zheleznyak M B, Mnatsakanyan A Kh and Sizykh S V 1982 High Temp. 20 357-362
2.5 Corona Discharges
2.5.1
Phenomenology of corona discharges
Similar to lightning, corona discharges in ambient air can be observed under
natural conditions, for instance, corposant or 'St. Elmo's Fire' in a thunder-
storm. As a rule, a naturally occurring corona arises at points and wires
--- Page 57 ---
42
History of Non-Equilibrium Air Discharges
having high electrical potential with respect to the environment and exhibits
itself around sharp edges like a faint glow in the form of a crown. An appear-
ance of a corona may produce useful or undesirable effects. For instance, a
corona arising spontaneously around high-voltage wires of an electrical
power transmission line results in a loss of electrical energy. On the other
hand, coronas are widely used in many practical applications like dust
collection with electrical precipitators, atmospheric pressure non-thermal
plasma surface treatment of polymers, cleaning of exhausted gases, etc.
The corona discharge is a low-current discharge caused by partial (or
local) breakdown of a gas gap with strongly inhomogeneous electric field.
To form a non-uniform electric field distribution in the gap, at least one of
the electrodes must be sharpened with a radius of curvature of far less
than the length of the inter-electrode gap. The most typical configurations
of electrode systems used in practice to generate corona discharges are
pin-to-plane, multi-pin-to-plane, wire-to-pipe, wire-to-plane or wire between
two planes, multi-wire-to-plane or multi-wire between two planes, coaxial
wire-cylinder and so on (Goldman and Goldman 1978, Sigmond 1978,
Goldman and Sigmond 1982).
Steady dc corona discharges exist in several forms depending on the
polarity of the electric field, the electrode system and discharge current. A
schematic view of different forms of dc coronas in static ambient air at
atmospheric pressure in pin-to-plane gaps under positive and negative
polarities of the high-voltage stressed pin electrode is shown in figure 2.5.1
(figure is taken from Chang et at 1991). The sequence of pictures in the
left-to-right direction corresponds to increasing discharge current. A typical
range of corona current, averaged in time, extends approximately from 1 to
200 IlA per pin. Characteristic voltages applied to sustain dc coronas depend
mainly on the geometrical parameters of the electrode system (such as the
radius of the tip of a pin and the length of the inter-electrode gap) and
ranges over several units or tens of kV. For the same electrode system, the
onset voltage is roughly the same for positive and negative corona in air.
For a positive corona, the discharge, apparent already to the naked eye,
starts with a burst corona. This regime exhibits seldom and non-regular
current pulses accompanied with short and faint streamers originating
away from the pin. The burst regime proceeds to the streamer corona,
silent glow corona and finally the non-stationary spark as the applied voltage
increases. However, in most cases, a glow regime of a positive corona
precedes the streamer regime. The positive glow corona is known as the
Hermstein glow (Hermstein 1960). It is similar to the low-pressure discharge
in a Geiger tube. A steady current at a fixed voltage, quiet operation, and
almost no sparking characterize this glow corona.
On the contrary, the streamer regime is non-steady, quite audio noisy
and emits strong radio noise. This regime corresponds to the existence of
numerous thin, short-living and repetitive current filaments (streamers)
--- Page 58 ---
BUIlIt
Pulse
Corona
I-
,.tI\
T
1HchaI
Pulse
Corona
Slreamer
Corona
I-,
T
PuIae\e88
ColOna
Corona Discharges
43
+
Spark
Figure 2.5.1. Schematic view of types of corona discharges (from Chang et aI1991).
originating from the pin. Due to branching of fast-moving streamers, their
instant image in the gap shows up as a bush 'growing' from the tip of the
pin. The streamer regime can be regarded as an uncompleted breakdown
of the gas gap. Therefore it is the direct precursor to the spark: once the
streamers bridge the gap, the spark occurs. However, the transition from
corona to spark is not sharply defined. For a wire-to-pipe or wire-to-plate
electrode configuration, the corona generated at the positively stressed
electrode may appear as a tight glow sheath around and along the wire or
as streamers moving away from different locations of the wire.
For the de negative corona in a pin-to-plane geometry, the initial form
of a discharge is a non-steady Trichel pulse corona (Trichel 1938), charac-
terized by regular current pulses, glow luminosity around the tip of a pin
and a dark inter-electrode gap. The repetition frequency of Trichel pulses
increases linearly with corona current and ranges over 1-100 kHz. For
static air at atmospheric pressure, the Trichel pulse regime is continued up
to 120--140 ~A and is followed by a pulse-less negative glow corona as the
applied voltage increases. The negative glow usually requires clean, smooth
electrodes to form. For parallel wire-to-cylinder, wire-to-plate or coaxial
wire-cylinder electrodes, the corona generated at negative electrodes may
--- Page 59 ---
44
History of Non-Equilibrium Air Discharges
take the form of rapidly moving glow spots or it may be concentrated into small
active spots regularly placed along the wire, called 'tufts' or 'beads'. The glow
corona often changes with time into the tuft form. The tuft corona is also noisy
and has a sparking potential similar to that of the glow form (Lawless et al
1986). In static air, the steady pulse-less negative corona is followed directly
by a spark. The sparking potential of the negative corona is much higher
than that of the positive streamer corona. This is the reason why the negative
corona is used in electrical precipitators (see section 9.2).
For a pin-to-plane geometry, Warburg (1899) found that the radial
distribution of the current density j at the plane electrode follows an
empirical relation j( 0) ~ jo cosn 0 == jo (1 + tan2 0) -nI2, which was confirmed
later by others (Jones et a11990, Allibone et aI1993). Herejo is the current
density at the plane at the axis of the corona, tan 0 = r / d, r is the current
radius, and n ~ 5 ± 0.5 for different experiments. There are exceptions to
this Warburg relation (Goldman et a11988, 1992, Akishev et aI2003a).
A significant concentration of electric field exclusively around the
sharpened electrode plays a key role in the formation of special properties
of coronas in comparison with discharges in uniform electric fields. First,
an inception voltage of the corona is far lower compared with Paschen's
breakdown voltage, corresponding to uniform inter-electrode gap of the
same length. Second, due to a minor contribution of ionization processes
in the total balance of charged particles in the drift region of the corona,
the inter-electrode gap is filled mainly with negative or positive space
charge. This implies that the corona discharge is space-charge limited in
magnitude, and that the volt-ampere characteristic (V AC) of the corona
has a positive slope: an increase in current requires higher voltage to drive
it. Third, intensive ionization processes at the point, accompanied by an
intensive local energy deposition, provoke the development of ionization
instabilities resulting in an appearance of streamers in the corona gap
under conditions, in which the Meek's (or Reather's) criterion for streamer
breakdown is not fulfilled.
Outstanding contributions to the development of the fundamentals of
corona discharges were reported in the past century by researchers belonging
to the scientific schools of Kaptsov (Kaptsov 1947, 1953) and of Loeb (Loeb
1965 and literature cited therein). Both of these schools used intensively a
conception of the electron avalanches originally developed by Townsend
(Townsend 1914). Indeed, from a physical point of view, the corona
discharge belongs to the same class of self-sustained discharges as the
extremely low-current (10- 15_10-7 A) dark Townsend discharge and the
medium-current (3 x 10-4-3 x 10-3 A) glow discharge. In these discharge
types the emission of charged particles from electrode surfaces does not
play an essential role in the transport of the electric current through the
metal-gas boundary, but electron avalanches playa key role in sustaining
the discharge.
--- Page 60 ---
Corona Discharges
45
B
- - -/- - - --
Subnormal
-5
glow discharge
10
A
Townsend discharge
10 -8
-9
10
1O-1-L....:::;;;.. _________
---I
u
Figure 2.5.2. Schematic classification of self-sustained gas discharges.
It is well known for low-pressure discharges in a plane-to-plane
geometry (von Engel and Steenbeck 1934, von Engel 1955, Brown 1959)
that the dark Townsend discharge goes directly to the glow discharge
(figure 2.5.2, path A-B).
In principle, for an electrode system with initial non-uniform distri-
bution of the electric field there is also the chance to transit from the dark
Townsend discharge to the glow discharge. For the positive corona, this
transition is achieved only at lower pressures and it is accompanied by a
non-monotonic behavior of the voltage drop across the inter-electrode gap
(figure 2.5.2, path A-C-B): there is a reduction in the discharge voltage in
the glow regime similar to that observed in discharges in a plane-to-plane
geometry. For the negative corona, a transition to a glow discharge can be
realized in air up to atmospheric pressure (Akishev et a11993, 2000, 2001),
and this transition is followed by a monotonic increase of the discharge
voltage (figure 2.5.2, path A-C-D). For both cases, contrary to gas
discharges in a plane-to-plane geometry, the corona discharge is an
additional intermediate discharge stage between the dark Townsend
discharge and the glow discharge.
For discharges sustained due to the development of electron avalanches,
a self-sustained steady regime occurs if the replenishment criterion for
electron avalanches in the gap is fulfilled:
t
(a -1]) dx = In (1 + ~).
(2.5.1 )
Here 'Y is the total coefficient of a positive feedback for electron avalanches
due to surface and volume processes: emission of electrons from a cathode
--- Page 61 ---
46
History of Non-Equilibrium Air Discharges
by positive ions, excited atoms/molecules, photons, and photo-ionization
of the background gas; a and TJ are the Townsend coefficients for direct
ionization of atoms/molecules by electron impact and attachment of
electrons to electronegative components of the background gas due to two-
and three-body processes, respectively.
The ionization coefficient a depends very strongly (exponentially) on the
reduced electric field strength E / N (E is the electric field strength, N is
density of the background gas), therefore discharge regions with a high
electric field strength (where a 2:: TJ, and the intensity of ionization is very
high) bring a major contribution to the total value of the integral written
above. For this reason, the magnitude of I usually does not coincide with
the length d of inter-electrode gap (commonly 1< d or I ~ d; the case
1= d corresponds only to dark Townsend discharge between plane
electrodes, in which space charge is negligible.
The electric properties of a corona are reflected totally in the relation
between the discharge current I and the applied voltage V. Therefore
knowledge of the volt-ampere characteristic of a corona is desirable for
many practical purposes. The initial inhomogeneous distribution of the
electric field in the corona allows in some cases for substantial simplification
of analytical and numerical calculations of the V AC. Indeed, the strong
concentration of the electric field around the electrode with a small radius
of curvature results in a division of the inter-electrode gap of coronas into
two very different parts: a thin generation zone with intensive ionization
located in the vicinity of the electrode with small curvature, and a drift
zone with a space charge occupying the rest of the gap. As a rule, the voltage
difference across drift region is higher than the voltage drop across the
generation zone (about 0.5 ± 0.2 kV). In this case, the V AC of the drift
region can be attributed with good accuracy to the V AC of the corona
in total.
Townsend (1914) was the first to use this idea and calculated the VAC
for a steady corona in a coaxial wire-cylinder geometry:
'" 8 m::o lLi
1= 21
/
Uo(U-Uo)·
R nR ro
(2.5.2)
Here lLi is the mobility of carriers of the current in the drift region (for
instance, negative or positive ions for negative and positive coronas in air,
respectively); co is the permittivity of a vacuum; Rand ro are the radii of
the outer cylinder and the inner wire respectively; Uo is so-called inception
voltage of the corona, corresponding to an appearance of a very noticeable
corona current (as a rule, I> O.I11A) and luminosity around the wire or
the sharpened electrode.
Equation (2.5.2) is obtained under the assumption that the space
charge in a drift region is small enough. Therefore this formula describes
only the initial current of a corona under the influence of an applied voltage
--- Page 62 ---
Corona Discharges
47
U not far from the inception voltage Uo. Loeb (1965) suggested that the
time-averaged V AC of a corona discharge can be approximated by a
universal parabolic dependence
1= kU(U - Uo)
(2.5.3)
which can describe the corona current in any geometry and at any voltage up
to the spark transition. In this case, the proportionality factor k and the
corona ignition voltage Uo depend on the geometrical features of the elec-
trode system (for instance, on the tip radius of the pin and the inter-electrode
distance), the polarity of the applied voltage, the pressure and the mixture of
the background gas) and has to be determined by experiment. This idea is
very popular in the literature at present, and some results on fitting of the
parabolic approximation with experiment can be found in Lama and Gallo
(1974), Sigmond (1982), Vereshchagin (1985), and Akishev et al (2003).
2.5.2 Negative dc corona discharges
For definiteness, the emphasis in this section is on the physical properties of a
negative corona for a pin-to-plane geometry mainly in air. The mechanism of
Trichel pulses and the transition of the negative corona to the spark are
discussed in detail.
Regularly pulsing corona
As mentioned above, while studying the negative point-to-plane corona in
air, Trichel revealed the presence of regular relaxation pulses (Trichel
1938). The qualitative explanation given by him included some really impor-
tant features like the shielding effect produced by a positive ion cloud in the
vicinity of the cathode. In later work (Loeb et a11941) it was stated that the
Trichel pulses exist only in electronegative gases, and particular emphasis
was put on the processes of electron avalanche triggering. It was also stressed
that, usually, the time of the negative ion drift to the anode is much longer
than the pulse period. More detailed measurements of the Trichel pulse
shape demonstrated that the rise time of the pulse in air may be as short as
1.3 ns (Zentner 1970a), and a step on a leading edge of the pulse was observed
(Zentner 1970b). Systematic studies of the electrical characteristics of Trichel
pulses were undertaken (Fieux and Boutteau 1970, Lama and Gallo 1974),
and relationships were found for the pulse repetition frequency, the charge
per pulse and other properties.
Among attempts to give a theoretical explanation for the discussed
phenomena the work of Morrow is most known (Morrow 1985a), in which
the preceding theories were also reviewed. The continuity equations for
electrons and for positive and negative ions in a one-dimensional form
were numerically solved together with Poisson's equation. The negative
--- Page 63 ---
48
History of Non-Equilibrium Air Discharges
corona in oxygen at a pressure of 50 torr was numerically simulated. Only the
first pulse was computed, and extension of calculations for longer times
showed only continuing decay of the current. In Morrow (198Sa) the
shape of the pulse was explained while practically ignoring the ion-secondary
electron emission. In the following paper (Morrow 1985b) the step on the
leading edge of the pulse was attributed to the inclusion of photon secondary
emission, and the main peak was explained in terms of the ion-secondary
emission. This explanation was criticized later by Cermik and Hosokawa
(1991), pointing at the importance of an ionization-wave-like evolution of
the cathode layer at early stages.
A more detailed analysis of the mechanism of Trichel pulses based on
numerical simulations was proposed by Napartovich et al (1997) with the
use of a I.S-dimensional numerical model. This numerical model, succeeding
in reproducing the established periodical sequence of Trichel pulses in dry air
in short-gap « 1 cm) coronas, was formulated for the first time. The three-
component simplified kinetic model was used with only one type of negative
ions, namely O2, produced in an electron three-body attachment process.
The electron-ion and ion-ion recombination may be neglected for the
conditions of the corona discharge.
To describe the pulse mode of the negative point-to-plane corona it is
sufficient to solve the continuity equations for electrons, positive and nega-
tive ions and Poisson's equation under the assumption that the current
cross section discharge area S(x) is a known function of coordinate x. The
boundary conditions for positive and negative ions are self-evident: their
number density is equal to zero at the anode and cathode, respectively.
For electrons, in contrast to Morrow, only the ion secondary emission is
included.
It was assumed that all physical quantities are constant jn every cross
section of the discharge current. The same approximation was used by
Morrow, but he assumed unrealistically the form of discharge channel to
be cylindrical. However, it is well known from numerous experiments that
the discharge current is concentrated near to the point and occupies a
comparatively large area on the anode surface. The ratio of the current
spot radii on the anode and cathode is of the order of 104 .
A sample of a calculated current pulses and the time dependence of the
replenishment criterion integral M = fa dx during pulsation are shown in
figure 2.5.3 (a is the ionization coefficient).
To illustrate effects of non-linear evolution of the corona in the pulse
regime, spatial distributions of physical quantities in the active zone at the
moments listed in table 2.5.1 corresponding to the front of the pulse are
presented in figure 2.5.4.
When the number density of positive ions becomes larger, it causes an
increase of the electric field strength near the cathode. This increase is in
turn followed by a rapid growth of the electron multiplication factor, and
--- Page 64 ---
10
51--_~""""
•••••• 71\
....
o
88
a
89
.,'
Corona Discharges
49
.. '
.
.
'
.'
In(1+1fgamma)
- -~. -
. ,,-
",
'. . ....... .
. .'
.. '
l
90
91
Time (10
.. s)
,.'
.'
....
.
'
7
92
,
.
. ...
....
- -
93
". . .,-
....
94
Figure 2.5.3. Calculated current pulses and replenishment criterion integral M = fa dx as
a function of time.
the ion number density. This feedback is strongly non-linear because of the
exponential growth of the electron current with the ionization coefficient
a, which is also a steep function of the electric field strength. As a result of
the strong electron multiplication a plasma region is formed where the
electric field strength diminishes due to high electron mobility (in other
words, due to plasma shielding). This structure propagates at very high
speed to the cathode (see the transition from curve 2 to 3). As a result of
this wave propagation, the voltage drop across the active zone diminishes
while the electric field strength at the cathode grows. This means that the
dynamical differential resistance of the shrinking cathode layer is negative.
At this phase the electric current at the cathode is predominantly the
displacement current.
To illustrate in more detail the processes during the pulse decay, the
spatial distributions of the physical quantities at the moments listed in
table 2.5.2 are presented in figure 2.5.5.
Table 2.5.1.
Time (Ils)
Current (IlA)
Moment
2
3
4
5
6
7
89.99907 89.99952 90.00000 90.00050 90.00125 90.00325 90.00525
319
548
2351
1728
1216
2249
2741
--- Page 65 ---
50
History of Non-Equilibrium Air Discharges
600
6
5
400
200
0.005
0.01
0.015
0.02
Distance from cathode (cm)
Figure 2.5.4. Time evolution of the electric field distribution in the active zone. Moments
1-7 correspond to table I (leading edge of current pulse).
In conclusion, the decay of the Trichel pulse is governed by the decay of
a cathode layer formed in the course of the preceding evolution. This cathode
layer is similar in many respects to the well-known cathode layer of the glow
discharge. In particular, the cathode current density at the maximum is of the
order of the so-called normal current density. However, certainly this layer
does not coincide with the classical cathode layer. In particular, figure
2.5.5 demonstrates that the electric field distribution controlled initially by
space charge (moments 1-4) evolves to the 'free-space' distribution
(moment 5). Due to the strong increase of the 'free-space' cathode layer in
thickness, the replenishment criterion integral M = f Q: dx grows again,
and the pulse process repeats.
More recent three-dimensional calculations of a negative corona with
Trichel pulses (Napartovich et at 2002) revealed a new feature in the
dynamics of the active zone (cathode layer) during the leading and trailing
edges of a current pulse: the cathode layer shrinks in axial direction and
Table 2.5.2.
Time (Ils)
Current (1lA)
90.02200
1579
2
90.06200
678
Moment
3
90.10005
367
4
90.20217
12.1
5
90.40041
0.67
--- Page 66 ---
400
300
100
2
__ \
4
~--
"0:- -
- __
-
__
Corona Discharges
51
5
""","
~ - - - - - - - ~
--=
0~~~~'~_~·~·'··="·=""~"·=····~"·~m5 ... ~.~.~~ .. ;.;
m.~~~.~._~.~._~=--~.;.~_~.~ .. ~P'~' ~~
o
0.005
0.01
0.015
0.02
Distance from cathode (cm)
Figure 2.5.5. Time evolution of the electric field distribution in the active zone. Moments
1-5 correspond to table 2 (trailing edge of current pulse).
extends in radial direction when the current increases, and it shrinks in radial
direction and extends in axial direction when current decreases.
The results presented above show that the negative ions do not play an
essential role in the mechanism of Trichel pulses. This implies, in contra-
position to popular opinion, that the pulsed regime can also be observed
for a negative corona in electropositive gases like Ar, He, and N2 • Indeed,
experiments performed by Akishev et al (200 1 b) proved this conclusion.
Current oscillations caused by the existence of a negative differential resis-
tance of the dynamic cathode layer at its formation were also observed in
dielectric barrier discharge in He (Akishev et al200lc).
Spark formation
There is scanty information on spark formation in negative coronas. For
instance, for a pin-to-plane configuration Goldman et al (1965) stated that
spark occurs due to development of ionization phenomena on both sides
of the gap resulting in the propagation of a positive streamer originated at
the plane anode if the critical electric field strength ("-'25 kVjcm) is reached
at the anode. However, this general statement does not take into account
in an explicit form the existence of glow discharge regime (see section 6.7),
which follows the true negative corona and precedes the spark.
The corona-to-glow discharge transition is accompanied first by the
appearance of an intensive light emission near the anode corresponding to
the formation of an anode layer of the glow discharge, and second by the
--- Page 67 ---
52
History of Non-Equilibrium Air Discharges
j I jo
1,0
0,8
0,6
0,4
0,2
rid
0,0f4:;::;=;~~~;:;:;=;=P--':"';"'::'
0,0
0,5
1,0
1,5
2,0
Figure 2.5.6. Evolution of radial distribution of anode current density with increase in
current of a pin-plane discharge.
formation of a plasma column in the gap. The V AC of a glow discharge
anode layer with a current density of several tens to hundreds of IlA/cm2
has a negative slope. It means that the anode region is unstable and tends
to shrink into small current spot(s), which provoke glow discharge constric-
tion and spark formation. Therefore, in order to understand adequately the
mechanism of the corona-to-spark transition in a pin-plane geometry, it is
necessary to take into account the physical properties of glow discharge,
which is the intermediate stage of this transition. Experiments on the evolu-
tion of the current and light emission radial distribution under transient
process true negative corona --; glow discharge --; spark were carried out by
Akishev et at (2002, 2003a). Some data from these investigations are
presented in figures 2.5.6-2.5.8. Experiments were performed in static air
at 300 torr. The gap length was d = lOmm, the radius of a pin tip was
0.06mm.
One can see (figure 2.5.6), as the total current increases and the pin-plane
discharge is switched from corona to glow discharge, that the electric
current concentrates more and more around the pin-plane axis. The radial
distribution of light emission near the anode exhibits a different behavior.
At the initial currents of the glow discharge, light emission concentrates
predominantly at the pin-plane axis. However, the effective radius of the
glow region near the anode grows slowly with increasing total current.
This tendency is seen in the glow discharge regime up to glow discharge-
to-spark transition. Nevertheless, the effective radius of the current channel
always exceeds the radius of glow column.
The corona-to-spark transition was induced by the superposition of a
saw-tooth pulse on a steady corona at low current. The appropriate wave-
forms of current and voltage of the discharge in the course of its induced
sparking are presented in figure 2.5.7. The data in figure 2.5.6 correspond
to those in figure 2.5.7. The region of the oscillogram with low amplitude
of discharge current corresponds to quasi-stationary true negative corona;
--- Page 68 ---
I -
.,. . ..
.-
-.-~ ..... -...•... -..
..
'*
•
:0
.-
Corona Discharges
53
.: t
Figure 2.5.7. Time behavior of current (I) and voltage (U) under induced corona-spark
transition. [t] = 100IlS/div, [I] = 2mA/div, [UJ = 2kV/div. Initial current! = 1001lA.
the region with a rapidly growing current corresponds to the transient glow
discharge, and an extremely short region with vigorously growing current
corresponds to spark formation.
Some shots of a pin-plane discharge in the course of its induced sparking
are presented in figure 2.5.8.
The five pictures in figure 2.5.8 present the development of spatial
structure of the transient glow discharge from its forming up to the spark
transition. The numbers of the pictures correspond to the moments indicated
in this figure. No. 1 corresponds to the formation of an anode layer of
the glow discharge; No.2 corresponds to the formation of plasma column
in the gap; No. 3 corresponds to constriction of anode layer into two
The uprise of an
anode layer of the
glow discharge.
Exposition: 5 JI.S
"
•
2
4
Formation of
Constriction of the
plasma
anode layer into
column in bulk of two high-current
glow discharge.
spots.
Exposition: 5 JI.S
Exposition: 1 JI.S
•
5
Elongation of
current
filament originated
from anode current
spot.
Exposition: 1 JI.S
1
6
Bridging of a
Gap by current
filament;
formation of
spark
Exposition:
5J1.S
Figure 2.5.8. Scenario of spark formation III pin-to-plane negative corona in air.
P = 300 torr.
--- Page 69 ---
54
History of Non-Equilibrium Air Discharges
high-current anode spots; No.4 corresponds to the elongation of a current
filament originated from one of the spots; No.5 corresponds to bridging
of the gap by the filament and formation of a spark.
Figure 2.5.8 shows that a sharpened cathode pin does not initiate
sparking but that the plane anode does. The presented scenario of spark
formation in a pin-to-plane negative corona is the same in principle as the
constriction of a glow discharge observed in experiments with diffusive
glow discharges in air flows at medium pressures (Velikhov et a11982, Napar-
tovich et al 1993, Akishev et al 1999a). The characteristic velocity of the
current filament propagating towards the cathode pin through the plasma
column of the glow discharge equals lO4_lO5 cm/s. This is much slower
than the velocity of lO7_lO8 cm/s typical for classical positive streamers.
2.5.3 Positive dc corona discharges
Burst corona
The self-sustained Townsend regime of a positive corona (/ ~ lO-7 IlA) is
characterized by almost the same voltage compared with that of the negative
corona. This regime exhibits so-called burst pulses, the frequency of which
increases with current, and which disappears towards the end of Townsend
regime to be followed by quiet glow corona. The burst corona is a difficult
problem for quantitative description because of its statistical nature.
Glow corona
The generation zone of the glow corona consists of two regions: a very thin
anode layer with negative space charge, and a positively charged glow or
ionization zone. The anode layer has the V AC with negative slope. The
glow zone is very similar to the cathode layer of a classical glow discharge.
Once the corona current increases, the thickness of glow zone also grows.
At lower pressure, the transition corona-to-glow discharge occurs when
the glow zone of the corona occupies the whole inter-electrode gap. Sub-
sequently, the glow zone breaks off from the wire or pin and attaches to
the plane or cylindrical cathode in the form of a thin and uniformly extended
glow cathode layer. This process is accompanied by oscillations of discharge
current and reduction in discharge voltage. In static air (1 atm), the cathode
layer and plasma column of the glow discharge at a current of several rnA are
very constricted (~1 mm).
It is widely believed that self-sustaining of a positive corona is provided
exclusively due to photo-ionization of the background gas. On the other
hand, if the background gas is a pure mono-atomic or mono-molecular gas
like pure He or N2, it is hard to explain an emergence of the needed high-
energy photons in such gases because information about electron-atom and
--- Page 70 ---
Corona Discharges
55
electron-molecule collision processes, resulting in emission of quanta of
energy greater than the ionization potential, is not known. However, there is
no necessity to take into consideration the photo-ionization in the case of a
steady or slowly changing corona. Indeed, the characteristic time of a positive
feedback for the development of electron avalanches due to photoemission of
secondary electrons from cathode equals the drift time for electrons,
Te ::::0 10-6-10-5 s across an inter-electrode gap filled with electropositive gas
or the drift time of negative ions, Tin ::::0 10-4_10-3 s for given electronegative
components in the background gas mixture. In the latter case it is presumed
that negative ions release electrons at the generation zone in the vicinity of a
pin due to fast detachment processes in strong electric fields. For positive
ion ,-emission of electrons from the plane electrode, the total time of the
feedback is the sum Tf = Te + Tip ~ Tip and Tf = Tin + Tip in the case of electro-
positive and electronegative processing gases, respectively. So, for steady or
slowly changing conditions (i.e. characteristic time in the changing of corona
parameters exceeds Tr) the positive corona can be sustained by a feedback
mechanism identical to that in the negative corona. The V ACs of positive
coronas calculated with the use of this idea are in good agreement with the
experimental ones (Akishev et al1999b).
F or a long time, it was believed that the electrical current of the positive
corona in the glow mode is stable. It seems likely Colli et al (1954) were the
first to report on oscillatory behavior of the glow corona current in a cylind-
rical geometry. In pioneering studies on non-linear oscillations (Fieux and
Boutteau 1970, Beattie 1975, Boullound et al 1979, Sigmond 1997) it was
revealed that the current and luminosity of the glow corona were in fact
not constant, but oscillated regularly with a high frequency (105-106 Hz).
It was also found that the waveform of the current self-oscillations had a
relaxation type with a sharp increase of current at the leading edge of
pulse and a slow decay at the pulse tail. The waveform of a light emission
signal was more symmetrical. The maximum of the light emission signal
was correlated with the maximum of the current pulse. According to Fieux
and Boutteau (1970) and Beattie (1975), the period of self-oscillations fell
with the decrease in radius of the corona electrode and practically did not
depend on the average current of corona. The region of existence of free-
running oscillations in plane of the IP parameters (current I, gas pressure
P) for coaxial wire-cylinder glow coronas in N2 is given in figure 2.5.9
(taken from Akishev et alI999b).
For the description of the positive corona between a wire and a cylinder,
the fluid model equations were solved by Akishev et al (1999b) on the
assumption that the ionizing agent in the vicinity of a wire is the soft x-ray
radiation produced in collisions of electrons accelerated in a strong electric
field near wire with the wire surface. This is the so-called Bremsstrahlung
radiation. The total electric current was a sum of displacement and conduc-
tivity currents. A numerical model developed in Akishev et al (l999b)
--- Page 71 ---
56
History of Non-Equilibrium Air Discharges
700
-< 600
::I.
..z e 500
.. ..
::I
~ 400
~
B 300
&'., S 200
;.
-<
100
0
0
100
200
.---------- --- .... _-
-<>-I,IlA
-o-I,IlA
.-•. - I, IlA
-+-I,IlA
300
400
500
Pressure, Torr
600
700
800
Figure 2.5.9. IP-region of existence of oscillations for a coaxial wire-cylinder corona in N2.
The oscillation region is bounded by curves I) and h Radii of anode and cathode are 0.75
and IOmm, respectively. Empty and filled markers correspond to a mesh and to a solid
cathode.
provides a description of the V AC averaged in time and non-stationary
effects in glow positive corona with a satisfactory accuracy.
Streamer corona
The quiet glow corona follows a noisy streamer regime. The threshold
current depends on the degree of inhomogeneity of the electric field in the
gap: in general, the greater the radius of curvature of the electrode, the
lower the threshold current. As a rule, the streamer regime of the steady
corona in fact is a regime with intermittent transitions between glow and
streamers. The repetition frequency of the streamer appearance in the
corona gap increases with total current.
First, it should be particularly emphasized that the mechanism of
initiation of streamers in the steady glow corona is not the same as that in
a non-pre-ionized gap stressed with a high-voltage pulse. In the latter case,
a necessary condition for formation of a positive streamer is a high initial
value of the replenishment integral M = f6 (0: - ry) dx :::: 18-20 (Meek's or
Raether's criterion). Recall that M is the resulting coefficient of ionization
multiplication of an electron avalanche across inter-electrode gap. However,
the value of M in a self-sustained glow corona always stays much lower
(M = In((1 + 'Y)h) ::; 3-6) at any current. Therefore, it is not clear from
the point of view of Meek's criterion how it is possible to induce streamers
in glow corona if Meek's criterion is not met.
--- Page 72 ---
Corona Discharges
57
.
~,"-
Figure 2.5.10. The sequence of eight frame pictures illustrating the chaotic dynamics of
high-density current spots on the anode surface of a glow positive wire-cylinder corona.
Air, P = 30 torr, radius of inner wire (anode) ra = 0.5mm, radius of cylinder
Rc = IOmm, reduced corona current per em of its length 1= 80IlA/cm, U = 1.6kV.
Time exposition of each frame picture is 51ls. The time interval between neighboring
frames is 51ls. A typical diameter of current spot is 0.5 mm.
Second, the streamers developing in the gap of a glow corona propagate
through well pre-ionized gas with a marked concentration of charged
particles (electrons and/or negative ions), which is higher or of the same
order compared with the number density of the seed electrons obtained in
the numerical calculations due to using photo-ionization in the model.
This means that it is not necessary to engage a disputable photo-ionization
process for the description of streamer development in a glow corona.
A search for the reasons responsible for initiation of streamers in a glow
corona at low M was carried out in Akishev et at (2002b). The anode region
of the glow corona appears to the naked eye as homogeneous, but in fact
glow is not uniform. Akishev et at (2002b) revealed the formation of
numerous and non-stationary small current spots on the glowing anode
(figure 2.5.10).
To obtain controlled conditions in the experiment, they used a positive
corona at lower pressure. The critical current for the appearance of spots
decreases with pressure, and at atmospheric pressure it is close to the
threshold current for the initiation of streamers (about 50-7011A per pin
for a corona in air). The anode spots become more intensive and appear
more frequently when the total corona current increases. This finding
correlates with the same behavior of the streamers.
Akishev et at (2002b) suggest that the current spots arise due to
development of an ionization instability in the anode region, and that
these spots induce streamers in a glow corona. As a matter of fact, each
current spot corresponds to a local breakdown of the glow generation
zone. This breakdown releases a voltage drop of about 0.5-1 kV, which
results in an instantaneous and strong increase of the local reduced electric
--- Page 73 ---
58
History of Non-Equilibrium Air Discharges
field that is sufficiently large to induce a streamer at the anode. The time it
takes to develop an ionization instability depends on the mixture of the
processing gas. The use of admixtures like Ar or CO2 injected in the anode
region results in an increase of intensity and frequency of streamers in a posi-
tive corona in air (Yan 2001 and literature cited therein). This is consistent
with the idea mentioned above about provocation of streamers by anode
current spots.
Streamers-to-spark transition
This phenomenon is presented here using the example of sparking of a
positive steady corona in a pin-to-plane electrode configuration and based
on experimental results obtained at different times by the teams of Loeb,
Kaptsov, Goldman, Marode, Sigmond, Rutgers, Veldhuizen, Ono, Yamada,
and many other groups.
An increase in the corona current precedes the elongation of the
streamers and finally bridging of the gap by some of them. Each bridging
results in a current pulse of several tens of mA (see figure 2.5.11 taken
from Akishev et at 2002b), which is not yet a spark pulse. The amplitude
of a streamer pulse is much higher compared with the average corona
current. Such an amplitude is possible due to existence of stray capacitance
in the external circuit.
For low current steady corona, a sequence of several bridging streamers
is required for a spark to happen, with the time interval between two
streamers not longer than about 100 J.LS. Such a short interval ensures that
the local energy deposited by the foregoing streamer in a gas volume of
tiny size (of the order of the streamer diameter) is not dispersed due to
diffusion before the subsequent streamer occurs. In such a case, energy will
accumulate in time within a small volume near the tip of the pin. The high
Figure 2.5.11. Waveform of a positive corona current under self-running streamers and
regular streamers-to-spark transition. Horizontal and vertical scales are 50 JlS and 10 rnA
in division. Air, I atm. Pin-to-plane gap, 17 mm.
--- Page 74 ---
I
11 -0.2-0.8 A
,
,
1.
1
.. I
- SOOns'
Corona Discharges
59
12 -0.01 A
2-4
- 0,5 - 100 Ils
-l.SIl~
,
,
,
,
:1
t'
Figure 2.5.12. Generalized behavior in time of positive corona current under induced
sparking. Each scale is an arbitrary one. Gap length 17 mm. Ambient air at atmospheric
pressure. U = 20.7 kV, I = 551lA, !1U = 1.8 kV.
level of specific energy deposited in the gas will result in a dramatic
intensification of ionization and detachment processes and in the creation
at the pin of the embryo of a pre-spark current filament, which will elongate
and propagate towards the cathode plane and eventually form a spark.
Estimations of the specific energy locally deposited by streamers gives a
minimal value of the order of 0.6-1 J Icm3•
High-speed photography is used to investigate the spatio-temporal
evolution of the discharge during sparking. Pioneering experiments were
done with high over-voltage of a pin-plane gap with the use of streak
cameras. It was revealed that spark formation takes two stages. The first is
a fast propagation (with velocity about 108 cm/s) of the so-called primary
streamer traveling from the pin towards the plane cathode. The second
stage occurs with some delay, heavily depending on the magnitude of the
over-voltage. At this stage, the so-called secondary streamer propagates
slowly with a velocity of about 106 cmls along the same trajectory. Upon
bridging of the gap by the secondary streamer, the discharge current
increases abruptly, and spark formation is completed. The experiments
with a steady corona under stepwise small change in applied voltage (low
over-voltage) showed that several generations of primary streamers take
place during the first stage (Akishev et at 2002b). The secondary streamer
develops very slowly (with velocity about 105_104 cm/s) supported by a
low magnitude of the discharge current (figures 2.5.12 and 2.5.l3).
So, in contrast to a primary streamer developing due to intensive direct
ionization in strong electric field around its head, the secondary streamer
propagates due to an increase of the ionization processes associated mainly
with a slow process of energy deposition into its body (gas heating, vibra-
tional excitation, etc). In this respect, propagation of the secondary streamer
is analogous to the non-homogeneous constriction of a pulsed glow
discharge at atmospheric pressure and to steady glow discharge in gas
--- Page 75 ---
60
History of Non-Equilibrium Air Discharges
Figure 2.5.13. Typical temporal evolution of positive pin-plane corona morphology
under induced sparking. Experimental conditions are the same as in figure 2.5.14. Time
exposition for frames 1, 2, and frames 3, 4 is 0.2 and 0.51ls respectively. Time interval
between neighboring frames is Ills.
flows at sub-atmospheric pressure (Velikhov et al 1982, Napartovich et al
1993, Akishev et aI1999a). Finally, the mechanisms of propagation of both
the secondary streamer (pre-spark filament) in the positive corona and
pre-spark filament in the negative corona are based on the development of
ionization instabilities in the discharge and therefore have much in common.
The completion of spark formation is the bridging of the gas gap and is
accompanied by a dramatic growth of the discharge current (current ampli-
tude of several amperes and slope of current rise oJ/at ~ 1 07 A/s). As a rule,
the external circuit of a typical corona discharge includes a power supply
delivering several units or tens of kV in output voltage and a ballast resistor
of several units or tens of MO. It is clear that such huge current amplitudes of
the spark can be sustained only by a displacement current in the external
circuit. However, there is one problem. Calculations of the charge transferred
by spark, require a capacitance much in excess of a static stray capacitance
(about units or tens of pF) of an external circuit. A possible reason for this
discrepancy is that the quasi-static approach commonly used for the analysis
of the corona circuit does not work in the case of a spark with rapidly
changing current generating a vorticity of the electric field.
2.5.4 AC corona discharges
Alternating voltages applied across a corona gap introduce new features in
the physics of this discharge. First, due to low mobility of the charge carriers
in air (f.-tr ~ 2 x 10-4 m2 V s for positive and negative ions) and low concen-
tration of ions in the bulk, the displacement current can be a marked or
even dominant component of the total corona current at relatively low
frequencies
of the
supply
voltage.
Indeed,
from
the
condition
co(aE/at) ~ ef.-tjEnj for E(t) = Eo coswt, one can obtain an estimate for
minimal circular wand cyclic f frequencies satisfying this inequality:
w ~ 3 x 1O-7nj and f ~ 5 x 1O-8nj (nj is the local density of ions in cm-3
--- Page 76 ---
Corona Discharges
61
in the bulk) of the gap, and which result in a displacement current being an
essential component of the total current. For centimeter gaps of pin-plane
coronas, the number density of the ion space charge may range over
ni ~ (2 x 109)-(2 x 1010) cm-3 depending on the magnitude of the corona
current. This means that the displacement current has to be taken into
account in ac coronas at frequencies of applied voltages f 2: 102_103 Hz.
Second, the drift of ions across the inter-electrode gap takes a finite time
of the order of Tj ~ d I f..liE and governs the establishment of a unipolar posi-
tive or negative dc corona (for a negative corona in a electropositive gas, it is
necessary to take the time of the electron drift). In the case Ti > T 12 (T = llf
is the period of the applied ac voltage), ions (say, positive ions) formed
during the preceding half-period are trapped in the bulk of the gap by an
electrical field of opposite direction in the succeeding half-period. The
same situation will occur with negative ions. This means that the drift
region of an ac corona is filled with ions of the opposite sign that tend to
diminish the resultant space charge in the drift region and that are subjected
to volume recombination. So, in some respect, an ac corona at frequencies
f 2: f..liE 12d is akin to the bipolar dc corona between two wires or sharpened
pins. A quantitative estimate for the critical frequency of the supply voltage is
f> (2 x 103)-(2 x 104)
-
d(cm)
Hz.
(2.5.4)
Finally, for high frequencies f 2: 105 Hz, the ac corona is called a torch
corona, which has nothing in common with dc coronas. Detailed informa-
tion about the properties of ac coronas can be found in Loeb (1965 ch 7D).
Interesting types of atmospheric pressure ac discharges for the genera-
tion of non-thermal plasma at/on dielectric surfaces were published recently
by Akishev et at (2002c) and by Radu et at (2003). These discharges are
sustained in the electrode configuration combining the electrode elements
of both corona (metallic pines)) and dielectric barrier discharge (metallic
plate covered with a thin dielectric layer) and called barrier corona or pin-
to-plane barrier discharge. In Radu et at (2003), the authors investigated
experimentally and theoretically the glow mode of a pin-to-plane barrier
discharge in He at atmospheric pressure. In Akishev et at (2002c), the glow
and streamer regimes of a barrier corona in ambient air, Ar, He, and N2
are investigated. Some results of the latter investigation are presented below.
Properties of ac barrier corona (A CBC) in air
The properties of ACBC in air, widely used as a processing gas for the
generation of non-thermal plasma at atmospheric pressure, are interesting
in themselves, but the main goal here is a comparison of discharges in air
and Ar, in order to show an important advantage of the latter. The presence
--- Page 77 ---
62
History of Non-Equilibrium Air Discharges
~B:~j.
.................
(a)
(c)
Figure 2.5.14. Side view of ac barrier corona in air with a sharpened electrode and barrier
of PE-film, at a frequency of 50 Hz and different inter-electrode gaps, h: (a) h = 1.5 cm,
U = 25kV; (b) h = 2.5cm, U = 32kV. (c) Typical voltage (above) and current
oscillograms of an ac barrier corona in air with a sharpened electrode and a barrier of
PE-film. Frequency: 50 Hz. The time scale is 5 ms/div, the voltage amplitude is 32 kV.
of electron attachment processes in air results in great differences between
discharge parameters and visual appearance observed for ACBC in air and
argon. An ac discharge in air requires a substantially higher voltage (more
than ten-fold) to sustain the discharge than that in Ar. Images of ACBC in
ambient air are presented in figure 2.S.14(a) and (b), where the ac barrier
corona appears almost homogeneous in the gas gap and above the surface
of a dielectric film. In fact, the ACBC in air has two different current
modes, depending on positive or negative polarity of the applied voltage.
These modes clearly reveal themselves in the waveform of the ACBC current.
Representative examples of current and voltage oscillograms are presented in
figure 2.S.14(c).
During the positive half-period, the ACBC is non-uniform because it
operates in the streamer regime. Streamers manifest themselves in the form
of sharp spikes in the current oscillogram. The number and amplitude of
spikes increases with rising voltage amplitude and inter-electrode gap
length. As a rule, each current spike correlates with a separate group (or
generation) of streamers. These streamers, which originate at the sharpened
metal electrode, the anode during the positive half-period, are distributed
randomly within a dome over the dielectric film. The diameter of this
dome-shaped volume increases with the length of inter-electrode gap
(figure 2.S.14(a), (b)). Each streamer strikes the surface and branches over
it in the form of short sliding surface streamers. The streamer length in the
bulk of the gap is much greater than those on the surface. Volume streamer
characteristics are identical to those in the streamer regime of steady-state dc
positive pin-plane corona in air with metallic electrodes, while the properties
of the short surface streamers are close to those observed in classical ac
barrier discharges (Eliasson et a11987, Eliasson and Kogelschatz 1991).
The negative half-period of the ACBC corresponds to a homogeneous
glow regime without any spikes in the current oscillogram. The discharge
--- Page 78 ---
Corona Discharges
63
properties of ACBC in the gap (the magnitudes of average electric field and
current density) during this half-period are practically the same as those in a
steady-state dc negative pin-plane corona in air with metallic electrodes. The
properties of the ACBC near the surface of the polymer film are similar to
those of the anode region of both the classical barrier discharge in the low-
current, uniform glow mode, and of the steady-state dc negative pin-plane
corona with a resistive anode plate.
There are two reasons why streamers are absent during the ACBC
negative half-period. First, pins do not provoke streamers in a negative
corona, and second, the uniform anode region formed near the dielectric
film is highly tolerant to streamer initiation as well.
In summary, low frequency ACBCs in air simultaneously exhibit
properties that are inherent in both steady-state dc negative and positive
pin-plane coronas with metallic electrodes, and in classical ac barrier
discharges under uniform glow and streamer current regimes.
In comparison with air, Ar is an easily ionized gas. Therefore sliding
surface streamers in Ar spread over a surface very readily. This is a distinctive
property of ACBC in Ar, which is an extremely important property with
respect to surface treatment. The cross-section of the surface occupied by
the ac barrier corona in He was markedly smaller than that in Ar at the
same frequency and voltage, but larger than the surface area in N2 •
2.5.5 Pulsed streamer corona discharges
Pulsed coronas are referred to as streamer discharges, which are used in
practice to generate non-thermal plasma at atmospheric pressure. As a
rule, plasma generators based on positive pulsed corona in air are used
because of their higher efficiency in the generation of streamers compared
with that of the negative pulsed corona. In the latter case less streamer
branching is observed. Therefore, the main attention here is paid to experi-
mental techniques and different properties of pulsed positive coronas.
Typical geometries of electrodes for the generation of positive pulsed
coronas are coaxial wire-cylinder, multi-pins-to-plane and multi-wires-to-
plane(s). For example, for a cylindrical geometry the outer electrode is a
metallic tube about 2m in length and 20-30cm in diameter. The inner
electrode is either a smooth wire or a rod with lots of small spikes designed
to increase a number of streamers.
It is common that high-voltage pulses of 50-150 kV in amplitude and
100-1000 Hz repetition rate are used to generate streamer coronas. This
amplitude ensures the fulfillment of Meek's criterion for streamer breakdown
of the gap. The leading edge of the voltage pulse has to be short enough
(::SO.IIlS) with a current rise dI/dt > 1010 A/s that guarantees a high ampli-
tude of the current density per 1 cm along the wire (up to 10 A/cm) and
correspondingly a high density of streamers (up to several streamers per
--- Page 79 ---
64
History of Non-Equilibrium Air Discharges
1 cm). The duration of the pulse trailing edge of the voltage pulse has to be
kept short «0.5 /ls is common) to avoid a spark formation in the gap. It
should be noted that the appearance of a spark in a pulsed corona device
operating at huge peak currents of several hundreds amperes creates much
more danger compared with a spark in a steady corona because of possible
damage to the electrode system due to melting.
For a coaxial configuration, the excitation of the gas gap by a pulsed
corona is non-uniform, because the density of streamers decreases with the
distance from wire approximately as l/r. Because of this, an effective
volume excited by streamers equals only 60-80% of the total volume of
tube. The average deposited power is low (~l W/cm\
Simultaneous electrical and optical measurements of a pulsed positive
corona in a cylindrical geometry were combined into one picture (see figure
2.5.15 taken from Blom 1997), which allows a direct comparison of the
electrical and optical parameters of pulsed streamer discharge, and an obser-
vation of streamer and spark formation. A number of ICCD images (shutter
time 5 ns) are recorded in the course of the development of the corona
discharge. During a single pulse, only one image was recorded. Repetitive
production of similar corona discharges, and variable delay between the
images and the initial rise of the voltage pulse, allow an investigation of the
temporal and spatial behavior of the pulsed corona. From each recorded
image, an appropriate slice was taken, and figure 2.5.15 was constructed.
In figure 2.5.15 one can see that primary streamers arrive at the surface
of cylindrical cathode after 120-140 /lS. After this time, slow development of
the secondary streamers begins at the wire (pre-spark embryos are apparent).
So, the bridging of the gap by primary streamers is not a danger for the safety
of the electrode system. To avoid in this experiment the undesirable develop-
ment of any secondary streamer into a spark, the duration of the applied
voltage pulse is restricted to 200/ls. Additional experimental information
about streamer formation/propagation in pulsed coronas can be obtained
from Marode (1975), Sigmond (1984), van Veldhuizen and Rutgers (2002),
and Ono and Oda (2003).
Results of numerical modeling of positive streamers in air can be found
in papers by Babaeva and Naidis (1996a,b, 2000), Kulikovsky (1997a,b,
1998), Morrow and Lowke (1997) and Naidis (1996). Numerical simulation
of streamer formation and propagation is a rather complicated task. In
general, the simulation of the negative streamer in N2 at atmospheric
pressure is a simpler task compared with that for positive streamers in air.
A two-dimensional simulation model is used by Vitello et at (1993) for the
description of the development of a negative streamer in short gap (0.5 cm)
in N2. This simplified model does not take into account the loss of charged
particles in the body of streamer due to electron-ion recombination. This
means that model does not describe a formation of a realistic state in
plasma behind the head of a streamer.
--- Page 80 ---
100
(a)
_ ....... ,
/
.I.~.,..:-.-:':-:,
Corona Discharges
65
,
\ ,
Time [ns]
Figure 2.5.15. Combined presentation of the electrical and the optical measurements.
(a) Electrical measurements, and image slices taken from a full ICCD image such as in
(b). The electrical measurements are the voltage pulse Vp (solid curve, left axis), the
external charge Qe (dotted curve, axis), and the displacement charge QgD (dashed curve,
axis).
Discharge parameters: positive voltage pulse
Vp = 93 kV,
air pressure
P = 360 torr, cylinder diameter 29cm.
The modeling shows that head of a short negative streamer in N2 tends
to the deformation in spatial structure such as branch off. The same results
were obtained recently by Arrayas et at (2002). Nevertheless, it is difficult
to say unambiguously whether such simplified models describe a real
branching of streamer because in fact the branching of negative streamers
is as a rule observed in long gaps (as a rule, d > 10 cm). In our opinion,
--- Page 81 ---
66
History of Non-Equilibrium Air Discharges
the deformation in spatial structure of the developing electron avalanches in
a short gap obtained by Vitello and Arrayas and their co-authors can be
interpreted as the initial stage of the near-cathode process, which can
result in the formation of several current cathode spots (consequently, of
several streamers originating from the cathode) but not as branching of a
single negative streamer in space.
References
Akishev Yu Sand Leys C 1999a J. Techn. Phys. (Polish Acad. Sci., Warsaw) 40127-143
Akishev Yu S, Deryugin A A, Kochetov I V, Napartovich A P and Trushkin N I 1993
J. Phys. D: Appl. Phys. 26 1630-1637
Akishev Yu S, Grushin ME, Deryugin A A, Napartovich A P and Trushkin N I 1999b
J. Phys. D: Appl. Phys. 32 2399-2409
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N I 2000 Plasma Phys. Rep. 26 157-163
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Trushkin N I 2001a J. Phys. D: Appl. Phys. 342875-2882
Akishev Yu S, Grushin M E, Karal'nik V Band Trushkin N I 200lb Plasma Phys. Rep. 27
520-531 (part I) and 532-541 (part II)
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Plasma Phys. Rep. 27 164-171
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55th Annual Gaseous Electronics Conference, 76
Akishev Yu S, Karal'nik V Band Trushkin N I 2002b Proc. SPIE 4460 26-37
Akishev Yu S, Grushin M E, Napartovich A P and Trushkin N I 2002c Plasmas and
Polymers 7 261-289
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Akishev Yu S, Grushin ME, Karal'nik V B, Kochetov I V, Monich A E, Napartovich A P
and Trushkin N I 2003b Plasma Phys. Rep. 29 176-186.
Allibone T E, Jones J E, Saunderson J C, Taplamacioglu M C and Waters R T 1993 Proc.
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Babaeva N Yu and Naidis G V 1996b Phys. Lett. A 215 187-190
Babaeva N Yu and Naidis G V 2000 in van Veldhuizen E M (ed) Electrical Dischargesfor
Environmental Purposes: Fundamentals and Applications (New York: Nova Science
Publishers) pp 21-48
Beattie 11975 PhD Thesis, University ofWaterioo, Canada
Blom PPM 1997 High-Power Pulsed Corona, PhD Thesis, Eindhoven University of
Technology
Boullound A, Charrier I and Le Ny R 1979 J. Physique 40(C7) 241
Brown S C 1959 Elementary Processes in Gas Discharge Plasma (Cambridge, MA: MIT
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--- Page 82 ---
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Cerlllik M and Hosokawa T 1991 Phys. Rev. A 431107-1109
Chang J-S, Lawless P A and Yamamoto T 1991 IEEE Trans. Plasma Sci. 19 1102-1166
Colli L, Facchii U, Gatti E and Persano A 1954 J. Phys. D: Appl. Phys. 25429-432
Eliasson B, Hirth M and Kogelschatz U 1987 J. Phys. D: Appl. Phys. 20 1421-1437
Eliasson Band Kogelschatz U 1991 IEEE Trans. Plasma Sci. 19309-323
von Engel A V 1955 Ionized Gases (Oxford: Clarendon Press)
von Engel A V and Steenbeck M 1934 Electrische Gasentladungen, Berlin
Fieux Rand Boutteau M 1970 Bull. Dir. Etude Rech. serie B, Reseaux Electriques Materiels
Electriques 2 55-88
Goldman A, Goldman M, Rautureau M and Tchoubar C 1965 J. de Physique 26 486-489
Goldman A, Goldman M, Jones J E and Yumoto M 1988 Proceedings of the 9th Inter-
national Conference on Gas Discharges and their Applications, Venice, Padova:
Trip pp 197-200
Goldman A, Goldman M and Jones J E 1992 Proceedings of the 10th International
Conference on Gas Discharges and their Applications, Swansea, pp 270-273
Goldman M and Goldman A 1978 in Hirsh M Nand Oskam H J (eds) Gaseous Electronics
vol. I (New York: Academic Press) pp 219-290
Goldman M and Sigmond R S 1982 IEEE Trans. Electrical Insulation EI-17 90-105
Hermstein W 1960 Archiv fur Electrotechnik 45 209-279
Jones J E, Davies M, Goldman A and Goldman M 1990 J. Phys. D: Appl. Phys. 23 542-
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Kaptsov N A 1947 Corona Discharge (Moscow: Gostekhizdat), 1953 Electronics (Moscow:
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Kulikovsky A A 1997a J. Phys. D: Appl. Phys. 30441-450 and 1515-1522
Kulikovsky A A 1997b IEEE Trans. Plasma Sci. 25439-445
Kulikovsky A A 1998 Phys. Rev. E 577066--7074
Lama W L and Gallo C F 1974 J. Appl. Phys. 45103-113
Lawless P A, McLean K J, Sparks L E and Ramsey G H 1986 J. Electrostatics 18 199-217
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Napartovich A P and Akishev Yu S 1993 Proceedings XXI ICPIG, vol. III, Ruhr-
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N I 1997 J. Phys. D: Appl. Phys. 302726--2736
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--- Page 83 ---
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History of Non-Equilibrium Air Discharges
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2.6 Fundamentals of Dielectric-Barrier Discharges
2.6.1
Early investigations
In 1857 Siemens in Germany proposed an electrical discharge for 'ozonizing'
air. The novel feature of this configuration was that no metallic electrodes
were in contact with the discharge plasma. Atmospheric-pressure air or
oxygen was passing in the axial direction through a narrow annular space
in a double-walled cylindrical glass vessel (figure 2.6.1). Cylindrical elec-
trodes inside the inner tube and wrapped around the outer tube were used
to apply an alternating radial electric field, high enough to cause electrical
breakdown of the gas inside the annular discharge gap.
Due to the action of the discharge, part of the oxygen in the gas flow was
converted to ozone. If air was used as a feed gas traces of nitrogen oxides
were also produced. The glass walls, acting as dielectric barriers, have a
Figure 2.6.1. Siemens' historical ozone discharge tube of 1857 (,natiirl. Grosse' means
natural size).
--- Page 84 ---
Fundamentals of Dielectric-Barrier Discharges
69
strong influence on the discharge properties, which is therefore often referred
to as the dielectric-barrier discharge (DBD) or simply barrier discharge (BD).
Also the term 'silent discharge', introduced by Andrews and Tait (1860), is
frequently used in different languages (stille Entladung, decharge silentieuse).
It was soon realized that the Siemens tube was an ideal plasma chemical
reactor in which many gases could be decomposed without using excessive
heat (Thenard 1872, Berthelot 1876, Hautefeuille and Chapp ius 1881,
1882, Warburg 1903, 1904). Much of the older work was reviewed by
Warburg (1909, 1927) in handbook articles on the silent discharge and in
the books by Glockler and Lind (1939) and by Rummel (1951). Investiga-
tions on the mechanism of 'electrodeless' discharges, and especially on the
influence of radiation on breakdown, were carried out by Harries and von
Engel (1951, 1954) and by El-Bakkal and Loeb (1962).
An important observation about breakdown of atmospheric-pressure
air in a narrow gap between two glass plates was made by the electrical
engineer Buss (1932). He observed that breakdown occurred in many
short-lived luminous current filaments, rather than homogeneously in the
volume. He also obtained photographic Lichtenberg figures showing the
footprints of individual current filaments and recorded oscilloscope traces
of the applied high voltage pulse. Buss came up with fairly accurate
information about the number of filaments per unit area, the typical duration
of a filament and the transported charge in a filament. Further contributions
to the nature of these current filaments were made by Klemenc et al (1937),
Suzuki and Naito (1952), Gobrecht et al (1964) and Bagirov et at (1972).
Today these current filaments are often referred to as microdischarges.
They play an important role as partial discharges in voids of solid insulation
under ac stress and in many DBD applications. The accomplishment of
recent years was that microdischarge properties were tailored to suit desired
applications and that the development of power electronics resulted in
efficient, affordable and reliable power supplies for a wide frequency and
voltage range. More recent investigations also showed that homogeneous
or diffuse DBDs can be obtained under certain well-defined operating
conditions (see chapter 6). Also regularly patterned DBDs can be obtained
in different gases. The phenomenology and discharge physics of these
different types of DBDs were reviewed by Kogelschatz (2002a).
Siemens referred to the process as an electrolysis of the gas phase. Today
we call it a non-equilibrium discharge in which chemical changes are brought
about by reactions of electrons, ions, and free radicals generated in the
discharge. The main advantage of the dielectric barrier discharge is that
controlled non-equilibrium plasmas can be generated in a simple and efficient
way at atmospheric pressure. In addition to its original use for the generation
of ozone (see section 9.3) many additional applications have evolved: pollu-
tion control, surface treatment, generation of ultraviolet radiation in excimer
lamps and infrared radiation in CO2 lasers, mercury-free fluorescent lamps
--- Page 85 ---
70
History of Non-Equilibrium Air Discharges
High
Voltage
AC
Geoeratof
a
c
High Voltage
Electrode
Barner
Discharge
d
Dielectric
b
e
Figure 2.6.2. Different dielectric-barrier discharge configurations.
f
High Voltage
Electrode
and flat plasma display panels (Kogel schatz et al 1997, 1999, Kogelschatz
2002b, 2003, Wagner et aI2003).
2.6.2 Electrode configurations and discharge properties
In addition to the original Siemens ozone discharge tube different electrode
configurations have been proposed, all of which have in common that at
least one dielectric barrier (insulator) is used to limit the discharge current
between the metal electrode(s). Figure 2.6.2 shows a number of different
dielectric-barrier discharge configurations covering volume discharges (a,
b, c, d) as well as surface discharges (e, f). The presence of the dielectric
barrier precludes dc operation because the insulating material cannot pass
a dc current. AC or pulsed operation is possible, because any voltage vari-
ation dU /dt will result in a displacement current in the dielectric barrier(s).
DBDs are operated with electrode separations between 0.1 mm and
several cm, frequency ranges from line frequency to microwave frequencies,
and at voltages ranging from about 100 V to several kV. DBDs in different
gases and gas mixtures have been studied at various pressure levels. In the
context of this book we will concentrate on DBDs operating close to atmos-
pheric pressure, mainly in air.
2.6.3 Overall discharge parameters
In the following sections some properties are described that are common to
all DBDs. Although the current flow and power dissipation in most DBDs
at about atmospheric pressure occurs in a large number of short-lived
--- Page 86 ---
Fundamentals of Dielectric-Barrier Discharges
71
2Umin
------y-
U
@
f-------~-----
20 r----'
12Umin!
l_t __ .
Q
(j)
Figure 2.6.3. Applied sinusoidal voltage, schematic representation of microdischarge
activity, and resulting voltage-charge Lissajous figure of a dielectric-barrier discharge.
microdischarges the overall discharge behavior, for many purposes, can be
described by average quantities. If an ac voltage is applied to a DBD config-
uration we always have periods of discharge activity (when the voltage inside
the gas gap is high enough to initiate breakdown and maintain a discharge)
and pauses in between (when the gap voltage is below that value). According
to the schematic diagram of figure 2.6.3 we observe alternating phases of
discharge activity and discharge pauses. Only at high operating frequencies
there may not be enough time for the charge carriers to recombine or be
swept out of the gap between consecutive half-waves. In this case some
electrical conductivity remains throughout the full voltage period.
The voltage-charge Lissajous figure given in the lower part of figure
2.6.3 is frequently used in ozone research and in investigations on partial
discharges. In general it is a useful tool to study DBD properties.
For most DBDs the voltage charge diagram resembles a parallelogram
(Manley 1943, Kogelschatz 1988, Falkenstein and Coogan 1997). This is true
for large DBD installations used for ozone generation comprising hundreds
of square meters of electrode area. It is also true for the tiny cells used in
plasma displays (Kogelschatz 2003). It can easily be obtained by using a
measuring condenser in the circuit to integrate the current and a high voltage
--- Page 87 ---
72
History of Non-Equilibrium Air Discharges
probe to measure the voltage. Both signals are then displayed on a scope in
x-y mode. As long as the peak to peak voltage is less than 2Umin we just see a
straight line and have no discharge in the gap. The slope corresponds to the
total capacitance of the electrode configuration: Ctotal = 1 I tan ct. After
ignition we observe discharge pauses in the time intervals 1 ----> 2 and
3 ----> 4. During the time intervals 2 ----> 3 and 4 ----> 1 we have discharge activity
in the gap and the slope corresponds to the capacity of the dielectric barriers:
Co = II tawy. This electrical behavior can be represented by a simple
equivalent circuit in which the discharge is represented by two antiparallel
Zener diodes which limit the discharge voltage at ±UOis . The discharge
voltage UOis represents the average gap voltage during discharge activity.
It is a fictitious though useful quantity which can be obtained from the
voltage charge diagram:
UOis = Umin/(l + (3)
(2.6.1)
where (3 = Col Co is the ratio of the capacitances of the gap Co and that of
the dielectric(s) Co. In the discharge pauses Co and Co act as a capacitive
divider. An exact definition of the discharge voltage Uo can be derived
from the power P:
P = ~ JT U(t)I(t) dt = Al
UOis J I(t) dt
TouT
AT
(2.6.2)
where the first integral is extended over one period T of the voltage cycle and
the second integral is extended only over the active phases during which the
discharge is ignited.
All capacitances are linked by the relation
1
1
1
--=-+-.
Ctotal
Co
Co
(2.6.3)
The well defined parallelogram in figure 2.6.4 with sharp corners is an
indication that all microdischarges have similar properties. As long as the
voltage in the gap is below UOis no micro discharges occur. Once we reach
that value microdischarge activity starts and continues until the peak value
-
Charge
Figure 2.6.4. Equivalent circuit of a dielectric-barrier discharge and recorded voltage-
charge Lissajous figure of an ozone discharge tube.
--- Page 88 ---
Fundamentals of Dielectric-Barrier Discharges
73
o of the external applied voltage is reached. At this point dU /dt is zero,
which implies that the displacement current through the dielectric(s) stops.
After voltage reversal, a certain swing of the external voltage is required
before the value of UDis is reached in the gap again.
As was first derived by Manley in 1943, the enclosed area of the voltage
charge Lissajous figure corresponds to the power dissipated during one
discharge cycle. The average discharge power is obtained by multiplying
with the frequency f:
P = 4jCD UDis[O - (1 + ,8)UDiSl{ for 0 ~ (1 + ,8)UDis ,
(2.6.4)
otherWise P = o.
This is the well-known power formula for ozonizers which has been used for
the technical design of many DBD applications. Using the minimum external
voltage Umin required to ignite the discharge, rather than the fictitious
discharge voltage UDis , the power formula can be rewritten as
P - 4'C (1
,8)-1 U . [0 - U . 1 {for 0 ~ Umin ,
-
'./' D +
mill
mill
.
otherWise P = o.
(2.6.5)
The somewhat surprising feature of this relation is that only the peak voltage
o enters and not the form of the applied voltage. For a given peak voltage
the power is proportional to the frequency. For a given discharge configura-
tion (Umin fixed) and given frequency the discharge ignites at U = Umin , and
the power rises proportionally to the peak voltage with the slope
4fCD Umin / (1 + ,8). A special and simple operating case is arrived at when
the voltage or current is adjusted until ignition occurs at zero external
voltage, which is always possible. In this case two corners of the voltage
charge diagram fall on the abscissa and 0 = 2Umin . For this special case
fairly simple relations can be derived. For a sinusoidal feeding voltage,
P = CD 02 = 2CD fU2
1+,8
1+,8
eff
(2.6.6)
A2 CD
. /
A
r,:,
Jeff =1ffU 1+,8yl+2,8(1+,8),
Ueff =U/v2
(2.6.7)
_..fi
1
Power factor:
cos!.p-- --;- JI + 2,8(1 + ,8)
(2.6.8)
U
_
0
_
Ueff
Dis - 2(1 +,8) -
(1 + ,8)J2'
(2.6.9)
Also for an impressed square-wave current simple relations can be derived
A
1 + 2,8
Jeff = 2UCD 1 +,8
(2.6.10)
--- Page 89 ---
74
History of Non-Equilibrium Air Discharges
(;
Ueff = v'3
Power factor: _
v'3
COs'P = 2(1 + 2(3) .
(2.6.11 )
(2.6.12)
The time average power factor cos 'P is an important parameter the knowledge
of which is required for matching the power supply to the DBD discharge.
Contrary to the power itself the power factor does depend on the voltage
form. Values for the power factors in the cases of sinusoidal feeding voltage
and impressed square-wave currents are given by Kogelschatz (1988). As a
consequence of the presence of the dielectric barrier(s), DBD configurations
always present a capacitive load. The load acts as a pure capacitance when
there is no discharge and still has a strong capacitive component at time
intervals when the discharge is ignited. These phases alternate twice during
each cycle of the driving voltage. While the discharge is ignited power is
dissipated in the gas gap and the current is limited by the dielectric(s). The
power factor is defined as an average quantity for a whole operating cycle
of duration T:
P
1
JT
Power factor:
cos'P = UT = U 1 T
U(t)I(t) dt.
eff eff
eff eff
0
(2.6.13)
In general it can be stated that square-wave current feeding results in higher
power factors. For large DBD installations power factor compensation is
mandatory. This can be achieved either by using matching boxes or by
using an LC resonance where the apparent capacity of the DBD is compen-
sated by an inductance L in the supply lines.
In this section the overall discharge behavior of DBDs was discussed
and some important 'engineering formulae' describing the ignition, temporal
behavior and power dissipation of the discharge were compiled. The physical
processes inside the discharge gap ofDBDs will be discussed in more detail in
chapter 6 in sections 6.2 to 6.4.
References
Andrews T and Tait P G 1860 Phil. Trans. Roy. Soc. London 150 113-131
Bagirov M A, Nuraliev N E and Kurbanov M A 1972 Sov. Phys.-Tech. Phys. 17495--498
Berthelot M 1876 Compt. Rend. 82 1360-1366
Buss K 1932 Arch. Elektrotech. 26 261-265
EI-Bakkal J M and Loeb L B 1962 J. Appl. Phys. 33 1567-1577
Falkenstein Z and Coogan J J 1997 J. Phys. D: Appl. Phys. 30 817-825
Glockler G and Lind S C 1939 The Electrochemistry a/Gases and other Dielectrics (New
York: Wiley)
Gobrecht H, Meinhardt 0 and Hein F 1964 Ber. Bunsenges. Phys. Chern. 68 55-63
--- Page 90 ---
References
75
Harries W L and von Engel A 1951 Proc. Phys. Soc. (London) B 64 916-929
Harries W L and von Engel A 1954 Proc. Royal Soc. (London) A 222490-508
Hautefeuille P and Chappius J 1881 Compt. Rend. 92 80-82
Hautefeuille P and Chappius J 1882 Compt. Rend. 94 1111-1114
Klemenc A, Hinterberger H and Hofer H 1937 Z. Elektrochem. 43 708-712
Kogelschatz U 1988 'Advanced ozone generation' in Stucki S (ed) Process Technologiesfor
Water Treatment (New York: Plenum Press) pp 87-120
Kogelschatz U 2002a IEEE Trans. Plasma Sci. 30 1400-1408
Kogelschatz U 2002b Plasma Sources Sci. Technol. U(3A) Al-A6
Kogelschatz U 2003 Plasma Chem. Plasma Process. 231-46
Kogelschatz U, Eliasson Band Egli W 1997 J. Phys. IV (France) 7 C4-47 to C4-66
Kogelschatz U, Eliasson Band Egli W 1999 Pure Appl. Chem. 71 1819-1828
Manley T C 1943 Trans. Electrochem. Soc. 84 83-96
Rummel T 1951 Hochspannungs-Entladungschemie und ihre industrielle Anwendung (Munich:
Verlag von R. Oldenbourg und Hanns Reich Verlag)
Siemens W 1857 Poggendorffs Ann. Phys. Chem. 10266-122
Suzuki M and Naito Y 1952 Proc. Jpn. A cad. 2469-476
Thenard A 1872 Compt. Rend. 74 1280
Wagner H-E, Brandenburg R, Kozlov K V, Sonnenfeld A, Michel P and Behnke J F 2003
Vacuum 71417-436
Warburg E 1903 Sitzungsber. der konigl. Preuss. Akad. der Wissensch. (Math-Phys) 1011-
1015
Warburg E 1904 Ann. der Phys. (4) 13464-476
Warburg E 1909 'Uber chemische Reaktionen, welche durch die stille Entladung in gasfOr-
migen Korpern heibeigefiihrt werden' in Stark J (ed) Jahrbuch der Radioaktivitiit
und Elektronik vol. 6 (Leipzig: Teubner) pp 181-229
Warburg E 1927 'Uber die stille Entladung in Gasen' in Geiger H and Scheel K (eds) Hand-
buch der Physik vol. 14 (Berlin: Springer) pp 149-170
--- Page 91 ---
Chapter 3
Kinetic Description of Plasmas
Ralf Peter Brinkman
3.1
Particles and Distributions
Partially ionized plasmas of gas mixtures like air are complex systems. One
may think of a plasma as a large collection of different particles that interact
among each other and with external fields: ground-state and excited atoms
and molecules, positive and negative ions, electrons, possibly dust. Also
radiation-in the ray limit-has particle properties. C'Ne will, however,
refer by 'particle' only to matter. Photons are sufficiently different to justify
separate treatment.)
• Heavy particles or baryons are species which have at least one nucleon
(proton or neutron). They are either atomic (one nucleus) or molecular
(several nuclei). Air, for example, consists of78% N2 (molecular nitrogen),
21 % O2 (molecular oxygen), 0.9% Ar (argon), and traces of CO2 (carbon
dioxide), H20 (water), 0 3 (ozone), He (helium), Kr (krypton), Xe (xenon)
etc. Neutrals carry no charge, q = 0, positive ions (cations) with charge
q = Ze can be singly (Z = 1) or multiply (Z> 1) ionized. In electro-
negative gases (for example oxygen and nitrogen), negative ions (anions)
can also exist, mostly singly charged (q = -e, Z = -1). Species are denoted
by the 'sum formula' (e.g. H30+) which suffices for most purposes. (Isomer
effects-sensitivities to structural differences of molecules having the same
sum formula-are, for example, analyzed by Deutsch et at [3].) Later in this
text it will be useful to view the sum formula as an integer vector
(R) = (Rz , RH , RHe , ... , Ru) of charge number and elementary content.
H30+,
e.g.,
denotes
(H30 +) = (1,3,0,0,0,0,0,0,1,0,0,0, ... ,0).
Neglecting electron contributions, the mass of a heavy particle is
mR = L~=H Rnmn ::;::j Aa, where A is the total number of nucleons of the
nuclei. Heavy particles are non-relativistic, i.e. at a given velocity v their
momentum is p = mvand their kinetic energy E = ! mv2• Except for fully
76
--- Page 92 ---
Particles and Distributions
77
------
]~~-
£1
£2
gl
3
E2
t_-
g2
2
------
g3
Figure 3.1. Schematic depiction of an energy level diagram of a heavy particle (taken from
[7]). Levels of increasing energy are labeled by increasing integers. The lowest level is called
the ground state and labeled 1. The energy of the first excited level is C2, the energy of the
second level C3 etc. The level of mimi mum energy above the ground level corresponding to
a free electron is called the series limit and defines the ionization energy Ci' Since all energies
are possible for free particles, depending on their relative kinetic energies, the energy region
above C; is called the continuum. The number of different quantum states corresponding to
the same energy level C is called the degeneracy or statistical weight of that level and
denoted by g.
ionized cations, heavy particles have also internal structure and may there-
fore exist in different energy states Ci' (For a schematic energy level
diagram, see figure 3.1.) Atoms or atomic ions have only electronic excita-
tions, with a typical scale of some eV. Molecules or molecular ions have
also vibrational and rotational excitations, with energies of a few meV
(rotation) or a few tens of me V (vibration). The energies of different species
can be compared by accounting the standard enthalpy of formation D..H'f
(e.g. [5]) .
• A particular type of heavy particles is dust. Dust grains can have diameters
up to the nanometer and micrometer scale and masses up to several
1012 amu. In a plasma environment, they are negatively charged and may
represent a sizable fraction of the total charge density. The presence of
dust considerably alters the dynamics of a plasma and gives rise to a
whole set of new phenomena. Accordingly, the theory of such complex
plasmas is very involved. In air plasmas, dust is mostly absent due to the
oxidative nature of the medium.
• Electrons are particles with a mass me that is much smaller than the mass of
the baryons. In this context, they are also non-relativistic. At a speed v their
kinetic energy is E = ! me v2, and the momentum is jJ = me V. Electrons have
--- Page 93 ---
78
Kinetic Description of Plasmas
no internal structure, except for their spin which can be ignored in most
plasma considerations. In the notation above, (e) = (-1,0, ... ,0) .
• Photons are massless relativistic 'particles' which propagate with the
speed of light c. For a photon of frequency 1/ and propagation direction
e, the energy is E = hl/ and the momentum p= hl/elc, where h is
Planck's constant. In plasma kinetics, the momentum carried by a
photon is normally negligible. Photons also have no internal structure,
except for their polarization which is typically not important in plasma
dynamics (but may, of course, carry important information for diagnostic
purposes).
Depending on the pressure, a plasma may contain from 1010 to 1022 particles
per cubic centimeter. (At a temperature of T = 300 K and a pressure of
P = 105 Pa, it is n = plkBT ~ 2 x 1019 cm-3.) The task of plasma physics is
to analyze and describe the dynamics of these particles under the influence
of their mutual interaction and possibly external fields.
Quantum mechanics aside (for the moment), this could in principle be
done by solving Newton's equation or their relativistic equivalents for all
particles, plus Maxwell's equations for the fields. A short calculation,
however, drastically shows that this 'in principle' actually means: 'not
really'. The combined information storage available on all computers on
earth would allow for a complete specification of roughly a picogram of
air plasma in terms of the position f, velocity if and inner state E of all
particles. (This does not even consider the problem of recording a temporal
evolution, nor does it account for the computer power required to solve the
equations of motion!)
There is of course a solution to this problem, well known under the
heading 'statistical mechanics': instead of attempting a complete description,
one considers the value of an incomplete description. Various decisions on
which information is essential and which can be disposed of are possible.
Kinetic theory denotes an approach which is particularly suited to describe
collections of weakly interacting particles, such as the particles in a gas or
plasma, or the 'quasi-particles' in a solid. The first example was developed
1877 by Boltzmann for a neutral gas; it is still the prototype (to the extent
that 'Boltzmann equation' is a synonym for kinetic theory in general) [10].
Kinetic theory is based on the assumption that the essential information
on the system is given by the one-particle distributionf, a real-valued, time-
dependent function of the phase space fL, which is the set fL = V X 1R3 of all
spatial and velocity positions (f, if) that a particle can assume. We assume
that there are N different species present, counting as such also different
internal states. They are distinguished by subscript indices, where we use
the convention that indices sand r run over all species, a and f3 are charged
species, a and b neutrals, e is the electron, i denotes ions. The distribution
function states that, at a given time t, the expected number 6.Ns of particles
--- Page 94 ---
Particles and Distributions
79
v
to_ 1<:·.: }N ~ f to.to.
~x
x
(a) Particle distribution function
(b) Radiation intensity
Figure 3.2. Visualization of the particle distribution function (left) and the radiation
intensity (right). The distribution function gives the number of particles !::.N in the
phase space volume !::.3r!::.3v as !::.N = f(r, 11, t)!::.3r!::.3v, while the radiation intensity
represents the energy flux !::.P per area !::.1 and frequency interval !::.V from the solid
angle !::.!1 as !::.P = IvU', e, v, t)!::.v !::.1. !::.!1.
of species s to be found in the volume ~J,~3v around the point (1, iJ) is given
as
(3.1 )
Alternatively, one may define the distribution function! as a suitably aver-
aged ('coarse grained') form of the exact microscopic distribution of an
ensemble of particles,
(3.2)
Radiation can be described in similar terms. In the geometric limit, it is seen
as a stream of massless photons propagating with the speed of light at a
position 1 and time t in a given direction e. The radiation intensity I describes
the energy flux ~P per frequency interval ~v flowing out of a solid angle ~n
around e onto a surface element ~1 as
(3.3)
At first glance, the definitions (3.1) for the particles and (3.3) for the photons
seem rather different. In actuality, the two concepts are quite similar, if the
--- Page 95 ---
80
Kinetic Description oj Plasmas
following is taken into account:
• The distribution functionJ makes reference to the particle number, while
the radiation intensity Iv does not count photons but refers to their energy.
• The distribution function is defined to account for the particle density per
volume 1:13r, while the radiation intensity represents the energy influx per
area 1:11.
• The distribution function assumes non-relativistic behavior (particles can
have any speed), while the radiation intensity sees the photons as 'ultra-
relativistic' (their speed is c).
To compare the two concepts, a quantity is needed that is defined for both
particles and photons. This can be found in the momentum p, or-more
convenient here-in the wave vector k = p/n. The corresponding phase
space distribution, a dimensionless quantity, shall be termed <I> (1, k). It
provides the number of particles in a volume 1:13 r 1:13 k as
(3.4)
and the flux of particles 1:1\11 through a surface element 1:11 as
1:1\11 = <I> iJ· 1:111:13k,
[1:1\11] = S-I.
(3.5)
The corresponding energy flux (with a quantum E per particle) is
I:1P = E<I>iJ.1:111:13k,
[I:1P]=W.
(3.6)
For a photon of frequency v, the energy is E = 27rnv, the speed is iJ = ce, and
the wave number is k = 27rv/c. Using also the representation of the
momentum element,
1:13 k = k21:1kl:10 = 87r3 c -3v2 I:1vI:10
one obtains for the energy flux
J\p
167r4nv3 m. -
J\
-
J\
J\ n
U
=
2
"¥ e· uA UVUH.
c
(3.7)
(3.8)
The comparison with the definition above shows that Iv can indeed, up to a
factor, be identified with a distribution function. In particular, one has
(_ _
)
167r4nv3
(_ 27rV _ )
Iv r,e,v,t =
c2
<I> r'-c-e,t .
(3.9)
Finally in this context, also the often used energy distribution function
(EDF) will be discussed. When the distribution function J(iJ) is isotropic
(or the anisotropy cannot be resolved), it is convenient to introduce a distri-
bution function F which depends only on the particle energy E, normalized
so that the number of particles between E and E + I:1E is
I:1N = J( v) 47rv2 I:1vl:13r = F(E)I:1EI:13r.
(3.10)
--- Page 96 ---
Particles and Distributions
81
Using the relation E = 4mv2, one arrives at
F(E) = 47rJgJ ( 1#;) .
(3.11)
The distribution function allows calculation of a variety of other quantities,
particularly the so-called moments, a systematic sequence of symmetric
tensors depending on 1 and t,
M; /11/12 ... /1" (1, t) = J
V/11 V/12 ... V/1" Is (1, V, t) d3v.
(3.12)
Also of importance are the contracted moments, i.e. integrals of the moment
type with two indices (or more generally,p index pairs) set equal and summed
over. They have the structure
M;/11/12···/1"_2P(1,t) = J
V/1I V/12·· .v/1"_2pv2PIs(1,v,t)d3v.
(3.13)
Connected to each moment is a moment of the next order, the corresponding
flux
r~/11/12···/1" (1, t) = J
V/11 V/12 ... v/1" vis (1, V, t) d3v
with a similar definition for the contracted moments,
r- n
(-
) - J
2Pil"(- - )d3
s /11/12···/1,,-2p r, t -
V/11 V/12 ... v/1n_2p V VJ s r, v, t
v.
(3.14)
(3.15)
By summation over the species index s the moments are also defined for the
plasma as a whole. The relative weights depend on the physical meaning of
the quantities. They are unity, ms or qs' for quantities related to the particle
number, mass, and charge, respectively.
Several of these moments have particular physical importance. The
zeroth, the first and the contraction of the second moment directly relate
to the conservation laws of mass, momentum, and energy. For each species,
the zeroth moment defines the particle density
(3.16)
A summation over the species yields the total densities of particle number,
mass, and charge. (In accordance with the standard notation, the symbol p
is used for both the mass density and the charge density. Whenever necessary,
a superscript differentiates the two.)
n(1,t) = LJ Is d3v= Lns
s
s
(3.17)
pM(1, t) = L J
msIsd3v = Lmsns
s
s
(3.18)
--- Page 97 ---
82
Kinetic Description of Plasmas
pC (1, t) = L J qsIs d3v = L qsns·
s
s
(3.19)
The first moment defines the flux of particles
rs= vIsdv.
~ J
~
3
(3.20)
An equivalent, but more frequently employed, definition is that of the
average particle velocity U" also referred to as the bulk speed
us(1, t) = J vis d3vlns = [-sins.
(3.21)
Summation over the species index s defines the fluxes of total particle
number, charge, and mass. The latter two have an direct interpretation as
current and momentum density
[-(1, t) = L J vj, d3v = L nsus
s
s
(3.22)
](1, t) = L J qsvIs d3v = L qsnsus
s
s
(3.23)
p(1, t) = L J msvIs d3v = L msnsus·
s
s
(3.24)
The average velocity of the plasma is defined with reference to the center-of-
mass motion,
u(1, t) = L J
msvIs d3vl pM = pi pM =J II pC.
s
(3.25)
As a consequence, the momentum density can be written as
~
M~
P = P u.
(3.26)
The difference of the species velocity Us and the center-of-mass motion is the
diffusion velocity
Os(1, t) = J (v - u)Is d3vlns = Us - u.
(3.27)
The higher moments are only important in mass-related form. The uncon-
tracted moment of second order is the (full) pressure tensor and represents
the flux of the momentum density
lIs = J
msvvj, d3v
(3.28)
II = L J msvvIsd3v = LIIs.
s
s
(3.29)
--- Page 98 ---
Particles and Distributions
83
The pressure tensor is also definable with respect to the center-of-mass
velocity, then denoted P. Its isotropic part (a third of the trace) defines the
pressure scalar p
Ps(r, t) = J
ms(v - us)(v - us)fs d3v
(3.30)
P(r, t) = L J
ms(v - u)(v - u)fs d3v = L(Ps + msnsUsUs)
s
s
(3.31 )
ps(r, t) = ~ J
ms(v - us)2fs d3v
(3.32)
p(r, t) = ~
~ J
ms(v - u)2fs d3v = ~
(Ps + ~msnsu;).
(3.33)
The irreducible remainder is known as the stress tensor (I denotes the unit
tensor)
1t = P - pl.
Using these definitions, the following identities arise:
IIs = Psusus + 1ts + PsI
II = puu + 1t + pl.
(3.34)
(3.35)
(3.36)
(3.37)
The contraction of the second moment gives the kinetic energy density
(counting only translation, the rotational and vibrational degrees offreedom
are part of the internal energies)
es(r, t) = J
~msv2fs d3v
(3.38)
(3.39)
The contracted second moment can also be used to define the so-called
kinetic temperature Ts. In equilibrium, it coincides with the thermodynamic
temperature (when measured in energy units). In situations far from equi-
librium the notion still provides a convenient shorthand for 'two thirds of
the average thermal energy'. (The kinetic temperature T of the whole
plasma becomes a questionable concept when different species differ strongly
in their thermal energy.)
Ts(r,t) =-3
1 Jms(v-us?fsd3v=PS
ns
ns
(3.40)
T(r, t) = 31n L J
mv(v - u)2fs d3v.
s
(3.41)
--- Page 99 ---
84
Kinetic Description of Plasmas
Each species of the plasma and the plasma as a whole obey the ideal gas
equation
Ps = nsT.,
p=nT
and the full kinetic energies can be expressed as
(-)
1
-2
3
T
es r, t = 'imsnsus + 'ins s
(3.42)
(3.43)
(3.44)
(3.45)
The flux of the energy is given by the contracted moment of the third order
r:(i", t) = J
~msv2v/sd3v
(3.46)
re (r, t) = ~ J
~msv2v/s d 3v.
(3.47)
The corresponding quantity in the co-moving system known as the heat flux
ifs(r, t) = J
~ms(v - ~,)2(v - us)!, d3v
if(r, t) = L J
~m,(v - u)2(v - u)/s d3v = L q,.
s
s
This gives rise for the following identities for the energy flux
r: = (! Ps~; + ~ ns Ts )us + ifs + Psus + 1ts 'us
re = (!pu2 + ~nT)u + if + pu + 1t·u = L r;.
(3.48)
(3.49)
(3.50)
(3.51 )
Also the 'distribution of the photons', the radiation density Iv, allows
suitable moments to be defined. In the field of low temperature plasma
physics, however, they are less frequently employed than their particle
counterparts: non-equilibrium radiation has such a pronounced structure
that spectral and other averages are not very meaningful. Also, in non-
relativistic plasmas, the photon momentum is negligible; radiation pressure
and related quantities are thus less important.
The radiation intensity Iv gives the radiation from a solid angle element
~n around a direction e, the corresponding spectral energy flux density is the
integral of Iv over all directions
(3.52)
The energy density of a radiation field is more difficult to calculate. Either by
geometric considerations (see figure 3.3), or by employing the representation
--- Page 100 ---
Particles and Distributions
85
BV
Figure 3.3. Geometric motivation of definition (53). The spectral energy flux t::,.Pv from the
solid angle t::,.o around the direction e onto the surface element t::,.l equals
t::,.Pv = IvCe, 1/) e· t::,.l t::,.O. The photons spend a travel time sic in the volume V, which
therefore has a total spectral energy content t::,.Uv = SS sIv(e, 1/) e· dl dO/c. By vector
analytic means, this expression can be transformed into the equivalent representation
t::,.Uv = V S Iv(e, 1/) dO/c.
(3.9) and equating the energy content in a volume element l:l.U = uvl:l.vl:l.3r
with the expression 27fnv Sf! F dO k2l:l.kl:l.3r one can motivate the definition
of the spectral energy density,
uAr, v, t) = ~ J
Iv dO.
(3.53)
All spectrally resolved quantities also have integral counterparts. The
integral radiation intensity I, radiation energy flux F, and radiation energy
density u, the total photon density n and the total photon flux r are given as
I(r,e, t) = J
Iv dv
F(r, t) = J~ Fv dv = In eI dO
u(r, t) = J~ UV dv = ~ J
I dO
(3.54)
(3.55)
(3.56)
(3.57)
(3.58)
In general, distribution functions are very complex and cannot be given in
simple analytical form. The following examples, however, represent certain
model situations and are frequently useful. Their parameters correspond to
the moments defined above; spatial homogeneity is assumed.
The first example is that of a mono-energetic beam, i.e. a collection of
particles which have the same velocity and direction ii. Often this distribution
--- Page 101 ---
86
Kinetic Description of Plasmas
is chosen to represent particles which enter the plasma from outside under
carefully controlled experimental conditions,
fB(iJ) = n 8(3) (iJ - i1).
(3.59)
The Maxwellian, on the other hand, arises when a plasma is allowed to relax
into equilibrium. It can also be employed when no other information is
available on the status of a plasma component other than the value of the
first three moments; the justification for this is either information theory
('maximum entropy estimate') or pragmatism ('easy to handle'),
~
n
(
m(iJ - 11)2)
fM(V)=(27rT/m)3/2 exp -
2T
.
(3.60)
Finally, Druyvesteyn's distribution shall be mentioned which is met, for
example, in certain simplified models of the electron component of a noble
gas plasma. It has the form
(3.61 )
with the two parameters C and 13 related to the density and the kinetic
temperature as
C r
13-3/4
n =
7r 3/4
T = (rS/ 4/r3/ 4)mj3-1/2.
(3.62)
(3.63)
Compared to a same temperature Maxwellian, it has a much steeper decrease
at high energies. Very often, Maxwellian and Druyvesteyn calculations are
compared to illustrate the sensitivity of certain results on the form of the
distribution function. (See figure 3.4).
Also the spectral radiation intensities Iv are generally complicated func-
tions which do not follow a simple analytical form. But again, some explicit
examples may be useful. Like the distribution functions f, they are given
under the assumption of spatial homogeneity.
The first example is that of a monoenergetic radiation beam of photons
with a frequency VB and a radiation intensity IB, propagating into the direc-
tion eB. Its spectral radiation intensity is (with 8(2) denoting the delta function
with respect to the solid angle)
The spectral radiation flux and radiation energy density are
Fv(v) = IB 8(v - VB) eB
I
uv(v) = - 8(v - VB).
c
(3.64)
(3.65)
(3.66)
--- Page 102 ---
Particles and Distributions
87
( a) Maxwellian distribution
T
-4
(b) Druyvesteyn distribution
Figure 3.4. Normalized Maxwellian (top) and Druyvesteyn (bottom) distribution functions
at the same density n, for different kinetic temperatures T. The Druyvesteyn distribution
is flatter for small v, but has a much steeper decrease at high energies.
The second example is that of the well-known black body radiation, given by
Planck's formula
(3.67)
As this radiation is isotropic, the radiation flux vanishes. The spectral energy
density is
(3.68)
--- Page 103 ---
88
Kinetic Description of Plasmas
2
4
6
8
10
12
14
Figure 3.5. Radiation intensity fAv) and energy density uv(v) of the Planck black body
function for different normalized temperatures T. (In arbitrary units, they differ only by
a factor 4/c.)
The total radiation energy density of the black body radiation follows the
well-known Stefan-Boltzmann T4 law. (Note here that the temperature is
given in energy units.)
(3.69)
Kinetic theory assumes the information in the distribution function as
mathematically complete: iff is known at a time to, along with all external
fields and the boundary conditions, then it can be calculated for all future
times t > to. More explicitly, kinetic theory postulates the existence of a
closed equation for f, called the kinetic equation (or Boltzmann equation,
for its prototype). In this chapter, we will establish and discuss the kinetic
description for the case of a complex, partially ionized plasma far from
equilibrium, such as air.
As all mathematical models, kinetic theory has its limitations. First, it
should be noted that we deal with a continuum theory that itself makes no
reference to the atomistic nature of its system. The probabilistic relation
(1) is a physical interpretation, not a strict mathematical definition. For it
to make sense, the phase space volume b.3rb.3v should be chosen small
enough to resolve macroscopic structures but large enough so that statistical
--- Page 104 ---
Particles and Distributions
89
fluctuations rv6.N;1/2 are negligible. If the smallest macroscopic length is not
much larger than the interparticle distance, the scales are not sufficiently
separated and the kinetic model breaks down. (Definition (2) embodies
similar problems because the invoked 'suitable average' also makes reference
to an intermediate scale.) Second, kinetic theory assumes that higher order
correlations are not dynamic, but can be calculated as functionals of the
one-particle distributionf. This assumption generally holds when the inter-
actions among the particles are sufficiently weak and/or rare.
Let us discuss the assumptions in more detail for the considered case of a
weakly ionized plasma, presupposing some material of the next section. The
neutral density is nN, the electron density nc , with the ionization degree
a = ne/nN « 1. The corresponding temperatures are TN and Te; typically
Te is much larger than TN.
The neutral particles will interact when the relative distance becomes
smaller than their diameter d; these interactions are rare when the particle
distance rN = n-;,1/3 is large, rN » d. Clearly, this condition is always met,
it simply implies that the density of the neutral gas component is small
compared to that of the condensed phase. For the Coulomb interaction, it
is custom to introduce three characteristic distances, namely the average
distance re = n;:1/3, the distance of closest approach for thermal particles,
rc = i /(41TcoTe), and the Debye length AD = (coTe/e2n)1/2. The scales are
not independent; using the plasma parameter A = AD/rc one has
AD/re = A/(41T)1/3. The condition that the Coulomb interaction is weak
implies that the interparticle distance is large compared with the distance
of closest approach, or equivalently, the total Coulomb interaction energy
is small compared with the kinetic energy. Because of the relation between
the scales, this is often stated as the condition that the number of particles
in a Debye sphere be large, Abne == A/3 » 1. Plasmas that fulfill the con-
dition are referred to as weakly coupled or 'ideal'.
The limitations of the kinetic description should not be overstated. For
most practical applications, the approach is very satisfactory, as ideal
plasmas cover the majority of cases under consideration. Important non-
ideal plasmas are high pressure arcs; also dusty plasmas are non-ideal with
respect to their dust component. From a pragmatic point of view, one may
state that the difficulties in treating the kinetic model alone are so huge
that one hardly ever is tempted to employ an even more general description.
In other words, the real challenge is to reduce the kinetic description itself to
a more tractable form. We will come to this later.
The rest of this chapter is organized as follows. In the next section, the
various interactions of the particles in a plasma will be discussed and physi-
cally classified into 'forces' and 'collisions'. Then the mathematical form of
the kinetic model will be established. The last section will briefly describe
the possibilities of evaluating the kinetic representation. In particular, we
will mention some simplifications that are based on the smallness of the
--- Page 105 ---
90
Kinetic Description of Plasmas
electrons' mass and other approximations, and sketch the connection to the
more elementary plasma descriptions.
3.2 Forces, Collisions, and Reactions
The particles of a plasma are subject to various types of interactions, among
themselves, with the surrounding walls, with radiation, and with externally
applied fields. All interactions are electromagnetic, except for a constant
gravity which is sometimes included. In the final formulation of kinetic
theory, however, they are represented by contributions of very different
mathematical form. A discussion of the processes and their description is
the subject of this section.
Kinetic theory regards the plasma constituents (except the photons, of
course) as classical and here non-relativistic point particles. As such, they
follow Newton equation of motion with the acceleration calculated from
the Lorentz force (and possibly constant gravitation),
dr
_
-=v
dt
dV'
q (-(_)
_
-(_))
_
-d = -
E r, t + v x B r, t + g.
t
m
(3.70)
(3.71)
The electromagnetic fields may be externally generated, but typically include
also contributions which arise from the charges and currents within the
plasma itself. The 'self-consistent fields' can be calculated directly from
Maxwell's equations, using the above expressions for p and]':
-
ajj
VxE+ 7ii =O
Eov.f = Lqs J
fsd3v
s
(3.72)
(3.73)
(3.74)
(3.75)
The self-consistent fields, however, do not account for all plasma inter-
actions. As described above, the one-particle distribution function neglects
information on the correlation of the particles, and processes related to the
individual encounters of particles are therefore not included in (3.70)-
(3.75). These 'collisions' (an obvious, but unfortunately misleading term)
--- Page 106 ---
Forces, Collisions, and Reactions
91
can be of very different type; they may be classified with the help of the
following considerations.
Neutral particles, typically the majority in the plasma, interact when
their electron shells overlap. The interaction vanishes rapidly when the
particle separation becomes larger than a few Bohr radii. The Lenard-
Jones model, e.g., assumes a form f'Vr- 6 in the potential and f'Vr-7 in the
force [4]. If one of the interaction partners is charged, it induces an electrical
dipole moment in the partner, the corresponding interaction is attractive and
behaves as r -5. Only if both partners carry charges, a long range interaction
arises which goes f'Vr-2.
The decrease of the forces with r must be compared to the increase in the
number of interaction partners which scales f'Vr2 for large r. For neutral-
neutral and neutral-charge interactions the accumulated interaction force is
finite and, in fact, is dominated by the small distance contributions. These
interactions are thus mainly few-body collisions, i.e. they can be understood
as the interaction of two or three particles which asymptotically are before
and after the collision free (for t ----+ ±oo). Charged particle interactions, on
the other hand, have an accumulated field which formally diverges for large
distances: charged particles are always under the simultaneous influence of
(many) other charges and the 'collision' concept breaks down.
Let us first consider the few body collisions (figure 3.6). Practically
speaking, 'few-body' means 'maximally three interaction partners', and
two-body collisions are by far the most important. None the less, it is
advantageous to start with a general discussion for an arbitrary number of
collision partners. We consider a set of free particles and photons, the
RJ
81
-
/-
~
R2
82
.-
--.
~
IvVvvv- WI
,.,
Figure 3.6. Schematic illustration of a few-body collision. Educt particles and photons
enter the 'black box' reaction zone and are scattered into product particles and photons.
The size of the reaction zone is small compared to the average interparticle distance, so
that the particles can be considered as asymptotically free before and after the collision.
Nothing specific is assumed about the interaction except the validity of the general laws
of physics (conservation of nucleon identity, charge, momentum and total energy,
principles of Galilei invariance and detailed balance).
--- Page 107 ---
92
Kinetic Description of Plasmas
educts RJ, ... , RM and <PI, ... , <PM, referred to also by the indices rJ, ... , rM
and cPI,"" cPM' They undergo an interaction for a finite time until they
appear as particles or photons which are again free (the products
SJ"",SN and wJ"",WN' referred to also by the indices SI, •.. ,rN and
1/JI, ... , 1/JN)' Such a process reads in a chemical notation (a variety of other
conventions exists):
RI + R2 + ... + RM + <PI + ... + <PM
--. SI + S2 + ... + SN + WI + ... + WN·
(3.76)
If the educts and products are the same particle set, one speaks of particle
conserving collisions, otherwise of (chemical) reactions. If the sum of the
kinetic energies before and after the collisions is the same, the collision is
elastic, otherwise inelastic (subelastic for negative energy differences, super-
elastic for positive ones). Chemical reactions are a particular kind of inelastic
collisions.
The investigation of few-body collisions is the realm of scattering
theory, which has been developed both within classical and quantum
mechanics. In both descriptions, the scattering event is described by a certain
probability p that is a function of the educt and product particle velocities. In
classical mechanics, input and output states are considered as beams, and the
stochastic character of the scattering is due to incomplete spatial informa-
tion. In quantum theory, input and output are interpreted as eigenstates of
the momentum operator, and the dynamic itself is genuinely stochastic.
For the purpose of kinetic theory these differences do not matter: The
scattering process is seen as a black box, subject only to the general laws
of physics.
The stochastic view of the interaction implies that the scattering rate li-
the number of scattering events per volume and time, [Ii] = cm-3 s-I-is
proportional to the density of the educt states. Assuming the absence of
microscopic correlations (,molecular chaos'), this is the product of the
phase space densities of the educt particles and the radiation intensities of
the educt photons. (For each photon, a factor of ljhv must be introduced
to transform the radiation intensity into the corresponding photon flux.)
Explicitly, the rate is calculated as
The physics of the scattering interaction is embodied in the factor p, which
gives the probability of a certain educt state being scattered into a certain
--- Page 108 ---
Forces, Collisions, and Reactions
93
product state. Independent of the details of the interaction, one can state that
it must equal zero for combinations of educt and product states that do not
meet the laws of energy and momentum conservation. Utilizing that the
momentum of the photons can be neglected, these laws read
(3.78)
N
M
"'" m" V, = "'" mrvr.
~ 'I '/
L.-t
I
I
(3.79)
i=l
i=l
Consequently, the probability p must be the product of a kernel K and
appropriate 8-functions,
K( ~
~
~
~
~
~
~
~ )
p =
VI', ' ... , VI'''' v'/J, ' e"i1 ' ... , V m ,e1J -,vs , ... ,V" ,e,/, , ... , v,;; -" e'tiJ-
,VJ
'1-
'f'
'('M
.'Ill
I
.v
1--'1
lv
,fI,'
x8((~~mri~~+cri+ ~hV1J') - (t~m'A~+Cli+ thVVJi))
x 8(3) (I=mrivr, -tmsiVI,).
i=l
i=l
(3.80)
The mathematical form of the kernel can be specified even further by noting
that the scattering relation (3.77) must hold for every inertial system. In the
non-relativistic formulation employed here, the kernel must be invariant
against arbitrary Galilei transformations. These consist of rotations,
which are given by an orthonormal matrix T and transform particles and
photons as
71----+ Tv
(V,e) ----+ (v, Te).
and of translations by a velocity V, which induce
71----+71+ V
(V,e) ----+ (v(l +e· Vlc),e).
(3.81)
(3.82)
(3.83)
(3.84 )
The form (3.80) and the invariances (3.81)-(3.84) are valid in the non-
relativistic limit, i.e. for transformation with small speed and photon
energies much below mc2 . In evaluating them, one typically encounters
quadratic errors in vic. This inconsistency may be healed, of course, by
switching to a relativistic treatment of the kinematics and requiring
invariance under Lorentz transformations. Traditionally, however, low
temperature plasma physics employs Newtonian formulations.
--- Page 109 ---
94
Kinetic Description of Plasmas
Besides observing the energy and momentum conservation laws, the
scattering probability must be symmetric against arbitrary permutations of
the educt and the product variables among each other, and must obey the
principle of detailed balance. (Quantum mechanically, the matrix elements
of the reaction and the back reaction must be the same.) Furthermore,
only those processes are possible where the total charge stays constant,
and all atoms of the educt also appear in the products. These constraints
do not appear as symmetries but are simply conditions for a non-vanishing
K. Employing the integer vector view of the sum formula (see section 3.1),
they can be formulated as
n =Z,H, ... , U.
(3.85)
Very often, the kinematic state of the scattering educts is not important, only
the event as such. It is then advantageous to introduce the absolute scattering
probability P as the integral of the differential probability p,
P(Vr,,···,v¢M,e¢J = gJ d3vs}]J d0,p, J
dv,p,
x p(vr,,···, V¢M' e¢M' vs,,···, V,pR' e,pR)·
(3.86)
In terms of this quantity, the scattering rate now reads
(3.87)
We will now leave the general discussion of the few-body collisions and
proceed by describing the most important processes in some detail. The
educts and products may be any combination of photons, electrons, neutrals,
excited neutrals, and positive or negative ions. To refer to them, we employ
the notation displayed in table 3.l. As the number of possible interactions
increases drastically with the number of reactions partners, we will essentially
restrict ourselves to one-body and two-body collisions. Collisions with three
or even more interaction partners are relatively infrequent under normal
conditions, and they will be addressed by only a few remarks.
The simplest case is the 'one-body collision', i.e. the spontaneous decay
of an isolated particle. Such reactions are, of course, only possible for excited
heavy particles; electrons and photons are stable. Typical examples are listed
in table 3.2.
--- Page 110 ---
Forces, Collisions, and Reactions
95
Table 3.1. Notation used for tables 3.2-3.5. Note the particular convention used for heavy
particles. For example, AB refers to a molecule of constituents A and B, but A is
not necessarily an atom but can be a molecule as well. (It may be also excited or
ionized, for that matter.)
Symbol
Meaning
e
Electron
</>,'lj;
Photon
A,B,C
AB
A*
Heavy particle
Molecule from constituents A, B
Electronically excited particle
Vibrationally excited molecule
Positive ion (cation)
Negative ion (anion)
Remarks
Atomic or molecular, possibly excited or
charged
Possibly excited or charged
Atomic or molecular, possibly additionally
excited or charged
Possibly additionally excited, possibly
charged
Atomic or molecular, possibly excited
Atomic or molecular, possibly excited
Referring to the educt by the name R or the index r, the kinematic
conservation rules of energy and momentum for a spontaneous decay are
N L
~
~
ms·vs· = mrvr·
, ,
;=1
The conservation laws of nucleon identity and charge read
N
LS;,n =Rn,
i=1
n =Z,H, ... , U.
(3.88)
(3.89)
(3.90)
Equation (3.86), specialized for the case of a spontaneous decay, states that
the total scattering probability P can only depend on the particle velocity if.
There is, however, no possibility of constructing a Galilei invariant out of a
Table 3.2. Examples of 'one-body' or spontaneous decay processes.
Reaction
A* -- A+¢
A* -- A+ +e+¢
AB* -- A+B
AB* -- A+B+¢
AB- -- A+B+e
Description
Photonic de-excitation
Auger effect (autoionization)
Autodissociation
Decay of excited dimers (e.g. in excimer lasers)
Auto detachment
--- Page 111 ---
96
Kinetic Description of Plasmas
single velocity vector V, and the dependence must actually vanish. This
corresponds to the fact that the decay probability of an unstable particle is
a constant, and a dimensional analysis shows that P must be identical to
the inverse of the particle life time T,
1
P=-.
T
The absolute decay rate can be calculated as
. J
1 J, (~) d3
nr
n = -
r Vr
Vr = - .
T
T
(3.91)
(3.92)
To some extent, the differential scattering probability is determined from the
constraints (3.88)-(3.90). When two educts result, their final energies are
fixed (as are their momenta, up to an arbitrary rotation in the rest frame).
Particularly in a photonic decay, the photon carries off (in an arbitrary direc-
tion) the full energy difference between the product and the educt state.
(Doppler shift must be taken into account.) This is, of course, the basis of
optical spectroscopy. If more than two educt particles are produced, their
energies may have a statistical distribution.
Each spontaneous decay of an excited particle requires a preceding
excitation. For some applications, it is reasonable to classify a process as
spontaneous decay when the lifetime of the state is long enough so that the
energy uncertainty .6.c ~ hiT is negligible. In other situations, it may be
advantageous to restrict the considerations to metastables. These are
particles with a life-time long enough so that transport effects can occur;
they exist for example in argon.
Next, we discuss the case of two-body interactions, where we distinguish
between collisions of matter particles and interactions of a particle and a
photon. We begin with the first, for which the conservation laws of energy
and momentum read
N L ms; vS; = mrl vrl + mr2 Vr2
;=1
and the conservation rules of charge and nucleon identity are
N L S;,n = Rn,1 + Rn,2,
;=1
n=Z,H, ... ,U.
(3.93)
(3.94)
(3.95)
Equation (3.86) now states that the total scattering probability must be a
function of vrl and vr2 • These velocities combine to only one possible Galilei
invariant, namely the absolute value of their difference g = Iii = IVrl - vrJ
--- Page 112 ---
Forces, Collisions, and Reactions
97
Dimensional considerations show that P must be a product of g and a factor
u which has the dimension of an area. This so-called total scattering cross
section is in general a function of the difference velocity,
P(vr!, vr2 ) = IVr! - vr2 1 u/(Ivr! - vr2 1)·
(3.96)
With the help of the total cross section, the reaction rate n can be calculated
as
(3.97)
The scattering relations become particularly transparent when the considered
collisions are elastic. Switching to standard notation, two particles of
mass m and M with initial velocities v and V are assumed to scatter into
the final velocities v' and V'. It is convenient to introduce as variables the
center-of-mass velocity w = (mv + MV)/(m + M) and difference velocity
l = v-V. Momentum is conserved when the center-of-mass velocities
remain unchanged; energy conservation implies It I = Ill. The scattering
probability p may thus be written as
p = :~ (g, e) 8(3)(w - w') 8(!i - !g'2).
(3.98)
Galilei invariance demands that the differential cross section du/dD intro-
duced by (3.98) may only depend on the absolute value g of the difference
velocity and on the scattering angle e = L.(l,t). (See figure 3.7.) By inserting
expression (3.98) into the two-body version of (3.86), and utilizing that the
transformation from (v, V) to (w,l) has a Jacobian of unity, one arrives at
J du
P= gdD dD.
(3.99)
Comparison of this result with relation (3.96) shows that the total cross
section of an elastic scattering process is the integral of the differential
cross section over all scattering angles,
(3.100)
The differential cross section represents the ratio of the scattering events (into
a given solid angle element ~D) to the incoming flux of collision partners. In
general, du/dD is a complicated function of both arguments g and e. For the
limiting case of a 'hard sphere' potential (one that rises from zero to (Xl at a
radius R), however, the cross section is constant and the scattering isotropic,
du ( e) = !!.!... = 7r R2
dD g,
47r
47r'
(3.101)
Isotropic scattering is a popular approximation for neutral-neutral inter-
actions, where the potential is at least comparatively hard. The dependence
--- Page 113 ---
98
Kinetic Description of Plasmas
Particles
Particles
I
21
_ .... _-.. _
..... ~---- .. lr
(a) Total cross section
(b) Differential cross section
Figure 3.7. Illustration of the total cross section u, (left) and the differential cross section
du/dO (right). The total cross section is the ratio of the number of scattering events per
particle, relative to the flux of incident interaction partners. The differential cross section
measures the number of particles which are scattered into the solid angle element
LlO = 27rsinBLlB. Note that du/dO is defined under more general conditions than u,
but, if both exist, they are related by u, = f(du/dO) dO.
on the velocity is often kept
dO' ( 0) = O't(g)
dO g,
41r .
(3.102)
Softer potentials (which rise less drastically with decreasing distance) favor
forward scattering. The extreme example is the very soft rvr-2 Coulomb
potential. Using q and Q for the charges of the particles and mR for their
reduced mass, the corresponding Rutherford cross section reads
d
2Q2
~(g,O) =
q
.
dO
(81rEo)2mig4 sin4(Oj2)
(3.103)
The total cross sections calculated from this expression, however, are infinite,
due to a divergence at small angles (large distances). This is the result again
that charged particles are never really free. The proper treatment of Coulomb
interactions will be discussed at the end of this section.
We now proceed to the inelastic two-body collisions, of which a large
manifold of variants exist. The educt particles may be any combination of
electrons, neutrals, excited neutrals, and positive or negative ions, only
inelastic electron-electron collisions do not exist in the plasma energy
range. The products may be an arbitrary number of particles plus possibly
photons. Each of the 14 categories a-n in table 3.3 may be further divided
into different reaction channels.
The following tables display a list of the most frequent types of inelastic
two-body collisions, ordered with respect to their main source of energy.
--- Page 114 ---
Forces, Collisions, and Reactions
99
Table 3.3. Overview on the possible inelastic two-body interactions. Except for inelastic
electron--electron scattering which does not exist at non-relativistic energies,
each combination is possible. Most of the categories actually represent several
physically different reaction channels.
Electron
Neutral
Excited
Cation
Anion
Electron
a
b
c
d
Neutral
e
f
g
h
Excited
j
k
Cation
I
m
Anion
n
Electron driven processes are contrasted with interactions that involve only
heavy particles.
Processes driven by electron impact (a-d)
Electrons as the lightest, fastest and normally the most energetic particles are
responsible for the bulk of the interactions in a plasma. The energy of the
electrons is due to external fields (heating); sometimes also externally
generated electrons (beams) play a role. Ionization is responsible for
plasma generation, and, together with electronic excitation, dominates the
energy balance. (Table 3.4.)
Table 3.4. Inelastic two-body interactions driven by electron impact. (For
notation see table 3.1.)
Reaction
A+e- A*+e
AB+e -
ABV +e
A* +e- A+e
ABV+e -
AB+e
A+e -
A+ +e+e
AB+e- A+B+e
AB+e -
A+ +B+e+e
AB+e -
A+ +B- +e
A + e -
A-* -
A- + </J
AB+e -
A- +B
A+ +e -
A +</J
AB++e-A+B
A- +e -
A+e+e
AB- +e -
A- +B+e
Description
Electron impact excitation
Electron impact vibrational excitation
Superelastic collision
Superelastic collision
Electron impact ionization
Electron impact dissociation
Electron impact dissociative ionization
Ion-pair production
Dielectronic attachment
Dissociative attachment
Radiative recombination
Dissociative recombination
Electron detachment
Electron impact dissociation of anions
--- Page 115 ---
100
Kinetic Description of Plasmas
Reactions among heavy particles (e-n)
Reactions among heavy particles can take many forms. A list-far from
exhaustive-of inelastic and reactive heavy particle interactions is given in
table 3.5. Some influence mainly the transport behavior and the energy
content of the plasma, others alter the composition. Reactions that change
the chemical identity of the particles are referred to as plasma chemistry.
Heavy particle reactions are typically driven by the internal energy of
the reactants, sometimes (for example, during space craft reentry or m
Table 3.5. Inelastic and reactive two-body interactions between baryonic particles.
Reaction
A+ +B-- AB+
A- +B-- AB-
A* + B -- A + B + P
A+B--A+B++e
A+B-- AB+ +e
A* +B-- A+B+ +e
A* +B -- AB+ +e
A +B-- A+ +B-
A+B-- A* +B
A+ + B -- A+ + B*
AB + C -- ABv + C
A* +B-- A+B*
A* +A -- A +A*
AB" + CD -- AB + CD"
A+ +B-- A +B+
A+ +A -- A+A+
A- +B-- A+B-
A- +A -- A +A-
A+ +B- -- AB
A+ +B- -- A+B
A+ +B- -- A* +B
AB* + C -- A + B + C
AB+ + C -- A + B + C+
A-+B--A+B+e
A- +B -- AB+e
A- +B- -- A- +B+e
A+BC-- AB+C
A+ +BC -- AB+ +C
AB+ CD -- AC+BD
AB + CD -- ABC + D
A* +B-- AB
A* +B-- A +B
AB" + C -- AB + C
Description
Polarization scattering (capture)
Polarization scattering (capture)
Band resonance radiation, dipole radiation
Ionization
Ionization
Penning ionization
Penning ionization
Electron capture
Excitation
Excitation
Vibrational excitation
Excitation exchange
Resonant excitation exchange
Vibrational excitation exchange
Charge transfer
Resonant charge transfer
Charge transfer
Resonant charge transfer
Positive-to-negative ion recombination
Positive-to-negative ion recombination
Positive-to-negative ion recombination with excitation
Dissociation
Dissociation
Collisional detachment
Associative detachment
Detachment
Chemical reaction
Chemical reaction
Chemical reaction
Chemical reaction
Deexcitation, quenching, deactivation
Deexcitation, quenching, deactivation
Vibrational deactivation
--- Page 116 ---
Forces, Collisions, and Reactions
101
other supersonic shocks) also by their kinetic energy. A particular case are
the resonant reactions that occur between differently excited molecules of
the same type (resonant excitation exchange), or between an ion and its
parent molecule (resonant charge exchange). These processes do not require
any reaction energy.
We now consider the two-body interactions of one particle, referred
to as R, and one photon W. The conservation laws of energy and momentum
are
~
(~ms,vs~ + Es,) + t
hv,p, = ~mrV; + Er + hv,p
(3.104)
N
"'" ms.vs = mrvr
~ II
(3.105)
i=!
and the conservation rules of charge and nucleon identity read
N
"'" Sin = R 1n ,
~,
,
n = Z,H, ... , U.
(3.106)
i=!
The total scattering probability depends on V" v,p' and e,p. The only invariant
combination of these quantities is v(l - e· VI c), which is the frequency of the
photon in the rest system of the particle. The scattering probability can thus
be written in terms of a total cross section at as
(_
_)
((
e,p.vr)
)
P v" v,p,e,p = at
1 - -c-
v,p .
(3.107)
Assuming that the particles are described by the distribution functionJ,.(vr )
and the photons by the radiation density Iv (v,p, e,p), the reaction rate n can
be calculated. The result is easily understood: the reaction probability per
particle is the flux of the incident photons times the cross section at,
integrated over all frequencies and directions. The reaction density is then
obtained by integrating over the particle distribution. Note that the Doppler
effect is correctly taken into account,
(3.108)
Again, the kinematic relations become much more transparent for the case of
elastic scattering. Consider a particle of mass m and velocity v scattering a
photon of frequency v and direction e. The respective educt quantities are
v', v', and e'. Evaluating (3.104) and (3.105) shows that the momentum of
the particle and the energy of the photon are conserved; the only quantity
that experiences a change is the direction of the photon. The differential scat-
tering probability can thus be expressed in the following form, where the
--- Page 117 ---
102
Kinetic Description of Plasmas
differential cross section da / dO may be a function of the reduced frequency
and the scattering angle () = L.(if, if'),
p = :~ ( (1 -if1/: ~ V,.) v.p, ()) 8(3) (v - v')8(v - v').
(3.109)
The total cross section is again the angular integral of the differential cross
section
at = J:~ dO.
(3.110)
An example for elastic photon interaction is Thompson scattering at free
electrons. With ro being the classical electron radius, the differential and
the total cross section are
da
1 2
2
dO = 2ro(1 + cos ())
(3.111)
87r 2
at = 3 ro .
(3.112)
The momentum and the energy of massive particles remain, to a good
approximation, uneffected by the elastic scattering of photons. Such
unaffected processes thus have little dynamical influence in plasmas. They
are, however, important for optical diagnostic methods. The scattering of
photons by free electrons, e.g., underlies the method of Thompson scattering:
the photons are provided by an external laser beam and the scattered light is
measured with high angular and energy resolution. It is possible to determine
the density and the distribution function of the free electrons in the plasma by
evaluating the differential cross section (3.111) together with the second
order in the photon energy shift, tlv = vv· (if' - if) / c.
More important for the plasma dynamics itself are inelastic photon
interactions, particularly the radiation driven reactions. Table 3.6 gives a
selection of some important processes.
Table 3.6. Inelastic processes and reactions driven by radiation. (For notations see table 3.1.)
Reaction
A +<1> -
A*
AB+<1>- ABv
A +<1> -
A+ +e
AB+<1> -
A+B
AB+<1> -
A* +B+e
A+<1>-A+<1>'
A* + <1> -
A + <1> + <1>
A- +<1> -
A+e
AB- + <1> -
A + B + e
Description
Photoexcitation, or bound-bound absorption
Vibrational photoexcitation
Photoionization, or bound-free absorption
Photo dissociation
Dissociative photoexcitation
Luminescence, fluorescence, Raman scattering
Induced emission
Photo detachment
Dissociative photo detachment
--- Page 118 ---
Forces, Collisions, and Reactions
103
The processes listed in tables 3.2 to 3.6 are only a selection of the
interactions possible in a plasma. When three-body (and higher) collisions
are considered, the situation becomes even more complex. An exhaustive
account which lists more than a hundred different types of many-body inter-
actions is given in reference [7]. In plasmas that are maintained in gas
mixtures such as air, the number of atomic and molecular species is typically
large and the number of different scattering and reaction processes can easily
be a few hundred.
The complete quantitative characterization of plasma dynamics is
difficult. A first orientation may be provided by the following general
rules. The principle of detailed balance states that the matrix elements of a
reaction and its back reaction must coincide. If radiation is included, this
extends to a relation between the coefficients of absorption, emission, and
spontaneous emission. Typically, inelastic processes are less likely than
elastic collisions (in a semi-classical picture, the motion of the nuclei is
adiabatic). Radiative transitions are less likely than non-radiative ones.
Three-body events are often negligible. (A counter-example is third-body
assisted recombination; non-radiative two-body recombination is often
suppressed by energy and momentum conservation.) Two-photon processes
take place only at very high radiation densities.
For more specific information, one can either turn to theory or to experi-
ment. True first principle calculations are difficult, and empirically found
data are seldom complete. As a rule, one can state that angular resolved
information on the products is difficult to obtain, so that the total reaction
cross section (J"t becomes the preferred data format. Frequently, even that
information is missing, and only empirical reaction rates are available,
often expressed in terms of Arrhenius' formula. The lack of reaction data
is a serious problem for all modeling efforts. The body of knowledge,
however, is in rapid growth; many gases-particularly those of technical
importance-are already well characterized, and new data are added on a
regular basis. (See reference [11] for a start.)
We now turn to the Coulomb interactions which cannot be described as
collisions in the strict sense. Instead, a charged particle is simultaneously
influenced by many other charges. For a rough consideration these 'field
charges' may be divided into three groups: (a) a small number of charges
inside the strong interaction zone r ~ rc (on average less than one, the
probability scales ",A-I), (b) a relatively large number that are in a Debye
sphere rc < r < AD (this number scales like ",A2), and (c) the other charges
beyond the Debye radius (in effect infinitely many).
Each group of field particles influences the test particle differently: the
close encounters-set (a)-change its momentum vector drastically, similar
to a hard sphere collision. The absolute frequency of these events is, however,
not very high, and their effect is masked by the influence of group (b). Each of
the (b) particles induces only a small velocity change, but their simultaneous
--- Page 119 ---
104
Kinetic Description of Plasmas
action gives rise to a substantial stochastic acceleration, describable as a
'random walk in velocity space'. Particles (c) also have a measurable
influence, but due to the large number their contribution loses its statistical
nature. The resulting average is, in fact, a regular acceleration which is
contained in the self-consistent fields calculated from (3.72) and (3.73).
As the final topic in the section, we discuss very briefly the interaction of
plasma particles with material objects, such as electrodes, walls, or
substrates. Their reaction rates are often substantial. Surfaces (solids or
fluids) have a high density of available quantum states. In addition, surfaces
are connected to a large sink of energy and momentum. This has the conse-
quence that surface reactions are not subject to any selection rules. The
detailed study of these processes is the subject of a separate science,
plasma surface chemistry, which has established a huge body of knowledge
(particularly within the past decade). See reference [2] for a start.
Electrons are always absorbed by the material surfaces. In metals, they
enter the Fermi reservoir; in insulators, they occupy the surface states and
accumulate. Typically, their flux is much higher than that of any other
species, so that a negative 'floating potential' develops which is a few times
the electron thermal voltage Te/e. (It can be much higher when a dc or rf
bias is applied.) The plasma, in turn, reacts to the wall potential with the
formation of a plasma boundary sheath, a positive space charge zone with
a strong wall-pointing electrical field. For details see [9].
Positive ions which enter the sheath are accelerated to the wall, and are
very likely to reach it. Very often, the wall forms the most prominent sink.
Close to the wall, the cations are neutralized by electrons tunneling into
the unoccupied quantum states. (When unbound states are accessed, free
electrons can be generated which escape into the plasma: this is secondary
electron emission.) The former ion, now a fast neutral, continues its trajec-
tory onto the surface.
Negative ions are repelled by the field of the sheath and reflected, as their
energy per charge unit is typically much less than the floating potential. They
tend to accumulate within the plasma, waiting to be neutralized either by
recombination or by detachment. Only when the wall potential vanishes
(for example, in the afterglow phase of pulsed plasmas), negative ions can
recombine at the walls.
The fate of a neutral that reaches a surface depends strongly on the
characteristics of both partners. One factor is the available energy. Excited
species, radicals and particles with a high impact energy are relatively
reactive; saturated or thermal ones are often simply reflected. A surface of
high temperature is more reactive than a cold one. Other factors are of
chemical nature.
Particles may also be emitted from a surface. Electrons can be liberated
by ions, by radiation, by a strong electric field, or thermally from heated
surfaces. Neutrals can be generated either by the impact of other particles
--- Page 120 ---
The Kinetic Equation
105
(e.g. sputtering, desorption), they can appear as free products of a chemical
reaction (e.g. etching), or the material may decompose due to thermal effects
(evaporation). Ion production at the surfaces is usually not important.
3.3 The Kinetic Equation
Section 3.1 discussed the various particles that are present in a partially
ionized plasma and introduced the one-particle distribution function f to
describe their state (at a given time t). Section 3.2 gave a physical account
of the forces that influence these particles, originating both from external
fields and from their mutual interaction. This section now combines the
two lines of thought and describes how the forces and interactions change
the distribution function over time. The mathematical formulation of this
is called kinetic equation. In its most compact form, it states that the convec-
tive or laminar term is equal to the collision term and reads as follows:
;(;=U)Sl s=l, ... ,N.
(3.113)
This, of course, must be explained. The convective term on the left is given by
a total derivative; it denotes the temporal change off evaluated with respect
to a moving frame of reference:
(3.114)
The motion of the reference frame is defined by Newton's equations, evalu-
ated with the external and the self-consistent fields, equations (3.70)-(3.75).
For charged particles, it reads
df" (~ ~ t) = oIr, + ~. of" + (~+!l!!... (E~ + ~ x B~)) . of"
d
r, v,
!')
v!')~
g
v
!')~ •
t
ut
ur
n1"
uV
For neutrals it is simply
dfa (~~ ) _ ofa
~. ofa
~. ofa
dt r, v, t - ot + v or + g OV'
(3.115)
(3.116)
Equation (3.113) states that, up to the 'action of the collisions', the distribu-
tion function is temporally constant in the co-moving frame. This statement
may be understood with the help of figure 3.8, which shows the temporal
evolution of a phase space element ~ V according to the laminar term.
Assuming that the equations of motion arise from a Hamiltonian-true
--- Page 121 ---
106
Kinetic Description of Plasmas
for equations (3.70) and (3.71)-the volume of the phase space element is
constant over time. (Its form, of course, will change!) Collisions absent,
the particles also follow the equations (3.70) and (3.71), implying that all
particles present in the element ~ V at to will end up in ~ V' at t \. Their
total number ~N is thus conserved. The phase space density, being the
ratio of ~N and ~ V, is then also a constant in time.
This fact is often stated by saying 'the phase space density behaves like
an incompressible fluid'. For a more direct verification of this analogy, one
may also note that the total derivative in (3.113) can be written as a partial
derivative plus the divergence of a flux in the phase space,
(3.117)
This is, if set equal to zero, similar to the fluid-dynamical equation of conti-
nuity. Its derivation uses the 'phase space analogy' of the incompressibility
condition \7 . iJ = 0, but this relation is, of course, not an equation of state
but a consequence of the Hamiltonian nature of the dynamics,
%,. (if) + %iJ • (g + !: (E + iJ x Ji)) = O.
(3.118)
The term (I) s on the right of equation (3.113) represents all forces and inter-
actions that are not accounted for by the external and self-consistent forces.
Summarily referred to as 'collisions', these interactions scatter particles in
and out of the co-moving phase space volume. (See figure 3.8.) The scattering
of a particle into the phase space element ~ V corresponds to a 'gain' process,
a scattering out of the element counts as a 'loss'.
The collision term in (3.113) is just a symbol, in contrast to the explicitly
displayed convective term. In reality, it is a quite complicated sum of several
contributions, each of which corresponds to one of the interaction processes
discussed in section 3.2. All contributions have in common that they are local
in the spatial dependence, i.e. act only on the velocity part off: only particles
at the same position can collide, and they only experience a change in
velocity, not a change in position. (That is, when they keep their identity.
In chemical reactions they may locally appear or disappear.) The dependence
on ,and t will be suppressed in the further notation.
It is advantageous to divide the collision term contributions into three
physically distinct groups. The first corresponds to the most frequent interac-
tions, the elastic two-body collisions; the second represents all other few-body
collisions (including the interaction with radiation); and the last represents the
Coulomb interaction. We use the subscripts el, in, and cb, respectively,
(3.119)
--- Page 122 ---
The Kinetic Equation
107
v
v
Gain
D~v
Loss
~x
x
x
(a) Phase space element at t = to
(b) Phase space element at t = tl
Figure 3.8. Schematic illustration of the kinetic equation (3.113). Shown is a phase space
element ~ V which evolves according to the equations of motion, keeping its volume
constant but not the shape. (This is a consequence of the Hamiltonian nature of the
dynamics.) Under the action of the convection term, the particles move in the same fashion
so that the phase space density is conserved. The collision term on the right of (3.113)
scatters individual particles into or out of ~ V, giving rise to gains or losses, respectively.
As shown in the figure, a particle-conserving collision is represented by a translation along
the velocity axis; the spatial position remains unchanged. In addition, there are chemical
reactions which create or destroy particles.
In the case of neutral particles there are, of course, no Coulomb interactions,
(3.120)
The radiation intensity Iv was introduced above as the photon analog of the
distribution function, with the particular situation of massless particles taken
into account. The analogy can be carried further to the photon equivalent of
the kinetic equation, termed the radiation transport equation. It is also a
scalar partial differential equation of first order, with a somewhat different
appearance. The differences are partially due to physics (photons propagate
with a constant speed c, so that iJ = ce and acceleration terms are missing)
and partially due to convention (the radiation intensity refers to energy
flux, not to photon number, and all terms are divided by c),
(3.121 )
Similar as in the kinetic equation, the terms on the left describe the propaga-
tion of the photons. The term e· yo Iv is called the streaming term. The expres-
sions on the right represent the interaction of the radiation with other plasma
constituents. As stated, photon-photon interaction does not exist in the
energy regime under discussion. The quantity Cv represents emission, Iiv
denotes absorption. These quantities are here defined with respect to the
--- Page 123 ---
108
Kinetic Description of Plasmas
volume, [cy ] = W IHzm3, [K;y] = 11m. A sometimes employed alternative
definition introduces emission and absorption coefficients per mass element;
practically, this corresponds to a substitution K;y ----; pK;y and Cy ----; pCy in
(3.121). Note that both the absorption and emission coefficient are functions
which in general depend on the time t, the position r, the propagation direc-
tion e, and the frequency 1/. Particularly the latter dependence often shows
very narrow and complex structures.
As discussed in section 3.2, several different elementary processes contri-
bute to the interaction of photons with matter. From the radiation transport
point of view, one distinguishes between emission (a photon is generated),
absorption (a photon is captured), and scattering (an absorption occurs
but a secondary photon appears with negligible time delay). Scattering is
further divided into elastic scattering and inelastic scattering. A particular
type of scattering is induced emission, where the incident photon is replaced
by two photons of the same direction and energy.
The physical meaning of the kinetic equation and the radiation trans-
port equation can be illustrated with the help of the appropriate moment
equations. For the particles, one multiplies the kinetic equation with the
combination vJ.!!' vI'" , ... ,vI'" and integrates over all velocities, to obtain
~Mn
+\7. rn
at
S,jll·j.t2,···,JlIl
S,J-LI,J-L2,···,MIl
(3.122)
The two terms on the left of (3.122) were already substituted using definitions
(3.12) and (3.14). The first is the time derivative of the moment M; of order n,
the second is the divergence of the corresponding flux. By structure it is a
derivative combination of moments of order n + 1. The first term on the
right represents the action of the macroscopic field. It is a linear combination
of moments of the order n - 1 and n. (The latter is only present when a
magnetic field is included.) The second term on the right represents the
change in the moment due to the action of the collisions. For this contribu-
tion we introduce the notation
(3.123)
Equation (3.122) shows that the time derivate of the moment M n of order n is
related to the divergence of the corresponding flux rn, i.e. to a moment of the
order n + 1. The balances thus form an infinite chain of coupled equations
which are together equivalent to the original equation itself. Only if the
chain of equations is terminated after a certain stage (using additional
--- Page 124 ---
The Kinetic Equation
109
assumptions), a simpler plasma model may be derived. We will return to this
question in section 3.4.
Here we will employ the first three moment equations, corresponding
to the balances of particle number, momentum, and energy. With the
definitions of section 3.1 they read
ans
n. r~n _ .
at + v
s - ns
(3.124)
a;; + \7. TIs = (msg + qs(i + Us x J1))ns + Is
(3.125)
aes
~e
(~
~) ~
.
7it+\7.rs = msg+qsE ·usns+e,.
(3.126)
As in the general form, the terms on the left are the derivative of the
considered moment and the divergence of the corresponding flux. The field
term vanishes for the particle balance; it represents the acceleration in the
momentum balance and the related power density in the energy equation.
The production densities of particle number, momentum, and energy are
explicitly
ns(1, t) = J (f) s d3v
Is(1, t) = J
msvs(f)s d3v
es(r, t) = J
~msv2(f)s d3v.
(3.127)
(3.128)
(3.129)
In analogy to the balances of the particles we now derive the balance
equations of the photons. By integrating the radiation transport equation
over the total solid angle 41f and invoking the definitions of the spectral
energy density U/l and the energy flux P/I-see (3.52) and 3.533)-we obtain
the spectral energy balance
aU/I
- J
J
at + \7 . F /I =
C/I dO -
IiJ/I dO.
(3.130)
Integrating this expression further over the full frequency range gives the
total energy balance, with the emissions counting as gains and the absorption
as losses,
au
n
F~
·G
·L
-+v· =e-e
at
(3.131)
eG = JJ c/ldOdv
(3.132)
eL = JJ IiJ/I dO dv.
(3.133)
--- Page 125 ---
110
Kinetic Description of Plasmas
Integrating (3.130) with the weight l/hv yields the photon number balance,
with the corresponding gain and loss terms on the right,
an
r7 r~
·G
·L
-+v· =n-n
at
·L
II 1
n = -
hv "'vIII dO dv.
(3.134)
(3.135)
(3.136)
Having established the framework of particle and radiation transport, we
now proceed with an explicit discussion of the interaction terms. We first
concentrate on the few-body collisions in general, of which elastic scattering
is a special case. In section 3.2, the total scattering rate of M educt
particles R" ... ,RM and M educt photons <I>" ... ,<I>M (referenced by
r" ... ,rM'¢', ... ,¢M) into the product S" ... ,SN,W" ... ,wN (referenced
by s" ... ,SN,'I/J" ... ,'l/JN) was described by (3.77). It is repeated here for
convenience:
The integrand of this expression can be interpreted as the rate of scattering
per element of phase space d3v (for the particles) and per frequency interval
dv and solid angle dO (for the photons). Each scattering event means a loss of
educt particles and a gain of products, represented by a corresponding loss or
gain term on the right side of the kinetic equation. For a particular educt Rb
the loss rate L in phase space due to a process is calculated by integrating the
scattering rate over the velocity coordinates of all other educts and over all
products,
Lrk(VrJ = iJJ",J d3vr; D I
dOqJ; I dvqJ; D I d\,; g I
dO,p; I
dv,p;
x p(Vr\,···, VqJM' eqJM' Vs\,· .. , V,pfl' 4f1)
(3.137)
By dropping the factor Irk (vrJ in this formula, one arrives at a notion which
expresses the particle loss per educt particle Rk . This quantity is often termed
--- Page 126 ---
The Kinetic Equation
111
the specific loss frequency
M
M
N
N
v\(vrk ) = ;=UfJ d3vr,}] J
dD¢, J
dv¢,}] J
d3vs,}] J
dD,p, J
dv,p,
x p(vr\, ... , V¢M' e¢M' VS\"'" V,pR' e,pR)
(3.138)
The relation between the loss rate and the loss frequency is, of course,
Lrk ( vrk ) = v~ ( vrk ) f,Ju,.J .
(3.139)
Both quantities can be utilized to calculate the total scattering rate:
it = J
Lrk(vrJd3vrk = J
v~CU,'k)f,k(vrk)d3vrk'
(3.140)
As the term Lrk refers to the losses of particle species Rb the respective
contributions to the balances of particle number, momentum, and energy
must be counted as negative,
(3.141)
(3.142)
(3.143)
Similar considerations can be made for a product particle St. To calculate the
total gain rate G, the integration must be performed over all educt variables
and all other product variables. (Note that the definition of a specific gain
frequency is not possible.)
M
M
N
N
Gs/(vs) = }] J
d3vr,}] J
dD¢, J
dv¢, ;XtJ d3vs,}] J
dD,p, J
dv,p,
x p(vr\,···, v¢M,e¢M'vS\"'" v,pR,e,pR)
rr
M J, (~ ) rrM I v¢, (v¢" e¢,)
x
r· vr ·
h'
,
,
V
;=1
;=1
Performing the final integration gives again the scattering rate
it = J
Gr/(v,J d3vr/.
(3.144)
(3.145)
--- Page 127 ---
112
Kinetic Description of Plasmas
As gains, the contributions to particle number, momentum, and energy are
positive,
·G IG d3
_.
nSI =
s,
V S1 = n
(3.146)
(3.147)
(3.148)
We now turn to the photons. By integrating the phase space resolved scat-
tering rate over all product variables and over all educt variables but those
of photon <I>k and dividing by the factor Iv¢) hV¢k' we obtain the absorption
coefficient of the considered process,
K = D I
d3vri iJ1~J dO¢i I
dV¢i g I
d3vSi g I
dO,"i I
dV,"i
x p(Vr,,···, V¢M' e¢M' iJ.", ... , V,"R' e'ljJR)
(3.149)
Performing the missing integrations gives again the total reaction rate n
according to equation (3.77). This justifies the interpretation of (3.149) as
the coefficient K.
. -II IV¢i(v¢i,i!¢) d" d
n -
K
hv
H¢k
V ¢k·
(3.150)
In a similar way, by integrating the phase space resolved scattering rate over
all educt variables and over all product variables but those of photon 1lT b we
obtain the emission coefficient,
c = D I
d3vri D I
dO¢i I
dV¢i}] I d\'i iJl~J dO,"i J
dV'ljJi
X p(iJ,o" ... , V¢M' e¢M' iJ.", ... , V,"R' e,"R)
(3.151)
The corresponding total reaction rate has the following form, also demon-
strating that the interpretation of (3.151) as emission coefficient is correct:
n = J
cdO¢i J
dV¢i·
(3.152)
--- Page 128 ---
The Kinetic Equation
113
We now consider two special cases of the general few-body formalism,
namely the elastic scattering of two particles and the elastic scattering of
particle and a photon. The first situation is the one originally investigated
by Boltzmann. Employing the probability formula (3.98) and combining
the loss and gain term into one formula gives
(J,!Is)el(V) = JJJg:~lr/(V- mr"::m,i- mr'::mst )
x Is (v +
my
if -
mr t) i dg dO dO'
m,. +ms
mr +ms
- JJ J
g :~ I r/ (v - if)Is (v) i dg dO dO'
(3.153)
In this expression, if = ge and t = ge' are the difference velocities before and
after the collision, () is the scattering angle L(e, e'), and the cross section
(do/dO)!rs is a function of g and (), symmetric with respect to the indices r
and s,
da I
da I
dO
(g, ()) = dO
(g, ()).
rs
sr
(3.154)
The elastic collision term is subject to the conservation of particle number,
momentum, and energy. Particle conservation holds for each species
separately, as the elastic collisions do not affect the identity of each particle,
(3.155)
Energy and momentum, on the other hand, can be exchanged between the
species, so that the conservation of these quantities is expressed as the
anti-symmetry of the production terms,
As = J
msv(J,!Is)el,rs d3v
JJ mrms -
I" (-
ms
_)
-
gga m rsJ r V -
g
mr + ms
'
mr + ms
XIs(v+
mr
if) d3gd3v = -Psr
m,.+ms
ers = J
~msv2(J,!Is)el d3v
JJ mrms - -
I" (-
ms
_)
-
v'ggamrsJr v-
g
mr +ms
'
mr +ms
I" (-
mr
-) d3 d3
.
XJs v+
g
g v=-es,.·
m,.+ms
(3.156)
(3.157)
--- Page 129 ---
114
Kinetic Description of Plasmas
The (Jm,rs is the cross section with respect to momentum transfer, calculated
as defined above,
(Jm,rs = J
(1 - cosO) :~ Irs dn.
(3.158)
The second special case, the elastic scattering of photons by particles, starts
from expression (3.107). The particles are not affected: only the absorption
and emission of photon must be represented. We assume that the cross
section depends only weakly on the energy and neglect the Doppler shift.
Inserting (3.107) into (3.149) and (3.151), carrying out all possible integra-
tions, and streamlining the notation leads to the following expression for
the combined absorption and emission processes
The net-effect of the scattering is that the photon only changes its direction.
The photon number and the energy stay the same, so corresponding quan-
tities vanish,
11 I scattering = 0
e I scattering = O.
(3.160)
(3.161)
The remaining term to be discussed is the Coulomb term (f)cb, arising from
the long range interactions of the charged electrons and ions. To a good
approximation (see below), it is also a bi-linear term which couples all
charged species,
(3.162)
Several different versions of the Coulomb interaction term are available; they
differ in their special physical assumptions and/or in their mathematical
complexity. Their general form, however, is the same, namely that of a differ-
ential operator of second order in velocity space. With two coefficients called
the friction vector and the diffusion tensor, respectively, it reads
8 _
1 82
(f;3lfa)cb,;3a = - 8:v(Aada) + 2: 8:v:v(Ba/Jia)'
(3.163)
This mathematical form can be understood from the remarks made above,
namely that the action of the Coulomb collisions gives rise to a random
walk motion in velocity space. The various theories for the Coulomb interac-
tion differ in the exact expressions for the coefficients; they are, in general,
complicated functionals of the distribution function.
--- Page 130 ---
The Kinetic Equation
115
We restrict ourselves to the simple case of a plasma which is not too
inhomogeneous, not collision dominated, and not strongly magnetized.
(The assumptions mean that the Debye length is smaller than the gradient
length, the mean free path for collisions with neutrals, and the Larmor
radius.) Using arguments that are essentially equivalent to the physical
discussion above [1], one arrives at the so-called Landau collision term
which expresses the dynamical coefficients as
A = q~q~(ma + m(3) InA .!!....I-1-h C') d3 ,
a(3
47rc2m2m
av Iv-v'l (3v
v
o a
(3
q~q~lnA a2II-
_'I (-') 3'
Ba(3 = 4
2
2 a--
V -
V h· V d V .
7rcoma
VV
(3.164)
(3.165)
The parameter A in these equations is the Coulomb ratio defined above. Its
appearance under the logarithm makes it insensitive to small alterations; it is
customary to replace In A in calculations by a value averaged over all species
and spatial locations (or, even more drastically, to set it equal to 10 for low
temperature plasmas and equal to 20 for fusion applications). The Coulomb
interaction terms then become exactly bi-linear. Balescu [1] proposes the
value
InA = In 67rco(Te + TJAo .
qeqi
(3.166)
As the elastic collisions, Coulomb interactions conserve particle number,
momentum, and energy. The first property holds for each species separately;
the latter two follow again from the anti symmetry of the exchange of
momentum and energy between the species,
n(3a = I
(f(3lfa)cb,(3a d3v = 0
ha = I
mrv(f(3lfa)cb,(3a d3v
= q~q~ InA ma+m(3 II v - v' J; (V)h (v') d3vd3v
47rc6
mam(3
Iv - v'I3 a
(3
=-ha
e(3a = J
~ mrv 2 (frlfs) cb,(3a d3v
= qaq(3 n
m(3v - maV
~ m:; - m(3 vv fa (v)f(3(v') d3vd3v
2 2 1 A II
-,2
-2
(
) --,
47rc6
mam{3lv - v'I3
(3.167)
(3.168)
(3.169)
--- Page 131 ---
116
Kinetic Description of Plasmas
Having discussed in some detail the propagation and interaction terms of
particles and photons, we can assemble them to the final forms of the kinetic
equation and the radiation transport equation. The terms Land G are the
building blocks of the few-body collision terms of the kinetic equations.
For a given species s, all loss terms (all instances where the particle appears
as an educt) must be added with a negative, all gain terms (appearances of s
as a product) with a positive sign. Summing over all processes (under restora-
tion of the index P) , one gets
(f)el,s + (f)in,s = L
GiPl(iJ) -
L
LiPl(iJ).
(3.170)
processes
processes
For neutral particles, the kinetic equation is thus
(3.171)
For charged particles, the action of the electromagnetic field and the
Coulomb collisions have to be taken into account, so that their equation
reads
afa + iJ. afr:, + (i + ~
(if + iJ x jj)) . 8/r:,
~
&
rna
~
= L
GiPl(iJ) -
L
LiPl(iJ) + L(f/3lfa)cb,/3a'
processes
processes
/3
(3.172)
Similarly, the emission and absorption terms are building blocks of the
radiation transport equation. All appearances of the photon as an educt
count as absorptions; all appearances as a product contribute to the
emissions. They are added corresponding to the rule
(3.173)
processes
processes
The particle production densities of all species are identical, up to the sign
which is negative for educts (losses) and positive for products (gains). This
reflects the conservation of chemical identity known as Dalton's law,
·L
·G
.
-nrk = nSl = n.
(3.174)
From the arguments of the delta functions embodied in the scattering prob-
ability P in (3.87), one can deduce the balance laws of momentum and
energy. Momentum is strictly conserved, energy only when the internal
contributions are included:
(3.175)
--- Page 132 ---
Evaluation and Simplification of the Kinetic Equation
117
(fel'l + te¢l) -(terk
+ teVJI) = (fEl'l -tErk)n. (3.176)
1=1
1=1
k=1
1=1
1=1
k=1
Adding all terms, we can finally state that the plasma as a whole obeys the
conservation rules of particle number, momentum and energy.
3.4 Evaluation and Simplification of the Kinetic Equation
Reviewing the material of the preceding sections, the reader might get the
impression that kinetic theory is a mathematical construction of over-
whelming complexity. This impression is true: as coupled sets of nonlinear
integro-differential equations in 6 + 1 dimensions, coupled to another
system of partial differential equations (Maxwell's), kinetic models are
indeed difficult to solve, both analytically and numerically. For all but the
most simple situations, exact solutions will remain elusive in the foreseeable
future. (This statement also applies to particle-in-cell simulations, which are
sometimes referred to as stochastic solutions of the kinetic equation: they
only provide satisfactory results under very limited conditions.)
In this situation, why bother with kinetic theory at all?
To this (rhetorical) question, there are basically two answers. The first
one was already given above: kinetic theory provides a general conceptual
framework, i.e. a formalism in terms of which (nearly) all relevant plasma
phenomena, in particular non-equilibrium features, can be understood. In
the last analysis, the underlying reason for the wide applicability of kinetic
theory lies in the fact that its sole assumption is met in (nearly) all plasmas
of practical interest: the particles in low temperature plasmas are weakly
bound, and their average potential energy is much smaller than their thermal
energy. The one-particle distribution function thus captures the essence of
the dynamics; higher order correlations are not of importance.
Other frameworks, like the one-particle picture, fluid dynamics, or the
traditional drift-diffusion model, are much more limited than kinetic
theory. Accordingly, kinetic argumentations have become very popular in
recent years. It has even been stated that 'all plasma physics must be reformu-
lated kinetically' [8].
The second possible answer to the rhetorical question will occupy us for
the rest of this section: kinetic theory, even if it is 'unsolvable' itself, forms the
foundation of simpler plasma models which are accessible to solution or
simulation. These simplified models can be formally derived from kinetic
theory, but, of course, only by invoking certain additional assumptions or
neglections. The derived descriptions are thus less general and less accurate
than the original kinetic model. Several such descriptions are available
--- Page 133 ---
118
Kinetic Description of Plasmas
which differ in their level of accuracy and complexity; choosing the right one
requires physical judgement and insight into the situation.
This is not the place to give a systematic overview of all the different
derived plasma descriptions and their relation to the underlying kinetic
theory. Some important examples, however, may serve as an illustration of
the various possibilities and the typical arguments that are employed.
One important class of model simplifications arises when symmetry
arguments can be invoked. Invariance with respect to time leads to steady
state situations. Invariance with respect to a spatial direction may appear as
Cartesian or cylindrical symmetry, reducing the distribution function in suit-
able coordinates to the formf = f(x,y, vv, vy, vz , t) or f = f(r, z, v" v¢' vz , t).
(Often stated as 'the kinetic description is reduced to 2d3vlt dimensions'.)
Two simultaneous spatial symmetries are also possible; they reduce the
kinetic description to 1d2vlt dimensions. A frequent example is planar
symmetry, where the distribution function turnsf = f(x, vx , V.l, t). Spherical
symmetry withf = f(r, v" V.l, t) is rare. The assumption that three invariant
directions exist is equivalent to assuming spatial homogeneity. In this case,
the distribution function reduces to Od2v1 t dimensions, i.e. to the form
f = f(vlI' V.l, t), where the notions II and ..1 refer to the direction of the
electrical field. (Note that these dimensionality arguments have implicitly
assumed that the magnetic field B is weak; magnetized plasmas require a
more elaborate discussion.)
Another important class of simplifications deserves discussion. It arises
when the components of the kinetic equation can be separated into groups of
different magnitude (which in the following will be termed the 'dominating
interaction' and 'a small perturbation'). Under certain conditions, the
resulting dynamics assumes a characteristic two-phase structure, where the
dominating interaction induces a 'violent relaxation' on a fast time scale,
which is followed by a perturbation-induced 'secular evolution' on a slow
time scale. Frequently only the latter phase is of physical interest, and it is
generally possible to describe it by a reduced model which is both mathema-
tically and conceptually simpler than the original kinetic equation.
The classic example, of course, concerns the dynamics of a neutral gas,
for which it is often possible to replace the gas kinetic description by the
simpler Navier-Stokes equations. (See, e.g., [10].) For low temperature
plasmas, a similar reasoning is possible, when one excludes the electrons
and restricts oneself to the heavy particles (ions and neutrals). In this
subsystem, one finds that the frequency of the elastic (two-body) collisions
is typically much larger than the frequency of all other events, such as
chemical reactions, electron-induced ionization and excitation, or recombi-
nation. The collision terms of the heavy particle kinetics can be therefore
split into two separate groups, the dominant elastic interaction and the
inelastic perturbation, with the corresponding collision frequencies Vel and
Vin' related by Vel » Vin. Also the laminar parts of the kinetics are accounted
--- Page 134 ---
Evaluation and Simplification of the Kinetic Equation
119
for under 'perturbation', implying that scale lengths are large against the
elastic mean free path Ael.
The violent relaxation phase in this situation takes place on the time
scale "-'vci1, where the elastic collisions are dominant and the perturbation
interaction is negligible. Boltzmann's H-theorem states that under these
conditions the particle system relaxes into local thermodynamic equilibrium,
i.e. it maximizes its local entropy under the constraints of particle number,
momentum and energy. Correspondingly, all heavy particle distributions
become close to local Maxwellians,
(
( ~
~)2)
~ ~
fast
ns
ms V - u
fs(r, V, t) ===}
3/2 exp -
2
.
(2rrT Ims)
T
(3.177)
The open parameters in these expressions, the fluid dynamic variables n,
(particle species density), U (common speed), and T (common temperature),
are arbitrary but slowly varying functions of 1. (Abitrary means that they are
not determined by the relaxation process but formally enter as its initial
conditions; slowly varying refers to the implicit assumption that their gradi-
ents are small compared to the mean free path Ael.) Physically, of course, the
fluid variables are not arbitrary; they just evolve on the time scale "-'Vi;l. The
equations which determine this secular evolution are referred to as the fluid
transport equations; after some algebra they assume the form of coupled
partial differential equations for ns, T, and u. They are, in fact, formally
similar to the moment equations discussed in section 3.3 (summed over the
species index s if applicable):
ans
~n.
8t + \7. rs = ns
ap
M
C ~
~
~
at + \7 . II = p if + P E + j x B
ae
~e
~ ~
~ -:'
.
at+\7·r =g·p+E·j+e.
(3.178)
(3.179)
(3.180)
The equations, however, are now closed. In particular, the fluxes f;, II, and
fe can be calculated from the gradients of n" T, and u. (The terms lis and e
contain interactions with the electrons. Their evaluation requires, of course,
knowledge about the distribution fe.) Details of the related algebra can be
found in reference [7]. Strictly speaking, the resulting fluid dynamic transport
theory leaves the realm of kinetic modeling and thus lies beyond the scope of
this section.
A second important application of the relaxation/evolution scenario
concerns the plasma electrons. Unlike heavy particle transport theory, the
resulting reduced model stays kinetic and shall be outlined here in more
detail. The argument starts again from a physically motivated separation
of the terms of the kinetic equation into two groups. Under typical
--- Page 135 ---
120
Kinetic Description of Plasmas
conditions, the predominant interaction of the electrons is elastic scattering
at neutrals. Because of the small mass ratio me/mN and the small thermal
speed of the neutrals, this process is much more likely to change an electron's
direction v/v than its speed v = IVI. Accordingly, the dominating interaction
is that of a pure isotropization, mathematically described as
) J
dVel (I ~I-;:"
J
dVel
(~)
Ue el = dr/;' v e J dO -
dO dO Ie v .
(3.181)
The residuum of the approximation me « mN and all other collision terms
are grouped into an inelastic collision term Ue)in' This term is viewed as a
perturbation; its absolute value is considered small compared to the elastic
scattering frequency Vel>
(3.182)
Also the laminar contributions to the kinetic equation must be small. This
requires the gradients to be small compared to the inverse mean free path
). = Vth/Vel> and the electrical field compared to Te/e).:
Iv, ~
I « vetfe
(3.183)
I ;e E. Z; I « vetfe·
(3.184)
The scaling conditions (3.182)-(3.184) determine the absolute magnitude of
the perturbation terms (with respect to the elastic collisions), but not their
relative magnitude (with respect to each other.) This still leaves some
ambiguity, and, in fact, different 'regimes' are possible which arise from
subtle differences in the relative scaling of the perturbations. A particularly
simple regime-suited for many applications-results from the assumption
that the inelastic collisions are comparable with laminar terms that are quad-
ratic in the gradients or fields. These scaling assumptions can be conveniently
expressed by ordering the kinetic equation as follows, with E being a formal
smallness parameter (of value unity) to indicate the size of the respective
terms:
ofe
~ We
e
~ ofe
()
2 (
)
~+EV' fl~-E-E. fl~= fe el+ E Ie in'
vt
vr
me
vV
(3.185)
Obviously, the dynamics separates indeed again into a fast relaxation and a
slow evolution phase. The relaxation takes place on a time scale vcl"l and
involves only the action of the elastic conditions. It leads to an angular
isotropization of the initial distribution:
I' (~~ ) fast I' (~
) -
I J (~ I ~~, ) 2
,
Je r, V, t ===} JO r, V, t = 47r fife r, vie, t dO.
(3.186)
--- Page 136 ---
Evaluation and Simplification of the Kinetic Equation
121
To focus on the subsequent slow evolution phase (which acts on a scale '"'-'c2),
we introduce the substitution t -----+ c-2t and write the kinetic equation
2 ofe
~ ole
e
oj~ ()
2 (
)
()
c --;:;- + cV'
"'~ - c-E· "'~ = fe el + c fe in-
3.187
vt
vr
me
vV
This equation can conveniently be treated by means of a power expansion.
We write all quantities as power series with respect to the formal smallness
parameter c,
ex;
j~(f, 11, t) = L cnf(f, 11, t)
(3.188)
11=0
x
E~(~ ~) '"' nE~(I1)(~ ~ )
r, v, t = ~
c
r, v, t
(3.189)
11=0
and compare the coefficients of (3.187) in powers of c. This procedure leads
to an infinite hierarchy of equations, out of which we need only the first three:
0= (fO)el
(3.190)
~ ofo
e
~ ofo
V· --::;-:; - -Eo' "'~ = (fl)el
vr
me
vV
(3.191)
(3.192)
The first of these equations contains only the information thatfo is isotropic;
this was already expressed in (3.186). The second equation can be solved
explicitly as
fl = -~ (11. o~ _ ~Eo' f)~)
Vm
or
me
OV
(3.193)
where Vm is the momentum transfer frequency defined as
vm(v) = J(1-cose)':;~I(v,1'J)dO.
(3.194)
From equation (3.192) only the angular average is used. Applying f dO on
it and utilizing all previous information directly leads to the desired closed
evolution equation for fa,
2
~
ofo _ \7. (~\7fo _ veE . of 0)
at
3vm
'
3vmme
OV
~
2 ~2
1 a 2 (veE
.
e E
ofo )
.
-2:- v --_·\7jO+--2-
=(JO)in-
V OV
3vmme
3vmme OV
(3.195)
Under slightly different assumptions-particularly suited for the analysis ofrf-
driven plasmas-one can directly employ the so-called two-term-expansion
--- Page 137 ---
122
Kinetic Description of Plasmas
f (v) ~ fo ( v) + II (v) . VI v to get
8fo+!v"V.f1 -!~~~(v2E·f) = (fO)in
8t
3
3 me if 8v
_I
(3.196)
811
e ~ 8fo
~
-+v"Vfo --E-= -Vmfl'
8t
me
8v
(3.197)
Apart from the two examples given above, other utilizations of the general
ideas are also possible. In particular, one can systematically expand the
distribution function into spherical harmonics,
00
1
!e(r,v) -=!e(r,v,e,cf;) = L L fim(r,V)Ylm(e,cf;).
(3.198)
1=0 m=-I
Formally, this procedure requires no assumptions on the gradients or the
fields, but the series only converges quickly when the conditions (3.182)-
(3.184) are met.
The various reduced kinetic theories have in common that they formu-
late equations (or systems of equations) for functions of r, v, and t. In other
words, they are generally of 3d1vlt dimensions. Compared to the original
kinetic equation which was of type 3d3vlt, the numerical effort is hence
reduced by two dimensions. Assuming for example that 100 grid points are
necessary to resolve a velocity axis properly, one can estimate that the
amount of storage is reduced by a factor of 104. (The numerical effort,
which scales nonlinearly, is probably reduced even more.)
The efficiency gained by switching from the original to a reduced kinetic
theory thus is dramatic. Particularly when combined with other methods of
reducing the numerical effort, it can bring the kinetic models into the range of
today's computers. Reviewing the current literature, it seems, for example,
that mathematically three-dimensional problems have become sufficiently
easy to handle. Reduced kinetic models are now studied for time dependent
situations with planar or spherical geometry (ldlvlt), or for steady state
situations with cylindrical or Cartesian symmetry (2d1 vOt). Particularly
when combined with appropriate transport models for the heavy species,
such reduced kinetic descriptions can be used as powerful tools to analyze
and simulate situations with high physical and technical complexity. A
good overview over this exciting development and many references can be
found in [6].
References
[1] R Balescu 1988 Transport Processes in Plasmas (Amsterdam: North-Holland)
[2] ME Barone and D B Graves 1966 Plasma Sources Sci. Technol.5 187
--- Page 138 ---
References
123
[3] H Deutsch, K Becker, R K Janev, M Probst and T D Mark 2000 J. Phys. B Letters 33
865
[4] A Kersch and W J Morokoff 1995 Transport Simulation in Microelectronics (Basel:
Birkhauser)
[5] M A Lieberman and A J Lichtenberg 1994 Principles of Plasma Discharges and
Material Processing (New York: Wiley)
[6] D Loffhagen and R Winkler 2001 J. Phys. D: Appl. Phys. 34 1355
[7] M Mitchner and Ch Kruger 1973 Partially Ionized Gases (New York: Wiley)
[8] L Tsendin 1999 private communication
[9] K-U Riemann 1991 J. Phys. D: Appl. Phys. 24491
[10] L Waldmann 1958 Handbuch der Physik Bd XII, Transporterscheinungen in Gasen von
mittlerem Druck (Berlin, G6ttingen, Heidelberg: Springer)
[11] NIST Online Data Base Electron-Impact Cross Sectionsfor Ionization and Excitation
http://physics.nist.gov/PhysRetData/Ionization/index.html.
--- Page 139 ---
Chapter 4
Air Plasma Chemistry
K Becker, M Schmidt, A A Viggiano, R Dressler and S Williams
4.1
Introduction
In a thermal plasma, all three major plasma constituents (electrons, ions,
neutrals) have the same average energy or 'temperature' and for polyatomic
species the rotational, vibrational and translational temperatures are in equi-
librium. The temperature of thermal plasmas may range from a few thousand
Kelvin (e.g. for plasma torches) to a few million Kelvin (in the interior of
stars or in fusion plasmas). In contrast, non-thermal or cold plasmas are
characterized by the fact that the energy is preferentially channeled into
the electron component of the plasma and/or vibrational non-equilibrium
of the polyatomic species. In non-thermal plasmas, the electrons may be
much hotter (with temperatures in the range of tens of thousands up to a
hundred thousand Kelvin) than the ions and neutrals, whose translational
temperatures are essentially equal and typically range from room tempera-
ture to a few times the room temperature. Non-thermal plasmas thus
represent environments where very energetic chemical processes can occur
(via the plasma electrons) at low ambient temperatures (defined by the
neutrals and ions in the plasma).
The processes that determine the properties of non-thermal plasmas are
collisions involving the plasma electrons and other plasma constituents.
Tables of relevant collision processes can be found in chapter 3 of this
book. Electron collisions are particularly important because of the high
mean energy of the plasma electrons. Ionizing collisions and, in molecular
plasmas, dissociative electron collisions are of particular relevance. Ionizing
collisions determine the charge carrier production by (i) direct ionization of
ground state atoms and/or molecules in the plasma and by (ii) step-wise ion-
ization of an atom/molecule through intermediate excited states. Ionization
of ground state atoms/molecules, which have a high number density in the
plasma, requires a minimum energy which is (for most species) above
124
--- Page 140 ---
Introduction
125
10 eV. Thus, only the high-energy tail of the electron energy distribution
function is capable of contributing to this process. Even though the density
of metastable species in a plasma is typically much smaller than the ground-
state density, the ionization cross section out of a metastable state is much
larger than the ground-state ionization cross section and the energy required
to ionize a metastable atom or molecule is much smaller than the ground-
state ionization energy. As the number of low-energy electrons is typically
much larger than the number of electrons with energies above 10 e V (see
above), stepwise ionization processes can contribute significantly to the
ionization balance in a non-thermal plasma.
The generation of chemically reactive free radicals by electron impact
dissociation in molecular plasmas is an important precursor for plasma
chemical reactions. As an example, fluorocarbons such as CF4 and C2F6
are comparatively inert and will not react per se with Si or Si02 • Etching
of these materials in plasmas containing fluorocarbon compounds in the
feed gas proceeds via F and CF x radicals formed in the plasma by dissoci-
ation of the parent molecules by the plasma electrons.
As discussed in detail in the previous chapter, the probability for a
particular electron collision process to occur is expressed in terms of the
corresponding electron-impact cross section CT, which is a function of the
energy of the electrons. All inelastic electron collision processes have
minimum energies (thresholds) below which the process is energetically not
possible. In plasmas, the electrons are not mono-energetic, but have an
energy or velocity distribution, f(E) or f(v), where E and v refer to the
energy and velocity of the colliding electron, respectively. In those cases, it
is convenient to define a rate coefficient k for each two-body collision process
k(v) = J
CT(v)vf(v) dv
(4.1.1 )
where CT( v) denotes the corresponding velocity dependent cross section. In
principle, the velocity v in equation (4.1.1) refers to the relative velocity
between the two colliding particles. As the electron velocity is much larger
than the velocity of the heavy particles (which are essentially at rest relative
to the fast moving electrons), the quantity v in (4.1.1) is nearly identical to the
electron velocity. Sometimes it is more convenient to express the rate coeffi-
cient as a function of electron energy E. As discussed in chapter 3, realistic
electron velocity/energy distribution functions exhibit complicated shapes.
The concept of a rate coefficient is used in a similar fashion to describe
reactive collisions between the randomly moving heavy particles, where the
reaction probability is determined by the relative velocity between the
colliding heavy particles. At equilibrium conditions, the velocity distribution
is determined by the heavy-particle temperature, T, and the temperature
dependence of the rate coefficient can be described by an Arrhenius law.
However, equilibrium models of chemical kinetic systems depend on rate
--- Page 141 ---
126
Air Plasma Chemistry
coefficients which are usually given by a modified Arrhenius dependence on
temperature:
(4.1.2)
where A is a scaling parameter, Ea is the chemical reaction activation energy,
kB is the Boltzmann constant, and n is a curvature parameter describing the
growth of the rate coefficient with temperature.
The time scales of the processes in a reactive plasma span a wide range
(Eliasson et al 1994). Electron-induced processes such as excitation and
ionization occur in the range of picoseconds or less. The electron energy
distribution function reaches equilibrium with the externally applied electric
field also within picoseconds (Eliasson et aI1994). Electron-induced dissoci-
ative ionization and dissociation processes, in which the molecular target
breaks up, take nanoseconds to micro-seconds. At atmospheric pressure,
the time scale for chemical reactions involving ground-state species is in
the range from milliseconds to seconds, while the free radical reactions
occur in the range between micro-seconds and milliseconds.
The atmospheric-pressure air plasmas that are the subject of this book
are weakly ionized. Their degree of ionization, a, defined as
(4.1.3)
where ne and no denote the density of respectively the plasma electrons and
the plasma neutrals, is of the order of 10-5, that is only one in every
100000 plasma neutrals is ionized. The degree of dissociation is typically
significantly higher. Despite the low degrees of ionization, both neutra1-
neutral and ion-neutral processes are important processes in the plasma
chemistry of weakly ionized, non-thermal molecular plasmas. Equation
(4.1.3) assumes that negative ions do not contribute significantly to the
total number of negative charge carriers, which may not be true in air
plasmas; in that case equation (4.1.3) must be modified to include negative
ions.
In the following sections, we will summarize the state of our current
knowledge of the most important plasma chemical reactions in atmos-
pheric-pressure air plasmas for both reactions involving only neutral species
(,neutral air plasma chemistry') and ionic species ('ionic air plasma chem-
istry'). In section 4.2, we discuss reactions of neutrals. As there is a larger
number of such reactions, we will not discuss selected reactions in great
detail, but rather give a survey summarizing the most important reactions
between neutrals in terms of their known reaction rate coefficients and, to
the extent available, the temperature dependence of the reaction rates. In
the case of ion-molecule reactions in high-pressure air plasmas, the
number of processes that have been studied extensively is much smaller
and we will cover those reactions in more detail in section 4.3. Section 4.4
discusses the challenge of modeling non-equilibrium air plasma chemical
--- Page 142 ---
Air Plasma Chemistry Involving Neutral Species
127
systems where the relative velocity distributions of heavy-body collisions
is not described by a temperature. Dissociative recombination, a principal
electron loss mechanism, is discussed in section 4.5.
4.2 Air Plasma Chemistry Involving Neutral Species
4.2.1
Introduction
Chemical reactions in an air plasma are initiated by electron impact on the
main air plasma constituents N2 and O2, Electron-driven processes with
N2 and O2 include
e-+X2 -
Xi +e-
(4.2.l.1a)
e- +X2
X+X+e-
(4.2.l.1b)
e- +X2
X*+X+e-
(4.2.l.1c)
e- +X2 - xi +2e-
(4.2.l.1d)
e- +X2
xi* + 2e-
(4.2.l.1e)
e- +X2
x+ +X+2e-
(4.2.1.1f)
e- +X2
x+ +X* + 2e-
(4.2.l.1g)
e- +X2
x-+x
(4.2.l.1h)
e-+X2+M
X2+M
( 4.2.l.1i)
(X: N2, O2; the asterisk denotes an excited state, which may be short-lived or
metastable.)
We note that reactions (4.2.l.1h) and (4.2.l.1i) involve primarily O2 as
N2 is not an electronegative gas. Furthermore, a third body 'M' is required in
reaction (4.2.l.li) in order to satisfy energy and momentum conservation
simultaneously. The most recent compilation of measured electron impact
cross sections for the molecules N2 and O2 as well as for the atoms Nand
o and for the most important molecular and atomic reaction products and
impurities in air plasmas (H20, CO2, CO, CH4, NO, N02, N20, 0 3, H, C,
Ar, ... ) can be found in the compilations of Zecca and co-workers (Zecca
et al 1996, Karwasz et al 200la,b). For subsequent chemical reactions,
ground-state neutrals and ions are important, as are electronically excited
species in low-lying states that are metastable. Short-lived excited species
that can decay radiatively via optically allowed dipole transitions on a time
scale of nanoseconds do not have a sufficiently long residence time in the
plasma to contribute significantly to the plasma chemical processes (even
--- Page 143 ---
128
Air Plasma Chemistry
though at atmospheric pressure their lifetime may become comparable to the
inverse collision frequency, in which case their reactivity must also be consid-
ered). In the case of molecular species, rotational and vibrational excitation
of the reactants can have a profound effect on the reaction pathways and
reaction rates of these species, as will be discussed in more detail later.
Several extensive compilations of gas phase processes relevant to air plasmas
have been published since 1990 including those by Matzing (1991), Kossyi
et al (1992), Akishev et al (1994), Green et al (1995), Herron (1999), Chen
and Davidson (2002), Herron and Green (2001), Herron (2001), Stefanovic
et al (2001), and Dorai and Kushner (2003) (see also the NIST Chemical
Kinetics Database, version 2Q98 (NIST Chemkin) and the online version
(NIST index».
4.2.2 Neutral chemistry in atmospheric-pressure air plasmas
This section deals with plasma chemical reactions in atmospheric-pressure
air plasma that involve only neutral species. Processes involving ions will
be discussed in subsequent chapters. Neutral chemistry and ion chemistry
are connected through ion recombination processes in the gas phase or at
surfaces as well as dissociative and associative ionization processes. A
complete summary of all chemical reactions in an air plasma cannot be
given here, because there are simply too many possible reactions. Thus, we
will limit the discussion in this section to what we believe are the most impor-
tant reactions. For a more detailed discussion of the various other chemical
reactions we refer the reader to the above-mentioned original references
including the NIST database. The examples presented here are limited to
reactions involving oxygen and nitrogen atoms and molecules, ozone, and
the NOx reaction products. Table 4.1 lists the most important low-lying,
Table 4.1. Low-lying metastable states ofN2, O2, N, and 0 (Radzig and Smirnov 1985).
Species
State
Energy (em-I)
Energy (eV)
N2
A3~~
50203.6
6.22
N2
B3IIg
59618.7
7.39
N2
a'l~;;-
69152.7
8.57
N2
C 3IIu
89136.9
11.05
O2
a l.6.g
7928.1
0.98
O2
bl~+
13195
1.64
2 og
N
D5/2
19224.5
2.384
N
2D O
19233.2
2.385
3/2
N
2pO
28839.9
3.576
1/2
0
ID2
15867.9
1.967
0
ISO
33792.6
4.190
--- Page 144 ---
Air Plasma Chemistry Involving Neutral Species
129
long-lived energy levels of the neutral species (N2' 02, N, and 0) relevant to
the neutral chemistry in air plasmas (Kossyi et aI1992) in terms of the energy
required for their formation via electron collisions (Radzig and Smirnov
1985).
The electron impact dissociation of nitrogen and oxygen molecules into
the reactive atomic radicals is an important step for the initiation of chemical
processes. The electron impact neutral dissociation of N2 requires a higher
minimum energy as the dissociation of 02 (Cosby 1993a,b, Stefanovic et al
2001). Furthermore, the 02 dissociation cross section in the low energy
range is significantly higher than that for N2 (Cosby 1993a). For instance, at
an electron energy of 18.5 e V, the neutral 02 dissociation cross section has a
value of 52.9 x 10-18 cm2 (Cosby 1993b) compared to 17.4 x 10-18 cm2 for
N2 (Cosby 1993a). However, both neutral dissociation processes are important
in the initiation of the neutral air plasma chemistry. We note that the dissoci-
ative electron attachment to 02 leading to the formation of 0- + 0 has a
threshold near 5 e V and a maximum cross section of about 1.5 x 10-18 cm2
around 7 eV. Even though this cross section is comparatively low, the process
is quite effective because of the higher electron density in this energy range
compared to the energy required for neutral dissociation. Non-dissociative
attachment to 02 leading to the formation of 02 (in the presence of a third
collision partner) occurs for electron energies near 0.1 eV (Christophorou
et aI1984).
Figure 4.1 presents schematically the main plasma chemical reaction
pathways in an air plasma starting with the electron-driven reactions
and at higher electron energies
N2 +e-
0i +e-
O+O+e-
O*+O+e-
0-+0
02+ M
Ni +e-
N +N +e-
N* +N +e-
(4.2.2.1a)
(4.2.2.lb)
( 4.2.2.1c)
(4.2.2.ld)
(4.2.2.le)
( 4.2.2.2a)
(4.2.2.2b)
(4.2.2.2c)
(where the asterisk denotes one of the low-lying excited states listed in table
4.1), which are followed by the neutral heavy particle processes:
(4.2.2.3a)
(4.2.2.3b)
--- Page 145 ---
130
Air Plasma Chemistry
N20 S
Figure 4.1. Schematic diagram of the primary chemical reactions in an air plasma (dry air)
following electron impact on N2 and 02' Only the formation reactions up to the formation
of N 20 5 are shown.
It is interesting to note that reactions involving ground-state and excited
species can have rate coefficients that differ by orders of magnitude. For
instance, the rate coefficient of reaction (4.2.2.3a) involving an excited N
atom has a value of 5 x 10-12 cm3/s (see table 4.5), whereas the rate coeffi-
cient for the corresponding ground state reaction is 7.7 x 10-17 cm3/s (see
table 4.3). The required activation energy for the reaction involving the
excited particle is lowered by the potential energy of the excited reaction
partner (Elias son and Kogelschatz 1991).
4.2.3 Summary of the important reactions for the neutral air plasma
chemistry
The following tables summarize the most important neutral chemical reac-
tions in an air plasma starting with two-body reactions involving 0 atoms
(table 4.2) and N atoms (table 4.3) in the ground states. Table 4.4 presents
three-body reactions involving ground-state species. Reactions with elec-
tronically excited species are presented in table 4.5 and in table 4.6 reactions
are listed involving ozone molecules. To the extent known from the
literature, we also list the temperature dependence of the rate constants.
For the three-body reactions, the rate constants are given as the product of
the temperature-dependent part and the gas density per cm3 (of the 'third'
body) at atmospheric pressure. This facilitates a meaningful comparison of
these rate coefficients with rate coefficients for two-body reactions. All rate
constants are given in units of cm3/s except for the data for three-body
--- Page 146 ---
Table 4.2. Ground-state, two-body reactions involving 0 atoms.
Reaction
0+03 ~
O2 +02
0+N02 ~
O2 +NO
o + N03 ~
O2 + N02
0+ N20 3 ~
products
0+ N20 5 ~
2N02 + O2 ~
products
k298
(cm3 mol- I S-I)
8 X 10- 15
9 X 10-12
1.7 X 10-11
1.0 X 10- 11
::::3 x 10- 16
1.0 X 10- 16
<3 X 10- 16
Temperature dependence
k(T) (cm3 mol- 1 S-I)
2.0 X 10- 11 exp( -2300/T)
8.0 x 10- 12 exp( -2060/T)
1.9 x 10-11 exp(-2300/T)
6.5 x 10- 12 exp(120/T)
5.6 x 10-12 exp(180/T)
1.13 x 1O- II (T/1000)OI8
5.21 x 1O- 12 exp(+202/T)
Temperature
range (K)
200-400
250-350
Reference
Kossyi et al (1992)
Herron and Green (2001)
Akishev et al (1994)
Herron and Green (2001)
Chen and Davidson (2002)
Kossyi et al (1992)
Matzing (1991)
Herron and Green (2001)
Chen and Davidson (2002)
Akishev et al (1994)
Herron and Green (2001)
Chen and Davidson (2002)
Kossyi et al (1992)
~
:;;.
""0
r::;-
'"
31
;::,
(J
;::-
'"
31
~.
~
~
'"
0 "-'"
S·
I)q
~
:s.
....
;::,
"-
~
'" '"'
Cli'
'"
......
w
--- Page 147 ---
Table 4.3. Ground-state, two-body reactions involving N atoms.
Reaction
k298
(cm3mol-1 S-I)
N+02 -
NO+O
7.7 x 10- 17
N +03 -
NO+02
5.7 x 10-13
:s: 2 x 10-16
N +NO -
N2 +0
3.2 X 10- 11
N+N02 -
N2O+O
1.2 x 10- 11
N + NOz -
NO + NO
2.3 X 10-12
N + N03 -
NO + N02
3 X 10-12
N + N02 -
N2 + 0 + 0
9.1 X 10-13
Temperature dependence
k(T) (cm3mol-1 S-I)
4.4 x 1O- 12 exp(-3220/T)
5 x 1O-12 exp(-650/T)
3.4 X 10- 11 exp(-24/T)
5.8 x 1O-12 exp(-220/T)
Reference
Dorai and Kushner (2003)
Stefanovic et at (200 I)
Herron (2001)
Dorai and Kushner (2003)
Herron and Green (2001)
Kossyi et at (1992)
Herron and Green (2001)
Kossyi et at (1992)
.......
w
tv
~
::;.
i
I:l
Q
~
1::;'
~
--- Page 148 ---
Table 4.4. Ground-state three-body reactions.
Reaction
k300 *
Temperature dependence
Temperature
Reference
(cm3 mol-1 S-I)
k(T) *
range (K)
O+O+M-Oz+M
9.8 x 10-14
4.5 X 10-34 exp(630/T) [Nz1
200-400
Herron and Green (2001)
O+N+M-NO+M
2.7 x 10-13
6.3 X 10-33 exp(140/T) [Nz1
200-400
Herron and Green (2001)
0+OZ+M- 0 3+ M
1.6 x 10-14
6.0 X 1O-34(T/300)-z.8 [Ozl
100-300
Herron and Green (2001)
0+OZ+M- 0 3+ M
1.5 x 10-14
5.6 X 1O-34(T/300)-z.8 [Nz1
100-300
Herron and Green (200 I)
0+ NO + M -
NOz + M
2.7 X 1O-1Z
I X 10-31 (T /300)-1.6 [Nz1
200-300
Herron and Green (2001)
0+ NOz + M -
N03 + M
2.4 X 1O-1Z
9.0 x 1O-3z(T /300)-z.0 [Nz1
200-400
Herron and Green (200 I)
N+N+M -Nz+M
1.2 x 10-13
8.3 x 1O-34 exp(500/T) [Nz1
100-600
Herron and Green (2001)
NO + NO + Oz -
NOz + NOz
3.3 X 10-39 exp(526/T)
Akishev et al (1992)
NO+NOz +M -
NZ0 3 +M
8.3 x 10-15
3.1 X 1O-34(T/300)-7.7 [Nz1
200-300
Herron and Green (2001)
NOz +NOz +M -
NZ0 4 +M
3.8 x 10-14
1.4 X 1O-33 (T/300)-3.8 [Nz1
300-500
Herron and Green (2001)
NOz +N03 +M -
NZ0 5 +M
7.4 x 10-11
2.8 X 1O-30(T/300)-3.5 [Nz1
200-400
Herron and Green (2001)
* The rate constants of Herron and Green (2001) are those in the low-pressure limit. The low-pressure third-order limit is characterized by a second-order
rate constant k300 = Af(T) x 2.68 x 1019 (cm3 mol- I s-l) (Herron and Green 2001).
~
~.
i
!:l
9
~
1:;'
~
~
~
c
~
~.
~
~
....
!:l -..
~
~
...,
~.
-
w
w
--- Page 149 ---
-"
w
.jO.
Table 4.5. Two-body reactions involving electronically excited species.
Reaction
k298
Temperature dependence
Reference
(cm3 mol-I S-I)
k(T) (cm3 mol- 1 S-I)
~
:::;.
OeD) +03 -
20+02
1.2 x 10- 10
Herron and Green (200 I)
'"i:l
is""
oe D) + 0 3 -
202(3~;-)
1.2 x 10-10
'"
Herron and Green (2001)
;::
OeD) + N20 -
2NO
7.2 x 10- 11
'"
Herron and Green (2001)
Q
Oe D) + N20 -
N2 + O2
4.4 X 10-11
Herron and Green (2001)
~
OeD) + N02 -
NO+02
1.4 x 10-10
;::
Herron and Green (200 I)
0:;'
NeD) +02 -
Oep, ID) +NO
5 x 10-12
1.0 X 10- 11 exp( -21O/T)
Herron and Green (2001)
~
NeD) +03 -
NO+02
1 x 10- 10
Herron and Green (2001)
NeD) +NO -
N2 +oep, I D , IS)
4.5 x 10- 11
Herron and Green (2001)
NeD) +N20 -
N2 +NO
2.2 x 10-12
1.5 X 10- 11 exp(-570/T)
Herron and Green (2001)
Nep) + O2 -
Oep, ID, IS) + NO
2 X 10-12
2.5 x 1O-12 exp(-60/T)
Herron and Green (2001)
02e L1g) + N -
NO + 0
::;9 X 10-17
Herron and Green (2001)
O2 e L1g) + 0 3 -
202 + 0
3.8 X 10-15
Herron and Green (2001)
02e~;-) + 0 3 -
202 + 0
2.2 X 10- 11
Herron and Green (2001)
N2(A3~n +02 -
N2 +20
2.5 x 10-12
5.0 X 10-12 exp( -210/T)
Herron and Green (2001)
N2(A 3~~) + 02e L1g) -
N2 + 20
<2 X 10- 11
Herron and Green (2001)
N2(A3~)+02 -
N2O+O
4.6 x 10- 15
Stefano vic et at (2001)
N2(A 3~~) + 0 3 _
N2 + O2 + 0
4.2 X 10- 11
Herron and Green (2001)
N2(A3~~) + N02 -
N2 +NO +0
1.3 x 10- 11
Herron and Green (2001)
--- Page 150 ---
Table 4.6. Reactions including 0 3, mainly two-body reactions.
Reaction
k300 (cm3mol-1 s-l)
Temperature dependence k(T)
Reference
0+ Oz + M -
0 3 + M
6.0 x 1O-34(T /300)-Z.8 [Oz]
Herron (2001 b)
0+ Oz + Oz -
0 3 + Oz
8.6 X 10-31 T-l. Z5
Stefanovic et at (2001)
O+Oz +M -
0 3 +M
5.6 x 1O-34(T /300)-Z.8 [Nz]
Herron and Green (2001)
0+ Oz + Nz -
0 3 + Nz
5.6 X 1O-z9 T-z
Stefanovic et at (2001)
N +03 -
NO+Oz
<2 x 10-16
Herron and Green (2001)
1 x 10-16
Chen and Davidson (2002)
I x 10-15
Akishev et at (1994)
0+03 -
Oz+Oz
8 x 10-15
8.0 X 1O-1Z exp( -2060/T)
Herron and Green (200 I)
1.9 X 10-11 exp( -2300/T)
Akishev et at (1994)
0+03 -
Oz(al~) + Oz
3 X 10-15
6.3 X 1O-1Z exp( -23QO/T)
Stefanovic et at (2001)
0+03 -
OZ(bl~) +Oz
1.5 x 10-15
3.2 X 1O-1Z exp( -2300/T)
Stefanovic et at (2001)
OeD) +03 -
Oz +20
1.2 x 10-10
Stefanovic et at (200 I)
Oe D) + 0 3 -
Oz + Oz
2.3 X 10-11
Stefanovic et at (200 I)
1.2 X 10-10
Akishev et at (1994)
Oe D) + 0 3 -
20ze~~)
1.2 x 10-10
Herron and Green (200 I)
OeD) +03 -
Oz(a1~) +Oz
1.5 x 10-11
Stefanovic et at (2001)
OeD) +03 -
Oz(b1~) +Oz
7.7 x 1O-1Z
Stefanovic et at (2001)
3.6 X 10-11
Akishev et at (1994)
Oe D) + 0 3 -
Oz(4.5) + Oz *
7.4 X 10-11
Stefanovic et at (200 I)
Oz(al~) +03 -
0 + Oz +Oz
4 x 10-15
5 X 10-11 exp( -2830/T)
Stefanovic et at (2001)
Oz(b 1~) + 0 3 -
Oz + Oz + 0
1.5 X 10-11
Stefanovic et at (200 I)
OZ(b1~) + 0 3 -
Oz(a1~) + Oz + 0
7 X 1O-1Z
Stefanovic et at (2001)
NO+03 -
NOz +Oz
1.8 x 10-14
1.8 x 1O-1Z exp(-1370/T)
Herron and Green (2001)
1.6 X 10-14
9 X 10-13 exp( -1200/T)
Stefanovic et at (200 I)
NOz + 0 3 -
N03 + Oz
3.5 X 10-17
1.4 x 1O-13 exp(-2470/T)
Herron and Green (2001)
3.4 X 10-17
1.2 X 10-13 exp( -2450/T)
Stefanovic et at (2001)
The rate constants of Herron and Green (2001) for the three-body reactions are the values in the low-pressure limit. See also table 4.4.
* Oz (4.5): Oz electronic levels near 4.5eV, Oz (c 1~, C3~, A 3~).
~
::t.
"t:I
i:S"'
~
!:l
Q
~
~
0; .
....
~
~
...: c -.
...: S·
~
~
:::: ....
....
!:l -.
~
~
'"'
~.
-
\.;.l
VI
--- Page 151 ---
136
Air Plasma Chemistry
reactions, which are in units of cm6/s. The results of modeling calculations
and simulations involving such processes, their rate coefficients, and the
temporal behavior of the concentrations of various chemically reactive
species and reaction products can be found in the paper by Kossyi et al
(1992) and to some extent also in other chapters in this book.
In addition to the gas-phase processes, heterogeneous processes such as
surface reactions should also be taken into account. Deactivation reactions
of excited particles as well as recombination processes of atomic species
and chemical reactions are important in this context. The reaction prob-
ability for a given process depends on the surface material and the state of
the surface in terms of its purity and temperature. In general, surface
processes at atmospheric pressure are less important than at lower pressure.
The modeling of a microwave atmospheric-pressure discharge in air (Baeva
et a12001) included the de-excitation ofN2 , O2, N, and 0 as well as the wall
recombination of 0 atoms. A comprehensive discussion of the chemical
reactions of the various air plasma components with a polypropylene
surface is given by Dorai and Kushner (2003) (see also chapter 9 in
this book). Other data for surface processes were given by Gordiets et al
(1995).
4.3 Ion-Molecule Reactions in Air Plasmas at Elevated
Temperatures
4.3.1
Introduction
Ion chemistry is a mature though continually evolving field. A wide variety of
techniques have been exploited to measure ion reactivity over a large range of
conditions (Farrar and Saunders 1988). In compilations of ion-molecule
kinetics, there are over 10 000 separate entries (Ikezoe et al 1987) and the
number of reactions studied continues to be impressive. This large body of
work has led to many insights into reactivity and numerous generalities
have emerged. In spite of the large number of studies, there are still several
areas of ion kinetics that are largely unexplored, one of which is the study
of ion-molecule reactions at elevated temperatures relevant to air plasma
conditions.
The vast majority of the work on ion-molecule kinetics has been
performed at room temperature (lkezoe et aI1987). Temperature dependent
studies have been mostly limited to the 77-600 K range. Outside of this
temperature range, significant technical difficulties are encountered, e.g. the
stability of materials and reactants at high temperature or condensation of
the reactant species at low temperature. Most of the effort to extend the
--- Page 152 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
137
temperature range has focused on low temperatures (Smith 1994) due to the
fact that many of the molecular species made in interstellar clouds are synthe-
sized by ion-molecule reactions at extremely low temperatures (Smith and
Spanel 1995). The techniques used to study low-temperature chemistry
have been quite successful and have provided good tests of theory, especially
with regard to ion-molecule collision rates (Adams et a11985, Rebrion et al
1988, Troe 1992).
In contrast, the number of studies made at high temperature (>600 K) is
very limited. Previous work on ion-molecule reactivity above 600 K was
performed in the early 1970s and was limited to temperatures of 900 K and
below (Chen et a11978, Lindinger et aI1974). The impetus for those studies
focused on reactions of the low density air plasma of the ionosphere that can
reach temperatures as high as 2000 K range (Jursa 1985). A further limitation
was that branching fractions could not be measured. Nevertheless, the tech-
nically challenging measurements provided useful and interesting data on
how temperature affected rate constants. However, the conclusions were
limited because only 10 reactions were studied in total.
The gap between the previous maximum laboratory operating tempera-
ture and relevant plasma temperatures was covered in other ways. In parti-
cular, the reactions were studied as a function of ion translational energy
in drift tubes and beam apparatuses (Farrar and Saunders 1988). This
allowed effective temperature dependencies to be calculated assuming trans-
lational energy, Et , was equivalent to internal, rotational and vibrational, in
controlling the reactivity (McFarland et aI1973a-c). As will be shown later,
this approach can lead to large errors although it was the only reasonable
way to extrapolate to higher temperature conditions at the time.
In high temperature air plasmas, most of the chemistry involves only
monatomic and diatomic ions and neutrals, and, therefore, very little vibra-
tional excitation is present at temperatures below 900 K due to the high
vibrational frequencies of the respective diatomic molecules or molecular
ions. Thus, the impact of both rotational and vibrational energy was not
seriously considered. One notable exception, however, was the reaction
(4.3.1)
For this reaction, a separate study on the vibrational temperature depen-
dence of the N2 reactant was made (Chiu 1965, Schmeltekopf et al 1968).
However, in that study both the ion center of mass (CM) translational
energy and the rotational temperature were 300 K. While this was an
obviously important step, no true temperature dependent study was made
over 900 K. Note that true temperature here refers to the case where the
translational, rotational, and vibrational degrees of freedom of the reactants
are in equilibrium and can be represented by a single temperature.
The lack of measurements over an extended temperature range was
one of several drivers leading to the development of a flowing afterglow
--- Page 153 ---
138
Air Plasma Chemistry
apparatus capable of reaching temperatures of 1800 K. This apparatus will
be hereafter referred to as the high temperature flowing afterglow (HTF A,
Hierl et al 1996). While ionospheric plasma chemistry was an important
driver for the development of the HTF A, there are other plasmas that require
accurate ion-molecule kinetic measurements at high temperature. Examples
include plasma sheathing around high speed vehicles during re-entry or
hypersonic flight, spray coating and materials synthesis, microwave reflec-
tion/absorption, sterilization and chemical neutralization, shock-wave miti-
gation for sonic boom and wave-drag reductions in supersonic flights, and
plasma igniters and pilots for subsonic to supersonic combustion engines.
In this section, high temperature air plasma; reactions studied to date are
discussed and compared to available results· from different experiments.
Most often the comparisons are between data taken in high temperature
flow tubes and drift tubes, but in certain cases comparisons are also made
to data taken in ion-beam experiments. The ensuing sections give a discus-
sion of the derivation of internal energy dependencies which allow the results
of different experiments to be compared. Then the results for relevant air
plasma reactions are presented.
The fate of an ion in an air plasma depends critically on whether it is
atomic or molecular. While atomic ions recombine slowly with electrons
through three-body recombination reactions (see table 4.1), molecular ions
undergo much more rapid dissociative recombination reactions. Conse-
quently, reactions that convert atomic ions such as 0+ and N+ to diatomic
ions, speed up recombination, and are therefore important in controlling
the ionization fraction of the plasma. Atomic ion reactions with N2, O2,
and NO are discussed first. While nothing inherently prevents negative ion
systems from being studied, relatively few reactions have been studied to
date. Of these negative-ion reactions, the temperature dependence of 0-
with NO and CO are discussed. As the number of atoms in a reaction
increases, the detailed derivation of how temperature affects the reactivity
becomes less clear, i.e. attributing the reactivity to a particular form(s) of
energy. The larger reaction systems discussed include Nt + O2, ot + NO,
Ar+ + CO2, and Nt with CO2 •
4.3.2 Internal energy definitions
The average reactant rotational energy, (Erot ), is !kBT for each rotational
degree of freedom, and the average reactant vibrational energy, (E~ibtral),
is an ensemble average over a Boltzmann distribution of vibrational energy
levels. The average translational energy, (Etrans), is ~kBT in flow tube
experiments and is the nominal CM collision energy in drift tube and ion
beam experiments.
In the HTF A all degrees of freedom are thermally excited by heating
the apparatus, i.e. the rotational, translational, and vibrational temperatures
--- Page 154 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
139
are in equilibrium. In a drift tube or beam apparatus, the translational
energy of the ion is increased by the use of electric fields. Fortunately, the
translational energy distribution in a drift tube operated with a Re buffer
gas can be approximated by a shifted Maxwellian distribution (Albritton
et al 1977, Dressler et al 1987, Fahey et al 1981a,b). The average trans-
lational energy can be converted to an effective translational temperature
by Et = ~ kB Teff and can be directly compared to the RTF A data since
the translational energy distributions are similar. The internal energy
dependence is derived by comparing data taken at the same translational
temperature or average energy but with the neutrals at different tempera-
tures. The internal energy dependence is most easily observed by plotting
the data as a function of translational energy or temperature. In this type
of plot, differences along the vertical, rate coefficient axis reflect the effect
of internal energy on reactivity. Comparison to beam data is done in the
same way but differences in translational energy distributions complicates
the analysis.
The analysis of atomic ions reacting with diatomic neutrals is relatively
straightforward. For most diatomics, little or no vibrational excitation
occurs below ca. 1000 K. Therefore, at lower temperatures, any internal
energy dependence is due solely to the rotational excitation of the reactant
neutral. To elucidate the energy effects further, it is useful to plot the data
as a function of average translational plus rotational energy, i.e. ~kBT.
For drift tube data at 300K, a constant value of kBT = 0.026eV is added
to the translational energy, and the average translational energy in the
RTF A is multiplied by i. As will be shown in the results section, plots of
this type often have the drift tube and RTF A data overlapping below
1000 K or 0.2 eV. This agreement suggests that rotational and translational
energy control the reactivity equally, at least in an average sense.
If rotational and translational energy are found to be equivalent at lower
temperatures, it is assumed that they are equivalent at higher temperatures
and that any differences between sets observed at higher temperatures are
due to vibrational excitation. In this case, the RTF A rate constants can be
written as
k = L pop(i) X k;
( 4.3.2)
where i represents the vibrational level, pop(i) is the fraction of the molecules
in the ith state, and k; is the rate constant (see equation (4.1.2)) for the ith
state. The populations of the various states can be calculated assuming a
Boltzmann distribution. Assuming all excited states react at the same rate,
the v 2: I rate constant can be extracted with the aid of equation (4.3.2). In
most cases, the derived v 2: I rate constant represents the v = 1 rate constant,
because even at the temperatures achieved in the RTF A, most of the vibra-
tional excitation is limited to v = 1. For some systems, either the RTF A or
--- Page 155 ---
140
Air Plasma Chemistry
drift tube data are multiplied by a constant near unity to account for
systematic errors between the systems.
In the case of diatomic ions reacting with diatomic molecules, the rota-
tional energy of the reactant ion must also be included in the analysis. The
rotational temperature of the ionic reactant in a drift tube is calculated
from the CM energy with respect to the buffer (Anthony et al 1997,
Duncan et al 1983). Vibrational excitation also occurs in both reactants
and can only be separated if independent information exists regarding how
vibrational excitation of one of the reactants affects the reactivity. In practice
if such information is available, it is likely to be the vibrational dependence of
the primary reactant ion.
For atomic and polyatomic ions reacting with polyatomic molecules, it
is often useful to plot the data as a function of total energy, i.e. the sum of
vibrational, rotational, and translational energy. This analysis does not
allow for separation of the effects resulting from the various types of
energy, but it does provide a test to determine if all types of energy control
the reactivity similarly. Thus, there are three types of plots used to facilitate
the discussion: reactivity versus (1) translational energy or temperature, (2)
rotational plus translational energy, and (3) total energy. Each plot type
yields useful information and examples of each type are given in the next
section.
4.3.3 Ion-molecule reactions
4.3.3.1
0+ + N2
The reaction of 0+ with N2 produces NO+ and N as the primary reaction
products as shown in reaction (4.3.1). This reaction has been thoroughly
studied in the 1960s and 1970s (Albritton et aI1977, Chen et aI1978, Johnsen
and Biondi 1973, Johnsen et a11970, McFarland et a11973b, Rowe et a11980,
Schmeltekopf et al 1968, Smith et al 1978). During that time period, the
temperature dependence of this reaction has been measured up to 900 K
(Chen et a11978, Lindinger et aI1974). However, at 900 K only 2% of the
N2 molecules are vibration ally excited. To overcome this shortcoming both
the translational energy dependence and the dependence on the N2 vibra-
tional temperature were measured independently (Schmeltekopf 1967,
Schmeltekopf et al 1968). Figure 4.2 shows HTFA measurements (Hierl
et al 1997) up to 1600 K along with the one of the previous temperature-
dependent studies (Lindinger et al 1974) and a drift tube study of the
energy dependence (Albritton et al 1977). The data from the drift tube
study is converted to an effective temperature by assuming that the average
translational energy equals ~kBTeff. The two thermal experiments agree very
well, and the other temperature-dependent study (Chen et al 1978) (not
shown) is similar and shows the rate constants decreasing to 900 K. The
--- Page 156 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
141
•
HTFA
0+ + N2 ~ NQ+ + N
8
•
NOAA(T)
~ 310-12
88
Predicted
• NOAA (KE only)
E
•
,88
~
..
c
~t
s
'~-+r~Ut+n
1/1
C
0
10-12
0
~ 810-13
tt
0:::
610-13
410-13
0
500
1000
1500
2000
Temperature K
Figure 4_2_ Plot of the rate constants for the reaction of 0+ with N2 as a function of
temperature. The HTFA (Hierl et al 1997), the NOAA (T) (Lindinger et al 1974), and
NOAA (KE) (Albritton et al 1977) data are shown as circles, squares and diamonds,
respectively. See the text for a description of the predicted values.
drift tube study also shows good agreement in this range, although the values
are slightly below the thermal rate constants. This may be due in part to the
difficulty of measuring such slow rate constants, which are approaching
the lower limit that can be measured accurately in low-pressure flow tubes.
The agreement between the drift tube data and the thermal data shows
that rotational energy does not have a big effect on the reactivity. Above
1200 K, the HTFA and drift tube data start to increase with increasing
temperature although the thermal data increase at a lower temperature
and increase more rapidly. This shows that vibrational excitation increases
the rate constants substantially.
There is a previous study on the effect of the vibrational temperature of
N2 on the rate constant (Schmeltekopf 1967, Schmeltekopf et aI1968). The
combination of the translational energy dependence of the drift tube data
with the vibrationally excited N2 data provides an interesting comparison
to the present data. The vibrational temperature data were reported relative
to the 300 K rate constant. Scaling these data to the drift tube translational
temperature (Tvib = Ttrans), however, allows a thermal rate constant to be
predicted with both vibrational and translational effects included, i.e. each
drift tube translational energy data point is scaled according to the vibra-
tional energy dependence at the corresponding effective temperature. This
procedure ignores the effects of rotational excitation, which is small at
temperatures below 900 K. This also assumes that the translational energy
dependence of the vibrationally excited species is similar to that for v = o.
--- Page 157 ---
142
Air Plasma Chemistry
The results of this prediction are shown in the figure 4.2. Very good agree-
ment is found with the thermal rate constants. Unsatisfactory agreement is
obtained (not shown) if the vibrational temperature data are plotted relative
to the 300 K rate constant. The agreement between the data indicates that the
above assumptions are good.
The large upturn in the rate constant above 1200 K is due to vibrational
excitation. At first glance one would assume that it was due to N2 (v = 1).
However, the NOAA group has shown that v = 1 reacts at almost the
same rate as v = 0 and that it is v = 2 and higher that react much faster,
a factor of 40 faster than the lower energy states (Schmeltekopf 1967,
Schmeltekopf et al 1968). Thus, the rather large difference between the
HTF A and drift tube data is due to the less than 2% of the N2 molecules
that are excited to v = 2 or higher in the HTF A experiments.
4.3.3.2 0+ + O2
The rate constants for the reaction of 0+ with O2 are shown in figure 4.3 as a
function of temperature (Hierl et aI1997). This is one of only two reactions
which was studied up to the full temperature range of 1800 K. The data
decrease with temperature up to about 800 K, go through a minimum
about 300 K wide and increase dramatically above that point. Two other
datasets are shown for comparison (Ferguson 1974a, Lindinger et al 1974,
McFarland et al 1973b). The previous temperature dependent data taken
510-11
ill
0++ O2 ..... O2++ 0
•
HTFA
-in
310-11 !I
-
NOAA(T)
-
•
NOAA (KE)
E
~ ..
c
I~_.
J!I
...
'"
c
.-
J
•
0
.-:
0 s
10-11
• •
~
.. , .•.. • •
810-12
610-12
•
100
1000
Temperature (K)
Figure 4.3. Plot of the rate constants for the reactions of 0+ with O2 as a function of
temperature. The HTFA (Hierl et al 1997), the NOAA (T) (Lindinger et al 1974), and
NOAA (KE) (McFarland et a11973b) data are shown as circles, squares and diamonds,
respectively.
--- Page 158 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
143
• HTFA
0++0 --+0++0
";
• KE*.88
2
2
III
-KEfit
10.10
-
·Tfit
E
.-- .. k ~V>O~
~
......... k v>1
..
c
J!
III
C
0
~ -....
()
---
S
./"
I'll
Q:
10.11
0.07
0.1
0.4
{E
} + {E } (eV)
irana
rot
Figure 4.4. Plot of the rate constants for the reaction of 0+ with O2 as a function of
average translational plus rotational energy. The HTFA (Hierl et al 1997) and the
NOAA (KE) (Ferguson 1 974a, Lindinger et a11974) data are shown as circles and squares,
respectively. See the text for a description of the fits and predicted rate constants.
up to 900 K are in good agreement with the present data except for the 900 K
point, which still agrees within the combined error limits. Only the NOAA
drift tube data are shown and are slightly higher than the present values at
low temperature with the difference increasing with higher temperatures.
The drift tube study also has a much wider minimum and increases more
slowly. Another drift tube study found values somewhat higher but with
similar trends (Johnsen and Biondi 1973).
Figure 4.4 shows a plot for the HTF A and NOAA drift tube data versus
rotational plus translational energy for the reaction of 0+ + O2, the NOAA
data have been scaled by 0.88 to better match the lowest energy HTFA
points. This is a small correction, considerably less than the error limits,
which accounts for a small systematic difference between the datasets. The
data agree almost perfectly up to almost 0.2 eV. In this range very little of
the O2 is vibrationally excited. Since the two datasets have considerably
different contributions from the two types of energy, the agreement indicates
that rotational and translational energy affect reactivity similarly, at least in
an average sense. At higher energies, the HTF A rate constant is significantly
greater than the drift tube data. The separation between the two curves
occurs at the temperature where an appreciable fraction of O2 starts to be
vibrationally excited.
For most of the high temperature range, only v = 0 and v = 1 of O2
are significantly populated (Huber and Herzberg 1979). This allows for a
determination of the rate constant for O2 in the v = 1 state. To facilitate
the derivation, the two data sets are fitted to a power law plus Arrhenius
--- Page 159 ---
144
Air Plasma Chemistry
type exponentia1. The results of the fits are shown in figure 4.4 and are excel-
lent representations of the data. The rate constants for vibrational excited O2
can then be derived, by assuming that all excited vibrational states of O2 react
at the same rate. Since most of the excited population is in v = 1, this appears
to be a reasonable assumption. The populations of v = 0 and v > 0 are calcu-
lated using the harmonic oscillator approximation, and the rate constant for
v = 0 is taken as the drift tube rate constant. Equation (4.3.2) is then solved
for k j • The result is shown in figure 4.4 as the dashed line. The vibrationally
excited rates are about 2-3 times higher than the ground state rate. Note this
analysis is different from our original paper (Hierl et al 1997) where
rotational energy was assumed not to influence the rate constant. The
increase in rate constant may be attributed to changes in Franck-Condon
factors. For near-resonant states the Franck-Condon factors are larger for
the v = 1 state than the v = 0 state (Krupenie 1972, Lias et aI1988). As an
alternative, rate constants were also derived for the assumption that v = 1
reacts similarly to v = O. This is shown in figure 4.4 as k (v > 1).
4.3.3.3 0+ + NO
The last of the 0+ reactions to be discussed is the charge transfer reaction of
0+ with NO (Dotan and Viggiano 1999). Figure 4.5 shows the rate constants
for this reaction plotted as a function of average rotational and translational
E
~ -
c i
o o
~
•
HTFA
•
CRESU· corr
to
FlowDrift
v Static Drift
-
Power + Exp + Exp
10.13 '--~~~~-'--~~~~'"'--~~~~,"",----~~~~..J
104
10~
1~
1~
1~
(Elnlns> + (Ero.> (eV)
Figure 4.5. Plot of the rate constants for the reaction of 0+ with NO as a function of
average translational plus rotational energy. The HTFA (Dotan and Viggiano 1999),
CRESU (Le Garrec et at 1997), flow drift tube (Albritton et at 1977), and static drift
tube data (Graham et at 1975) are shown as squares, circles, triangles and inverted
triangles, respectively.
--- Page 160 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
145
energy, as well as previous drift tube (Albritton et al 1977, Graham et al
1975) and ultra-low temperature data (Le Garrec et al 1997) corrected as
described in our original paper. The combined datasets fit on one curve,
showing the equivalence of rotational and translational energy in controlling
the reactivity. The agreement between the highest temperature points and the
drift tube data indicate that vibrational excitation to v = 1 does not substan-
tially increase the rate constant.
Only by combining several datasets can the typical behavior for a slow
ion-molecule reaction be observed, i.e. an initial decline in the rate constants
followed by an increase at higher temperature/energy. The minimum does
not show up clearly in anyone dataset. The combined data look as though
they could be fitted to a power law plus exponential, similar to what was
done for the O2 reaction. However, this does not fit the data well, but a
power law plus two exponentials does. This fit is shown in figure 4.5. The
slowness of the reaction has been attributed to a spin forbidden process
(Ferguson 1974b). The lower activation energy (0.25eV) appears well corre-
lated with the 3 Al and 3 BI states of the Not intermediate (Bundle et aI1970).
Production of NO+e S) is endothermic by approximately 2 eV, correlating
well with the 2.3 eV second activation energy.
The above systems all have concise stories as to how different types of energy
affect reactivity. In contrast, the reaction ofN+ with O2 is more complicated.
Three drift tube studies show fiat translational energy dependencies with the
rate constant approximately half the collision rate (Howorka et al 1980,
Johnsen et al 1970, McFarland et al 1973b). In contrast, both the early
HTFA data (Dotan et al 1997) and NOAA temperature dependence
(Lindinger et al 1974) found the rate constant to increase with increasing
temperature until the rate saturated at approximately the collision limit at
1000 K as shown in figure 4.6. Little vibrational excitation occurs at lower
temperatures where the difference occurs. An upper limit for the v > 0 rate
constant is shown (kmax ) and cannot explain the difference. This rate constant
is derived assuming that the v = 0 rate constant is given by the NOAA drift
tube data and that all vibrationally excited O2 reacts at the Langevin capture
rate. Another possibility is that N+ has three spin-orbit states. However, the
equilibrium distributions of the three states in the two types of experiments
are not different enough to completely explain the data, leaving rotational
energy as the likely explanation. This conclusion would indicate that
rotational energy is more efficient than translational energy in driving this
reaction.
However, in writing a recent review on internal energy dependencies
derived from comparisons of the HTF A data to kinetic energy data
(Viggiano and Williams 2001), it became clear that this reaction was an
--- Page 161 ---
146
Air Plasma Chemistry
o HTFA Old COlT
x
NOAA (KE)
•
SlFT~)
•
HTFA (present)
--kmax
t\ NOMm
o{lo
HTFA old I.I1COII'
-_.- 1.5 Torr
310.10 '--_-""'_--'-_"'--........... _
....... ____
...... ___
--1
200
400
600 8001000
3000
Temperature (K)
Figure 4.6. Rate constants for the reaction ofN+ with 02' The SIFT (present) and HTFA
(present) points are from the most recent study (Viggiano et aI2003). The NOAA kinetic
energy (KE) data are from McFarland et al (1973b), the temperature data NOAA (1) are
from Lindinger et al (1974). The HTFA old corr and HTFA old uncor refers to the
published HTFA data (Dotan et al 1997) with and without the thermal transpiration
correction. The error bars are ±15% on the present HTFA data. The old HTFA data
taken at 1.5 torr are indicated by an arrow.
anomaly. Most of the difference between the temperature and kinetic energy
data for this reaction had to be assigned to rotational energy. No other reac-
tion of the dozens studied had a similar dependence on rotational energy. In
all other cases involving species that do not have large rotational constants,
rotational energy either behaved similarly to translational energy or had a
negligible influence on reactivity. The unusual nature of the results prompted
us to re-examine the kinetics in both the RTFA and the selected-ion-flow
tube (SIFT) in our laboratory.
Figure 4.6 shows the rate constants as a function of temperature for
different experiments, including the most recent RTF A and SIFT results
(Viggiano and Williams 2001, Viggiano et al 2003), a previous drift tube
measurement (McFarland et al 1973b) and the two previous studies at
high temperature (Dotan et al 1997, Lindinger et al 1974). The previous
RTF A study is plotted with and without a thermal transpiration correction
for the capacitance monometer (Poulter et al 1983). The drift tube study
shown in figure 4.6 is in good agreement with two other studies that are
not shown for simplicity (Roworka et al 1980, Johnsen et al 1970). The
drift tube studies show rate constants that are independent of kinetic
energy. The SIFT data show no discernible temperature dependence from
200 to 550 K, in agreement with the drift tube results. The most recent
--- Page 162 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
147
HTFA results (Viggiano and Williams 2001, Viggiano et al 2003) show a
temperature dependence essentially equal to the relative error limits, i.e.
very small. The two previous studies at high temperature found rate
constants that increased with increasing temperature up to 1000 K. Above
this temperature, the previous HTF A study found a leveling off at the
collision rate. Thus, the new HTF A temperature studies are in disagreement
with the previous ones.
Part of the discrepancy is due to thermal transpiration (Poulter et al
1983) as can be seen in figure 4.6. However, this is only a small part of the
disagreement. Due to the disagreement between the two sets of HTF A
data, a number of checks were performed on the most recent HTF A data.
The SIFT data are in excellent agreement with the new HTF A measurements
in the overlapping range and both new datasets lack a strong temperature
dependence. In addition to remeasuring the rate constants, the original
HTF A data have been re-examined. Data run at 1300 and 1400 K have
both been taken at elevated pressure (l.5 torr versus 1 torr). The high pres-
sure points are indicated with an arrow in figure 4.6 and agree with the
present measurements. They are shown in the figure as the small circles on
the solid line. The difference between the 1 and 1.5 torr rate constants results
from incomplete source chemistry at the lower pressure. In other words, not
enough N2 was added to quench all the He+ and He before the beginning of
the reaction zone in the low pressure data. Because He+ reacts with N2 to
produce both N+ and Nt, insufficient N2 will lead to a situation where
He + is the dominant ion at the start of the reaction zone and N+ and Nt
are dominant at the end of the reaction zone, i.e. at the mass spectrometer.
Therefore, the disappearance of N+ with the addition of O2 was due to
He+ reacting with O2 rather than N2 as well as from the reaction of N+
with O2. The reaction of He+ with O2 is faster than for N+ and proceeds
with a rate constant equal to those in the plateau region of the previous
measurements (Ikezoe et aI1987). It is not possible to speculate if this was
also a problem in the NOAA temperature data as well. Due to the above
problem, selected points for 0+ and Nt reacting with O2 were also measured.
The rate constants were very slightly lower than the original values mainly
due to the thermal transpiration correction. The small differences are not
enough to change any of the original conclusions. No measurements of N+
reactions with other neutrals have been made in the HTF A.
From a chemical dynamics viewpoint, the new data are easier to inter-
pret. The old data required rotational energy to drive the reactivity much
more efficiently than translational energy. No other system studied to date
shows such a behavior (Viggiano and Williams 2001). Most systems studied
show that rotational and translational energy have the same influence on
reactivity. The drift tube data overlap within the error with the new HTFA
data except at the highest temperatures. The good agreement between the
SIFT and HTF A data with drift tube data implies that neither rotational
--- Page 163 ---
148
Air Plasma Chemistry
nor translational energy have a large influence on the rate constants. At
higher temperatures, the HTF A data are larger than the drift tube data
although just slightly above the 15% relative error limits shown in figure
4.6. This indicates that vibrational excitation probably promotes reactivity.
The line in figure 4.6 labeled kmax is calculated by taking the v = 0 rate
constant as the drift tube data and assuming that the rate constants for
vibrationally excited O2 react at the collision rate. The line is in excellent
agreement with the present data. This agreement suggests that O2 (v ~ 0)
reacts at close to the collision rate, but the small differences between the
data sets makes definitive conclusions impossible.
4.3.3.5 0- + NO, CO
The reactions of 0- with NO and CO are associative detachment reactions,
forming an electron and N02 or CO2 , The data are shown in figure 4.7
(Miller et al 1994). While the trends in the data mimic previous work, the
scatter is larger. Relative errors of 30% are probably more appropriate
and comparisons of translational and rotational energy are inconclusive.
Some of this scatter is a result of unwanted chemistry in the flow tube. 0-
is normally made in flowing afterglows from electron attachment to N20.
At low temperature, N20 does not attach electrons. However, at high
10-9
DO
B • !i. • ••
• If ~
A
O'+co
":'1/1
o~ 0
~.
A
q5'~ 0
A
A
E
A
~
I:>.
0
AA
-
I:>. CPI:>.
A
C
I:>.
A
~
10.10
A
C
0
9
0
CJ
•
HTFACO
0
I:>.
.A
S
I:>.
as
A
NOAA (KE), CO
I:>.
a:
• SIFT, CO
I:>.
'l!.
o HTFANO
O'+NO
I:>.
I:>.
NOAA (KE), NO
I:>.
0
SIFT, NO
10.11
0.01
0.1
1
(Elran.) (eV)
Figure 4.7. Rate constants for the reactions of 0- with CO and NO as a function of
average translational energy. Closed and open circles refer to HTFA data for CO and
NO (Miller et at 1994). Closed and open triangles refer to NOAA drift tube data for
CO and NO (McFarland et at 1973c). Closed and open squares refer to SIFT data for
CO and NO (Viggiano et at 1990b; Viggiano and Paulson 1983).
--- Page 164 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
149
temperatures a distributed source of 0- was found, which was believed to be
the result of the electrons from the detachment reactions re-attaching to N20
in the flow tube. To circumvent this problem, CO2 was used as the source of
0-, and SF6 was used to scavenge electrons. In retrospect, the scatter in the
data probably indicates that small problems remained. In addition, since the
time these measurements were made, it was realized that NO reacts on hot
ceramics and the possibility exists that NO may have also reacted on hot
stainless steel. In particular, the highest temperature point is lower than
the data trends which indicates that NO was destroyed on the surface.
Taken at face value, these reaction-rate data seem to indicate that rotational
energy does not change the rate constants.
4.3.3.6 Ar+ + O2, CO
Other interesting examples of vibrational enhancement are the reactions of
Ar+ with CO and O2 which are very similar (Midey and Viggiano 1998).
The rate constants for both reactions are in the 10-11 cm3 S-1 range and
initially decrease with temperature, have minimums at about 1000 K, and
increase at higher temperatures. Comparing rate constants from the
HTFA to drift tube experiments (Dotan and Lindinger 1982a) at the same
sum of translational and rotational energy shows good agreement before
the minimum, indicating that the two forms of energy control the reactivity
in a similar manner.
The higher temperature data for these two reactions not only indicate
that vibrational excitation increases the rate constants but also that vibra-
tional energy changes the rate constants faster than does other forms of
energy. In deriving state specific rates from comparisons to translational
energy data, it is usually assumed that all vibrationally excited states react
at the same rate. However, a couple of observations lead one to believe
that v = 1 reacts more like v = 0 and that v = 2 has the larger effect. Little
or no enhancement of the rate constants occurs at temperatures where
appreciable excitation of the v = 1 state occurs. Fits to a power law plus
exponential yields activation energies (41.8 and 57.4kJ/mol for O2 and
CO, respectively) in line with two quanta of vibrational excitation (37.8
and 51.84kJ/mol for O2 and CO, respectively) (Huber and Herzberg
1979). If one assumes that only states in v 2': 2 enhance the rate constants,
one finds the values about a factor of 100 greater than the v = 0 rate
constants and very close to the collisional limit and independent of tempera-
ture. When assuming that all states in v 2': 1 react at the same rate, one finds
about a factor of 5 enhancement and rates that increase with increasing
temperature. In either case the enhancement is much greater than can be
explained by energy arguments. The production of Oi(a) and CO+(A)
states may lead to the observed behavior. The O2 reaction will be compared
to the similar reaction of Ni below.
--- Page 165 ---
150
Air Plasma Chemistry
4.3.3.7 Nt + O2
The charge transfer reaction of Nt with O2 provides another example of the
equivalency of translational and rotational energy in controlling the reac-
tivity (Dotan et al 1997). This reaction is of lesser importance since it only
converts one diatomic ion to another. Figure 4.8 shows a plot of the rate
constants versus temperature. From room temperature to the minimum
value at 1000 K, the rate constants decrease over a factor of 4, and increase
by a factor of 2 from 1000 to 1800 K. Excellent agreement is found between
the RTFA results and the previous study up to 900 K (Lindinger et aI1974).
The drift tube study is distinctly different (McFarland et aI1973b). The rate
constants decrease with increasing translational energy but quite a bit more
slowly. The minimum is at a distinctly higher energy. At the minimum, the
drift tube rate constants are a factor of 2 larger than those measured in the
RTF A, a large difference. A power law plus exponential fits the data well,
with all residuals less than 11 % of the rate value. The activation energy is
0.2geV.
The data are shown replotted as a function of rotational plus transla-
tional energy in figure 4.9. In this plot there is excellent agreement between
the two datasets up to the minimum in the RTF A rate constants. This
shows that rotational energy and translational energy are equivalent in
10.10 .-•
N++O ~O++N
2
2
2
2
-0
•
...
,
E
r·
~ -
c s
;~:I-
II) c
0
•
0
CI)
,~ .
-
...
as
10.11
a:
•
•
HTFA
• •••••
• NOAA!~
• NOAA
)
100
1000
104
Temperature (K)
Figure 4.8. Plot of the rate constants for the reaction of Nt with O2 as a function of
temperature. The HTFA (Dotan et aI1997), the NOAA (T) (Lindinger et aI1974), and
NOAA (KE) (McFarland et a11973b) data are shown as circles, squares and diamonds,
respectively.
--- Page 166 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
151
•
Ar+ (HTFA)
o Ar+ (DT)
•
N + (HTFA)
2
o N + (DT)
2
Ar+ + 0 --+ 0 + + Ar
2
2
Figure 4.9. Plot of the rate constants for the reactions of Ar+ and Nt with O2 as a function
of average translational and rotational energy. The HTFA data for Ar+ and Nt are shown
as solid squares (Midey and Viggiano 1998) and circles (Dotan et aI1997), respectively.
Drift tube data for Ar+ and Nt are shown as open squares (Dotan and Lindinger
1982a) and circles (McFarland et aI1973b), respectively.
controlling the reactivity. The factor of two difference between the two
data sets in figure 4.8 disappears. The fact that the rotational effect is so
large is due in part to both reactants having rotational energy as opposed
the reactions described above where only one reactant had rotational
energy. This is one of the few cases for which conclusions about the
rotational energy of the ion were able to be made. Above the minimum in
the RTF A data, the two data sets diverge due to vibrational excitation in
the RTF A experiment.
Several previous studies have shown that vibrational excitation of Nt
does not affect the reactivity (Alge and Lindinger 1981, Ferguson et al
1988, Kato et a11994, Koyano et at 1987). This is probably a result of the
fact that there is good Franck-Condon overlap between Nt and N2 in the
same vibrational levels. These studies suggest that the differences above
0.3 eV are due exclusively to O2 vibrations. If this assumption is correct,
then the reaction of Ar+ with O2, which has similar energetics, should
behave similarly. A power law plus exponential fit to the RTF A data
yields an activation energy between the values for one and two quanta of
O2 vibrations. Therefore, rate constants for two cases were derived assuming
(1) that the rate constant for v = I equals v = 0 and (2) all vibrationally
excited states react at the same rate. The latter assumption yields rate
constants a factor of 6 higher than those for v = 0 while the former assump-
tion yields rate constants about a factor of20 higher. In both the Ar+ and Nt
reactions, the upturn has been attributed to the production of the ot(aITu)
--- Page 167 ---
152
Air Plasma Chemistry
state (Schultz and Armentrout 1991), which is endothermic in both reactions.
For the reaction of Ar+ with O2 it appeared that O2 (v 2 2) was the most
likely explanation for the upturn in the data. However, for the Nt reaction
the activation energy is in between that for the two states. This also shows
up in the minimum between the two datasets. If exactly the same processes
are occurring the minimum between the two curves should shift by the
recombination energy difference of 0.178 eV. However, the difference in the
minimums is slightly less than this, which is a further indication that O2
(v = 1) must already be enhancing the reactivity for the Nt reaction.
4.3.3.8 oj + NO
Previous studies of the ot with NO reaction have shown that the drift tube
dependence and the temperature dependence up to 900 K are flat (Lindinger
et a11974, 1975). The measurements up to 1400 K continue this trend and
show that neither translational, rotational, nor vibrational energy has a
large effect on the reactivity (Midey and Viggiano 1999).
4.3.3.9 Ar+, Nt + CO2
Ar+ and Nt have similar recombination energies and for some reactions
have similar reactivity, although one is atomic and the other diatomic. The
similarities and differences in the reactions of these two ions with O2 was
described above. The reactions of these ions with CO2 and S02 have also
been studied in the HTFA (Dotan et af 1999, 2000). The reactions with
CO2 proceed exclusively by charge transfer and the S02 reaction is mainly
charge transfer except at high temperature/energy, where SO+ is produced
by dissociative charge transfer which is endothermic at room temperature.
Only CO2 reactions are discussed here.
Plots of rate constants versus temperature show clear differences
between real temperature and kinetic temperature for the reactions of both
Ar+ and Nt with CO2 (Dotan and Lindinger 1982b, Dotan et al 2000),
showing that internal energy has some effect on reactivity. The ability to
separate rotational effects diminishes for molecules with three heavy atoms
since vibrations are excited at low temperatures. Therefore, the data are
replotted as a function of average rotational, translational, and vibrational
energy instead of just rotational and translational energy. Such a plot for
both reactants with CO2 is shown in figure 4.10. The Ar+ data fall on the
same line up to energies of 0.4 eV, after which the temperature data are
lower than the drift tube data. To test the high temperature behavior, data
were taken in both the ceramic and quartz flow tubes, and similar results
were found. In contrast, the Nt temperature data are lower than the drift
tube dependencies at all energies. Therefore, in both of these reactions
internal excitation hinders the reactivity more than translational excitation.
--- Page 168 ---
Ion-Molecule Reactions in Air Plasmas at Elevated Temperatures
153
10.8
0
0
Ar+ + CO2 -+ products
•
N2 + + CO2 -+ products
"",
~DDO~
•
0
E
.&
.
~ ~.
..
.dq.
c
•• reo
J!
III
0
C
•
0
•
•
0
At (HTFA)
• •
0
0
.!
0
Ar+(DT)
.,
III
0::
• N;(HTFA)
• •
0
N;(DT)
10.10
0.1
1
(Etran.> + (Erot>
+ (Evt.,) (eV)
Figure 4.10. Plot of the rate constants for the reactions of Ar+ and Nt with CO2 as a
function of average translational and rotational energy. The Ar+ HTFA (Dotan et at
1999), Nt HTFA (Dotan et at 2000), Ar+ drift tube (Dotan and Lindinger 1982b), and
Nt drift tube (Dotan et at 2000) data are shown as solid squares, solid circles, open squares
and open circles, respectively.
As shown above, rotational energy only occasionally has a different effect
than translational energy and the differences are probably due to CO2
vibrations since Nt vibrations are mostly unexcited (5% at 1400 K). The
data show that the rate constant difference is bigger for the Nt reaction.
4.3.4 Summary
One goal of high temperature experiments is to measure reactions at
conditions relevant to air plasma environments. The data so far have
demonstrated the importance of making 'true' high temperature measure-
ments. However, it is not always possible to measure every reaction due to
experimental and time constraints. Thus, it is useful to look for trends in
the data so that better extrapolations of lower temperature data can be
made for modeling applications. Trends are also important from a funda-
mental point of view. The study of internal energy effects has been summar-
ized previously and several trends were noted (Viggiano and Morris 1996,
Viggiano and Williams 2001). Some of the relevant conclusions of that
work are outlined below.
In most ion-molecule reactions, rotational and translational energy are
equivalent in controlling reactivity, at least in the low energy range where
most of the data have been taken. This is true for both the ion and neutral
rotational energy, although the conclusion has been tested for only a few
--- Page 169 ---
154
Air Plasma Chemistry
systems for ion rotations. In the higher energy range, the data are too sparse
to make a conclusion. There has been much more work on the effect of vi bra-
tiona1 excitation on ion reactivity and much of the work up to 1992 has been
summarized in two books (Baer and Ng 1992, Ng and Baer 1992). For
diatomic and a few triatomic molecules, it has been possible to detect the
product ion vibrational state by chemical means, the so-called monitor ion
method (Durup-Ferguson et al 1983, 1984, Ferguson et al 1988, Lindinger
1987). The most detailed work on internal energy effects is often done
using resonance enhanced multiphoton ionization (REMPI) to prepare
ions in specific vibrational states. This technique was used extensively by
Zare and coworkers (Conaway et a11987, Everest et a11998, 1999, GuttIer
et a11994, Poutsma et a11999, 2000, Zare 1998) and Anderson and cowor-
kers (Anderson 1991, 1992a, 1997, Chiu et al 1992, 1994, 1995a,b, 1996,
Fu et a11998, Kim et aI2000a,b, Metayer-Zeitoun et a11995, Orlando et al
1989, 1990, Qian et a11997, 1998, Tang et a11991, Yang et aI1991a,b) in
guided-ion beams. Leone and Bierbaum (Frost et al1994 1998, Gouw et al
1995, Kato et al 1993, 1994, 1996a,b, 1998, Krishnamurthy et al 1997)
have used LIF to monitor vibrational excited Ni ions in a selected ion
flow tube to study collisional deactivation and vibrational enhancement of
the charge transfer rate constant of Ni(v = 0--4).
The ability to predict the behavior of complex reaction systems is
particularly important for modeling applications, which often require
extrapolation of a limited amount of existing data to conditions of practical
interest. While the effect of rotational energy seems to be generally predict-
able, there are enough exceptions to warrant caution in making extrapola-
tions. Furthermore, vibrational energy often displays state-specific effects
both in overall reactivity and formation of new products. Therefore, it is
still very difficult to predict reactivity at high temperature by extrapolating
translational energy dependencies obtained at low temperature. In light of
this fact, the next section outlines recent experimental and theoretical efforts
aimed at developing a detailed understanding of the vibrational energy
dependence of chemical reactivity.
4.4 Non-Equilibrium Air Plasma Chemistry
4.4.1
Introduction
In the present section, we consider the plasma chemical dynamics of a domain
that is not in chemical equilibrium within a certain timescale and volume. This
can be the case in high EjN conditions, where ion velocity distributions can be
highly skewed with respect to a Maxwellian. Plasma kinetic models for non-
equilibrium chemical systems are significantly more challenging because
--- Page 170 ---
Non-Equilibrium Air Plasma Chemistry
155
kinetics based on equilibrium rate coefficients, k(T), described by some
Arrhenius form as discussed in section 4.1, are no longer applicable. Instead,
the models depend on knowledge of the non-Maxwellian heavy-body velo-
city distributions, the relative velocity dependence of chemical reaction
cross sections, as well as the molecular vibrational distributions and the
related vibrational state-to-state cross sections. In the following it is assumed
that rotational energy is equivalent to translational energy at the total
collision energies encountered in air plasmas. This assumption has been
shown to be valid in several reactions presented in section 4.3.
As we have learned in the preceding sections, when molecular ions are
formed through electron-impact ionization, photo-ionization or chemical
processes such as atomic ion reactions with molecules (e.g. 0+ + N2 --
NO+ + N, 0+ + H20 -- 0 + H20+) and three-body association, they are
formed in translational, rotational and vibrational energy distributions
that differ greatly from Boltzmann distributions. This is particularly the
case for three-body recombination processes:
(4.4.1)
which are important contributors to molecular ion formation in high pressure
plasmas. In process (4.4.1), the nascent vibrational distributions of AB+ are
highly skewed towards vibrational levels near the AB+ dissociation limit. If
the system does not equilibrate, an understanding of the plasma dynamics
requires knowledge of the chemical fate of these highly excited molecular
ions. The vibrational energy dependence of competing dissociative, chemi-
cally reactive and relaxation collisions dynamics then becomes a critical
component of a plasma kinetic model. The vibrational effects are particularly
strong for endothermic processes such as collision-induced dissociation
(CID). The latter is the reverse process of reaction (4.4.1), and microscopic
reversibility arguments suggest that if reaction (4.4.1) favors product
molecular ions in high vibrational states, the reaction probability of the
reverse reaction should also be enhanced by vibrational excitation of the
reactant molecular ion. Note that for endothermic processes, vibrational
enhancement, or vibrational favoring, signifies a greater increase in reactivity
due to vibrational energy than an equivalent amount of translational energy.
Vibrational effects of chemical processes tend to decrease as the number of
atoms of the participating molecules increases because the propensity to
randomize the vibrational energy in a collision increases with the number
of vibrational modes. Vibrational effects, however, cannot be neglected in
air plasmas, given the preponderance of diatomic molecular species.
The determination of the vibrational energy dependence of chemical
reactivity has been a particular challenge to experimentalists and theorists.
State-selected chemical dynamics studies have to a large degree been limited
to low vibrational levels where the vibrational energy represents only a small
fraction of the molecular dissociation energy. Meanwhile, accurate, fully
--- Page 171 ---
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Air Plasma Chemistry
three-dimensional quantum dynamics calculations at the current state-of-
the-art are rarely applied at total energies above 2eV, even for simple
triatomic systems, due to the rapidly increasing number of accessible product
quantum channels with energy (Clary 2003). The demand for knowledge of
kinetics at high levels of vibrational excitation has been particularly high in
the rarefied gas dynamics community, which is the source of a considerable
body of work dedicated to finding vibrational scaling laws for chemical reac-
tivity and energy transfer that cover vibrational energy ranges comparable
with bond dissociation energies. In section 4.4.2, concepts applied to
model the translational and vibrational energy dependence of chemical
processes will be presented. It is impossible to provide a satisfactory synopsis
of the field which encompasses the vast research area of chemical reaction
dynamics. The purpose of this section is to familiarize the reader with the
generally accepted theories of the reaction dynamics community and to
align them with the needs of the community that model non-equilibrium
environments on a molecular level, such as non-equilibrium air plasmas.
Arguments will be presented to adopt a universally applicable model with
minimal adjustable parameters based on the work by Levine and coworkers
(Levine and Bernstein 1972, 1987, Rebick and Levine 1973). In section 4.4.3,
recent advances will be presented on theoretical and experimental efforts to
study chemical dynamics at high levels of vibrational excitation.
4.4.2 Translational and vibrational energy dependence of the rates of
chemical processes
Equilibrium models of chemical kinetic systems as discussed in the previous
section depend on rate coefficients which are usually given by a modified
Arrhenius dependence on temperature defined in equation (4.1.2). In non-
equilibrium conditions, the temperature, T, no longer describes the energy
distributions of the system, and it becomes more practical in describing the
chemical kinetics in terms of cross sections as a function of the relative
velocity and reactant vibrational and rotational quantum states, au,J( v),
which are related to the equilibrium rate coefficient through an extension
of equation (4.1.1):
k(T) = ~
fr(u)fr(J) J: fr(v)au,J(v)vdv
(4.4.2)
where U and J refer to vibrational and rotational quantum numbers of the
reactants (note that each reactant, if polyatomic, has multiple vibrational
quantum numbers for each vibrational mode), the functionsfr refer to the
normalized velocity and quantum state Boltzmann equilibrium distributions
at a temperature T, and Va is the threshold relative velocity,
( 4.4.3)
--- Page 172 ---
Non-Equilibrium Air Plasma Chemistry
157
where J1, is the reduced mass of the reactants and Eu and EJ represent the
vibrational and rotational energy, respectively, for the specific set of
quantum states. The complete, accurate non-equilibrium model must also
account for the reaction product state distributions, and a rigorous model
thus requires state-to-state cross sections, au,~ u",J'~ r(v), where' and"
refer to the reactant and open product channel quantum states,
respectively. It is easily seen that the master equations of a non-equilibrium
plasma model can require thousands of state-to-state cross sections. The
problem is somewhat reduced by assuming that rotational energy has the
same effect as translational energy on cross sections.
Regrettably, there is not a one-glove-fits-all approach to modeling the
translational and vibrational energy dependence of chemical reaction cross
sections and associated product state distributions. Each bimolecular col-
lision system is governed by its own unique set of (3N - 6)-dimensional
potential energy surfaces, where N is the number of atoms of a particular
chemical system, as well as by the respective atomic masses and associated
kinematics. Meanwhile, there are no air plasma chemical processes that
have been comprehensively studied over the pertinent energy range using
either exact quantum scattering methods or state-resolved experiments.
Efforts to model non-equilibrium environments thus rely on approximate
approaches that recover some of the physical properties of chemical
processes as retrieved from existing physical chemical research.
Historically, the energy dependence of chemical reaction and inelastic
collision cross sections, and the determination of product energy distribu-
tions, has been treated using statistical approaches. This approach assumes
that molecular collisions form an intermediate complex that redistributes
the translational, rotational, vibrational, and in some instances electronic
energy equally among all quantum levels of the complex (Levine and Bern-
stein 1987). Vibrational or electronic effects, as discussed earlier, are then
regarded as a deviation from this so-called prior or statistical case. The devel-
opment of statistical chemical reaction models followed two separate schools
of thought: the rarefied gas dynamics community has used the semi-empirical
analytical Total Collision Energy (TCE) (Bird 1994) cross section and Borg-
nakke-Larsen energy disposal models (Borgnakke and Larsen 1975), while
in the chemical physics community statistical models were spearheaded
through the information theoretical approaches by Levine (Levine 1995,
Levine and Manz 1975), phase space theory (Chesnavich and Bowers
1977a,b, Light 1967, Pechukas et al 1966), and transition-state theories
such as the RRKM theory (Marcus 1952, Marcus and Rice 1951). While
the Borgnakke-Larsen approach targets computational efficiency and uses
parameterization based on viscosity and transport properties determined
for the gases, the physical chemical statistical models use known spectro-
scopic molecular constants. The methods of the rarefied gas community, as
applied to direct simulation Monte Carlo (DSMC) methods, have been
--- Page 173 ---
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Air Plasma Chemistry
described (Bird 1994) and more recently reviewed by Boyd (2001) The cross
section models derived by Levine (Levine and Bernstein 1972, 1987, Rebick
and Levine 1973) based on statistical arguments and calculations have been
used in both communities, and have found great utility in the interpretation
of countless experiments of chemical reaction dynamics.
In a statistical approach, barrier free, exothermic reactions involving
reactants in their ground electronic and rovibrational states occur with a
probability of 1 if an encounter occurs. At low translational energies, Et ,
an encounter can be defined by a capture collision associated with spiraling
trajectories induced by an attractive interaction potential, VCR) (Levine and
Bernstein 1972):
( 4.4.4)
where R is the distance between reaction partners. The capture cross section
is then given by
- AE-2/ s
u-
t
(4.4.5)
where A, as in equation (4.4.2), is a scaling parameter. In the case of an
ion-neutral encounter, the long-range attractive potential is given by a
polarization potential with s = 4, thus yielding the well-known Langevin-
Gioumousis-Stevenson (Gioumousis and Stevenson 1958) cross section
energy dependence with A = 7rq(2a)O.5, where a is the polarizability of the
neutral and q is the ion charge.
Assuming microscopic reversibility, the translational energy dependence
of the cross section for the reverse, endothermic process at translational
energies above the activation energy Ea is given by (Levine and Bernstein
1972):
(E
E )1-2/s
u(Et ) = A'
t -
a
Et
(4.4.6)
where A' is again a scaling factor. Unfortunately, microscopic reversibility
cannot be applied to integral cross sections blindly since the preferred
mechanism (e.g. direct or indirect) can vary significantly between the forward
and reverse reactions. Thus, for ion-molecule CID processes, equation
(4.4.6) is only adhered to when this process proceeds via a complex (indirect)
mechanism. This, however, is normally only the case at very low activation
energies. Equation (4.4.6) has been applied more frequently in its more
general form:
u(Et) = A' (Et - Eat
Et
(4.4.7)
where A' and n are adjustable parameters. It is worth noting that n = 1
corresponds to the line-of-centers (LOC) hard-sphere model that assumes
--- Page 174 ---
Non-Equilibrium Air Plasma Chemistry
159
straight-line trajectories and is readily derived from
J
Rl +R2
cr=27r 0
P(b)bdb
(4.4.8)
where b is the collision impact parameter and R J and R2 are the reactant
radii, and the reaction probability P(b) is 1 for all impact parameters
where the translational energy associated with the relative velocity com-
ponent along the line-of-centers when the hard spheres collide exceeds the
activation energy, and 0 for larger impact parameters (Levine and Bernstein
1987). Equation (4.4.7) is usually referred to as the modified LOC model,
where n < 1 is typical for highly indirect, complex forming processes, while
n > 2 usually signifies a direct, impulsive mechanism. n has also been related
to the character of the reaction transition state (Armentrout 2000,
Chesnavich and Bowers 1979). It has been shown (Levine and Bernstein
1971) that under the assumption that CID follows a reverse three-body
recombination (process (4.4.1)) mechanism, n = 2.5 can be expected.
The workings of the modified LOC model are nicely demonstrated in
figure 4.11 that compares collision-induced dissociation cross sections as a
function of translational energy of the Art + Ar and Art + Ne systems
(Miller et at 2004). Art has an accurately known dissociation energy of
1.314eV (Signorell and Merkt 1998, Signorell et al 1997). The solid lines
are nonlinear least-squares fits of equation (4.4.7) convoluted with the experi-
mental broadening mechanisms (ion energy distribution, target gas motion)
to the experimental data. The figure also provides the derived parameters. In
case of the Art + Ar system, a threshold or activation energy in good
agreement with the spectroscopic dissociation energy (Signorell and Merkt
8
Ar2+ + Ar -+ Ar+ + 2Ar
Ar2+ + Ne -+Ar+ + Ar + Ne
~
-2
~
";;"8
E. = 1.28 ± 0.15 eV
c
__ E.=2.27±0.15eV
~
.2
n = 1.45 ± 0.15
¥ 4
n = 1.17 ±0.15
]
1
(I)
______ E.= 1.3±0.15eV
:I
•
n=2.46±0.15
e 2
e
(.)
(.)
0
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
1
2
3
4
Collision Energy (eY, CM)
Collision Energy (eY, eM)
Figure 4.11. Guided-ion beam measurements (Miller et a12003) of the translational energy
dependence of collision-induced dissociation cross sections of the Art + Ar and Art + Ne
collisions systems. Solid lines are modified line-of-centers (MLOC, equation (4.4.7 fits to
the experimental data. The fits take experimental broadening due to ion energy distribu-
tions and target gas motion into account. Activation energies, Ea, and curvature
parameters, n, derived from the fits are also provided.
--- Page 175 ---
160
Air Plasma Chemistry
1998, Signorell et a11997) is obtained and the small curvature parameter is
close to the hard-sphere case. This relatively indirect behavior is not
surprising considering that this collision system is highly symmetric,
involving both resonant charge-exchange interactions as well as strongly
coupled vibrational modes within the complex. This is also consistent with
the low vibrational effects observed (Chiu et al 2000). In the Art + Ne
case, the onset is considerably more gradual. A free fit of the modified
LOC model results in Ea = 2.46 ± 0.15 eV, considerably higher than the
dissociation energy; however, the fit does not recover the weak signal just
above the dissociation energy. A second, dashed curve in figure 4.11 is an
alternative fit in which the threshold energy was frozen at the spectroscopic
value of 1.3 eV. This fit, although not optimal, provides a curvature
parameter of 2.46 ± 0.15 which is characteristic of a highly direct dissoci-
ation mechanism. The difference in dynamics in comparison with the
Art + Ar system can be attributed to the significantly weaker ArNe+ inter-
action and the lighter mass of Ne.
Using statistical theory, Rebick and Levine (Rebick and Levine 1973)
extended equation (4.4.7) to include the effect of vibrational excitation of
the reactants:
(E E· ) = A' (Et + EVib - Eot exp(->.F)
(J
t,
vlb
Et
(4.4.9)
where Eo is the activation energy not including zeropoint vibrational energy
of the reactants, F is the fraction of the total energy in vibration:
(4.4.10)
and >. is the so-called surprisal parameter and determines the degree of
vibrational enhancement of the respective reaction. >. = 0 corresponds to
equivalence of vibrational and translational energy (statistical), while
>. < 0 signifies a vibrational enhancement and>' > 0 a vibrational inhibition.
Equation (4.4.9) thus can provide a description of the translational and
vibrational energy dependence of reaction cross sections based on three
adjustable parameters. Similarly, surprisal analyses can be applied to
product state distributions (Levine and Bernstein 1987).
The derivation of correct non-equilibrium chemistry models is severely
hampered by the lack of experimentally determined cross section data. Apart
from some shock-tube experiments that suffer from poor knowledge of
molecular vibrational energy distributions (Appleton et al 1968, Johnston
and Birks 1972), there have been no experiments to validate the applied
scaling laws. Recently, Wysong et al (2002) have made a first attempt to
compare the various vibrational scaling laws applied in DSMC models for
dissociation collisions to experiments on the Art + Ar system (Chiu et al
2000). This system was studied with diatomic internal energies generated in
--- Page 176 ---
Non-Equilibrium Air Plasma Chemistry
161
the non-equilibrium conditions of a supersonic jet and was observed to
exhibit essentially no vibrational effects. The expression by Rebick and
Levine (equation (4.4.9), A ~ 0) as well as the simple TCE model (which
cannot account for deviations from the statistical result) provided the best
agreement with the observations while other models, such as the classical
threshold-line model with no adjustable parameters by Macharet and Rich
(Macharet and Rich 1993) and the maximum entropy model (Gallis and
Harvey 1996, 1998, Marriott and Harvey 1994) fared very badly. Other
attempts to validate vibrational scaling models of chemical reactions have
involved comparison with quasiclassical trajectory (QCT) calculations
(Esposito and Capitelli 1999, Esposito et al 2000, Wadsworth and Wysong
1997). As will be further iterated in the following section, this is an
incomplete description since QCT calculations based on a single potential
energy surface do not capture the fact that molecules like N2, NO, O2, and
their respective ions all have electronically excited states with equilibrium
positions well below the dissociation limits. These states can be expected to
interfere in the dynamics of the reaction at elevated excitation energies.
4.4.3 Advances in elucidating chemical reactivity at very high vibrational
excitation
Most of the work on the dynamics of highly vibrationally excited molecules
has focused on vibrational energy transfer. There is a considerable body of
experimental work where molecules are prepared in high vibrational states
using laser techniques such as stimulated emission pumping (SEP) (Dai
and Field 1995, Silva et aI200l), and their decay is probed while the mole-
cules undergo collisions in a buffer gas or in a crossed-beam configuration.
Note that most SEP experiments do not probe the fate of the highly-excited
molecules, merely the removal from the respective quantum state. The theory
of vibrational energy transfer of highly vibrationally excited molecules is also
extensive, ranging from three-dimensional quantum scattering studies, to
semi-classical methods (Billing 1986), as well as analytical models such as
the Schwartz-Slawsky-Herzfeld (SSH) theory (Schwartz et al 1952) and
more recently the nonperturbative model of Adamovich and Rich (1998).
One of the most intensively studied systems is the O2 (u) + O2 systems,
where stimulated emission pumping experiments in the group of Wodtke
(Jongma and Wodtke 1999, Mack et a11996, Price et a11993, Rogaski et al
1993, 1995) discovered relaxation rates in excellent agreement with quantum
dynamics calculations (Hernandez et a11995) up to u = 25, above which the
relaxation rates increase rapidly with u and dramatically diverge from the
theoretical values. The discrepancy has been interpreted to be due to an
electronic interaction associated with the O2 (b 1~;) state, for which the
respective potential energy surface was not included in the calculations. A
probe of the final state distribution for these high u states found a large
--- Page 177 ---
162
Air Plasma Chemistry
fraction of multi quantum vibrational relaxation (Jongma and Wodtke 1999),
consistent with an electronic mechanism. This example demonstrates nicely
that surprises can be expected at vibrational energies in the proximity of
excited electronic states which can participate in the dynamics.
The derived v-v and V-T rate coefficients determined for pure CO and
CO + N2 and O2 collisions have been successfully used to derive highly non-
equilibrium vibrational distributions of CO optically pumped by a CO laser
at near atmospheric pressures (Lee 2000). The literature on chemical reaction
dynamics at high levels of vibrational excitation is considerably sparser than
that of vibrational energy transfer. The main experimental problem is
producing sufficient quantities of state-selected reactants in order to be
able to probe reaction products. As mentioned in section 4.3, the field of
ion-molecule reaction dynamics has provided the most extensive studies of
state-to-state reaction dynamics at controlled translational energies where
absolute cross sections have been produced (Ng 2002, Ng and Baer
1992b). The significant body of work comes from the straightforward
means of controlling the translational energy of reactants, the high sensitivity
of mass spectrometric means to detect reactively scattered ionic products,
and the ability to prepare molecular ions in selected vibrational levels
using Resonance Enhanced Multiphoton Ionization (REM PI) (Anderson
1992b, Boesl et al 1978, Zandee and Bernstein 1979) or direct VUV
(Koyano and Tanaka 1992, Ng 1992) techniques. Ion-molecule reaction
studies using photo-ionization ion sources have provided an extensive under-
standing of state-to-state chemical reaction dynamics; however, the reactant
vibrational levels have been limited to low excitation energies representing a
small fraction of the dissociation energy of the respective molecular ions.
Very recently, Ng and coworkers have succeeded in preparing Hi beams
in all but the two highest vibrational states of the ground state (Qian et al
2003a,b, Zhang et al 2003). Their approach is based on recent advances in
high-resolution photoelectron spectroscopy using a synchrotron light
source (Jarvis et al 1999). A schematic of their apparatus is shown in
figure 4.12, which is situated at the Lawrence Berkeley Advanced Light
Source (ALS) synchrotron facility. Monochromatic (",lOcm- 1 FWHM)
VUV of the Chemical Dynamics Endstation 2 is used to promote hydrogen
molecules to high-n Rydberg states just below the ionization limit of a
targeted excited rovibrational state of the ion. In the multi bunch mode of
the ALS storage ring, there is a 104 ns dark-gap at the end of every 656 ns
ring period. Approximately 10 ns after the onset of this dark gap, a pulsed
electric field of approximately 10 Vjcm and 200 ns duration is applied to
the electrodes spanning the photo-ionization region. This pulsed field
causes field-ionization of the resonantly populated high-n Rydberg
molecules. This form of ionization is called pulsed-field ionization (PFI).
The PFI photo-ion (PFI-PI) is accelerated towards an ion beam apparatus,
while the associated, zero-kinetic energy photoelectron, or PFI-PE, is
--- Page 178 ---
Precursor
Molecules
Non-Equilibrium Air Plasma Chemistry
163
Wire
Gate I"
.~, .
. "' .
.....
Octopole Ion Guide
Quadrupole
Mass Filter
Figure 4.12. Schematic representation of the Pulsed-Field Ionization Photoelectron
Secondary Ion Coincidence (PFI-PESICO) apparatus constructed at Endstation 2 of the
Chemical Dynamics Beamline at the Lawrence Berkeley Advanced Light Source (Qian
et al 2003a).
accelerated towards an electron detector. As the Rydberg states are excited,
however, a significant number of ions in lower ionic states are also produced
with associated electrons that have excess energies, Ehv - E:J , where Ehv and
E:J are the photon and ionic internal energy, respectively. In order to get
state selection, the electron detector is gated to accept PFI-PEs within a
narrow time-window at a fixed delay with respect to the pulsed electric
field. If a PFI-PE is detected, a fast, interleaved comb wire gate (Bradbury
and Nielsen 1936, Vlasak et a11996) is opened at a specific delay with respect
to the PFI-PE pulse for ",100-200ns to allow the associated PFI-PI to
pass. This approach suppresses signal due to false coincidences by orders
of magnitude.
Ions transmitted through the wire gate enter a guided-ion beam (GIB)
apparatus (Gerlich 1992, Te10y and Gerlich 1974) that has the virtue of
examining ion-molecule collisions within the guiding fields of an rf octopole,
thereby ensuring 100% collection of all scattered ions. Qian and co-workers
(Qian et aI2003a,b, Zhang et a12003) used a tandem octo pole set-up, where
the first octopo1e guides the ions through a collision cell containing the target
gas. The second octopole transports reactant and product ions to a quadru-
pole mass filter for mass analysis prior to detection using a Daly ion detector
(Daly 1960). Cross sections are determined from the primary and secondary
ion true coincidence signals and the measured target gas density.
Zhang et al (2003) used this new coincidence approach in a systematic
study of the vibrational energy dependence of the Hi + Ne proton-transfer
reaction (NeH+ +H products) which is endothermic by 0.54eV. Figure
4.13 shows the translational energy dependence of the cross section for
the ground vibrational state of Hi. The dashed line is a fit to the data
points of equation (4.4.7) including a convolution of the experimental
--- Page 179 ---
164
Air Plasma Chemistry
1.0 r-r-r-r-r,...,r-r-"T"""1 .... T""T-r-T"'"T""T'""'1r-r-,....,"""T""T""'T-r-T'""T,
~
c
.2
~ 0.5
en
III
III e
o
0.5
•
Exp
o
aCT
-- MLOC
_._._. MLOC Convoluted
... _...... as (Gilibert et al.)
•
•• •
2
1.0
1.5
2.0
2.5
Collision Energy (eV)
Figure 4.13. Translational energy dependence of the Hi + Ne proton transfer reaction for
reactant ions in the ground vibrational state. A modified line-of-centers (MLOC) fit
including convolution of experimental broadening mechanisms is applied to the data
(dash-dot line). The deconvoluted fit (solid line) is also shown. The experimental data
are compared with QCT and quantum scattering (QS) calculations by Gilibert et at (1999).
broadening mechanisms, primarily governed by the ion energy distribution
with full-width at half maximum (FWHM) of ",0.3 eV. The solid line is
the deconvoluted best-fit function with parameters A' = 0.66A2 eV1- n ,
n = 0.353. The very low curvature parameter signifies an almost vertical
onset at the threshold of 0.54eV, which is characteristic of long-lived inter-
mediates. Fully three-dimensional quantum-theoretical studies (Gilibert
et a11999, Huarte-Larrafiaga et a11998, 2000) have discovered the existence
of a dense spectrum of resonances for this system that greatly enhances the
reactivity near threshold. The calculations of Gilibert et al are also shown
in figure 4.13, exhibiting excellent agreement with the measurements of
Zhang et al. Also shown are quasiclassical trajectory calculations by
Zhang et al (2003), demonstrating that classical methods do not capture
the mechanism near threshold.
Figure 4.14 shows Hi + Ne proton-transfer cross sections using the
PFI-PESICO approach measured for a large number of reactant vibrational
levels at three translational energies, 0.7, 1.7 and 4.5 eV. The proton-transfer
reaction becomes exothermic for u+ = 2. The measurements are compared
with QCT calculations, which also include the dissociation channel. The
latter could not be measured with the current experimental set-up of
Zhang et al (2003). The cross sections are shown on a vibrational energy
scale. At a translational energy of 0.7 eV, Zhang et al succeeded in measuring
cross sections for all vibrational levels from u+ = 0-17. All states were
produced in the N+ = 1 rotational level. The u+ = 17, N+ = 1 level is a
--- Page 180 ---
Non-Equilibrium Air Plasma Chemistry
165
'\)+ = 0
1 234 5
I I I I
10
15
I
I
I I I 111111
7rrTTTT"~rrrrTTTT"~~rrTTTT",
6
5
4
3
2
~ 8
S 6
t;
~ 4
3l e 2
(,) o
15
10
5
0
0.0
H2+(X,V+. N+=1) + Ne
•
ExpNeH+
o
QCTNeH+
I
4.SeV
A=-15.8
a -
a ••
• •
•
•
o
QCTH+
•
I
I
I
I !
I
I
I
o
0
0
0 00 oOa
I
__________________________________ L_
1.7eV
A = -6.9
I
_
~.
II II
_
8.
-.
~
.1 I
g
I
I
118
C
a
~
--~-_.--._-._-o--~---------------~-
gg
I
O.7eV
I
JIJI
II II
··.1
I
I • •
I
•
I
• I
.1
11111
I
I
a
al
0
I I
0.5
1.0
1.5
2.0
2.5
3.0
E"ib (eV)
Figure 4.14. State-selected Hi + Ne proton transfer cross sections determined using the
PFI-PESICO approach. The measurements at three translational energies are shown on
a vibrational energy scale and are compared with QCT calculations that also include
cross sections for the dissociation channel. The respective vibrational quantum states
are shown at the top of the figure. Also shown are the results of a surprisal analysis
based on equation (4.4.9) (solid lines).
mere 0.03 eV below the dissociation limit, also indicated in the figure.
Previous attempts to measure state-selected dynamics of Hi using ion
beams (Ng and Baer 1992) were limited to u+ = 0-4. The PFI-PESICO
measurements by Zhang et al provide the first glimpse of chemical reactivity
of molecules excited to levels near the dissociation limit.
At low vibrational levels, a significant enhancement of the reaction cross
section is observed at all translational energies. A surprisal analysis was
conducted at low vibrational energies based on equation (4.4.9) and the
--- Page 181 ---
166
Air Plasma Chemistry
parameters A' and n derived from the ground vibrational state translational
energy dependence (figure 4.14) to quantify the vibrational effects. The
results of the analysis are also shown in figure 4.14, where parameters, A,
of -3.9, -6.9, and -15.8 are determined for translational energies of
0.7, 1.7, and 4.5eV, respectively. At 0.7 and 1.7eV it is seen that this
approach allows good predictions of the vibrational effects at low vibrational
levels; however, the A parameter depends significantly on translational
energy. This is consistent with the change in dynamics as one goes from
low translational energies, where long-lived intermediates associated with
resonances that cause some energy randomization playa significant role,
to higher energies, where the mechanism is highly direct and vibrational
effects are higher, as expressed by a more negative A parameter. At higher
vibrational energies, the cross sections tend to reach a plateau due to both
saturation effects as the reaction cross section approaches a total cross
section (e.g. momentum transfer cross section) as well as the competition
with dissociation. At 4.5 eV, the CID channel is already open for the
ground vibrational state and the cross sections appear to oscillate outside
of the reported statistical errors.
The comparison with quasiclassical trajectory calculations allowed
Zhang et al to identify three total energy ranges: at low energies,
Etot < 1 eV, the state-selected experimental values exceed the QCT predic-
tions, which is consistent with the quantum scattering studies that identified
the importance of quantum resonances for this system; at intermediate
energies, leV < Etot < 3 eV, very satisfactory agreement is found between
experiment and QCT calculations, and the vibrational enhancement of the
proton-transfer reaction can be quantified with a surprisal formalism
according to equation (4.4.9), at high energies, Etot > 3 eV, the measured
proton-transfer cross sections mostly exceed QCT cross sections. This is
particularly marked at 0.7 eV, where the measurements exhibit significant
reactivity for states nearest the dissociation limit, while the QCT calculations
predict more suppression of reaction due to competition with the dissociation
channel. It is possible that QCT significantly overpredicts the dissociation
cross section for high vibrational levels. At 1.7 eV, the high u+ state cross
sections vary dramatically from one vibrational quantum state to the
other. The authors attribute the failure of the QCT calculations in capturing
the dynamics at the highest energies to inadequacies of the applied H2Ne+
potential energy surface (Pendergast et a11993) near the dissociation limit,
and/or the increased importance of nonadiabatic effects and excited-state
potential energy surfaces. So far, quantum studies of this benchmark
system have not been conducted at total energies exceeding 1.1 eV.
The experimental results for the Hi(u+) + Ne system demonstrate
again that, even for such a simple system, QCT can provide some answers,
but substantial deviations can occur at energies where quantum effects are
important and at energies where additional electronic states become
--- Page 182 ---
Non-Equilibrium Air Plasma Chemistry
167
accessible and the dynamics, therefore, is rendered more complicated by
dynamics involving multiple potential energy surfaces. This is usually the
case for dissociation channels because multiple states usually converge to a
dissociation limit. Multi-surface QCT calculations involving surface hopping
have in fact provided good agreement with state-selected experiments for the
Hi + He CID system (Govers and Guyon 1987, Sizun and Gislason 1989).
Both experimental and theoretical results provided evidence for the impor-
tance of a non-adiabatic mechanism involving electronic excitation to the
surface associated with the repulsive Hie~t) state. The situation is far
more complicated for dissociation systems involving air plasma neutrals
O2, N2, and NO or ions oi and NO+, since all of these molecules have
excited electronic states with equilibrium energies substantially below the
first dissociation limit. From these arguments, it must be considered doubtful
that QCT calculations based only on the ground-state potential energy
surface (and thus excluding surface-hopping mechanisms) can provide
realistic dissociation and reaction cross sections for such systems. However,
Capitelli and coworkers (Esposito and Capitelli 1999, Esposito et al 2000)
have conducted extensive QCT calculations on the N2(U) + N dissociation
system using a semi-empirical potential energy surface (Lagana et al 1987)
and the resulting state-specific dissociation rate coefficients, when converted
to global dissociation rates, were in good agreement with shock-tube
measurements of the temperature dependence of the dissociation rate as
provided by Appleton et al (1968). Esposito et al (2000) suggested that
dissociation rates from high vibrational levels of the ground state would be
similar to those of near-resonant low vibrational levels of electronic states.
While this may be the case for the N2(U) + N system, the work by Wodtke
and co-workers (Mack et al 1996, Price et al 1993, Rogaski et al 1993,
1995, Silva et al 2001) on 02(U) + O2 discussed earlier provided evidence
of marked interference by excited electronic states. The day has yet to
come when exact quantum approaches can address such complicated systems
at high levels of excitation.
Finally, we conclude that equations (4.4.7) and (4.4.9) provide a good
start to describe endothermic chemical processes, at least in the cross section
growth phase of energy. Cross section parameters can be obtained from fits
to measurements or calculations of the translational energy dependence of
cross sections for ground state reactants, or from the temperature depen-
dence of rate coefficients and an appropriate transformation. The latter
approach, however, can only be reliably applied at low temperatures,
where vibrational excitation of the reactants is insignificant. Vibrational
effects, however, as quantified through the>. parameter, need a more careful
consideration of the dynamics. The recent PFI-PESICO measurements (Qian
et aI2003a,b, Zhang et a12003) provide hope that similar studies will soon be
applied to larger diatomic systems of relevance to air plasmas, such as oi
and NO+.
--- Page 183 ---
168
Air Plasma Chemistry
4.5 Recombination in Atmospheric-Pressure Air Plasmas
An important loss process for total charge density in atmospheric plasmas is
the recombination of electrons with positive ions. In situations where
negative ions are present, ion-ion recombination will also occur. However,
the focus of this section is on electron-ion recombination. Atomic ions
recombine exceptionally slowly with electrons since the large amount of
energy gained during a recombination event must be emitted as a photon
or removed via an interaction with a third body (McGowan and Mitchell
1984). The exothermicity is equal to the ionization potential of the atom.
These processes, introduced in section 4.1, are called radiative or dielectric
recombination and three-body recombination, respectively. In molecular
ion recombination, energy can also be released as kinetic and internal
energy, and the rate constants associated with this mechanism are usually
extremely fast. This mechanism is called dissociative recombination and
for a diatomic species is represented as
AB+ + e- -
A + B + kinetic energy.
(4.5.1)
For poly atomic species, formation of three neutral particles is common
(Larsson and Thomas 2001). Process (4.5.1) is the major electron loss process
unless all positive ions are atomic or negative ions are present in concen-
trations of a factor of ten or greater than electrons. For air plasmas at
temperatures of a few thousand Kelvin, the dissociative recombination loss
process is dominant and involves mainly oi, NO+, Ni, and H30+ and its
hydrates (Jursa 1985, Viggiano and Arnold 1995). These systems are the
only ones discussed here. Note, however, that in low temperature air
plasmas, electron attachment to O2 to produce negative ions is a very
important electron loss mechanism.
Rate constants for dissociative recombination have been measured for
decades under thermal conditions and as a function of electron energy for
a variety of stable species (Adams and Smith 1988, McGowan and Mitchell
1984, Mitchell and McGowan 1983). In contrast, little was known about the
product distributions of such reactions until the recent advent of storage ion
rings (Larsson et al 2000, Larsson and Thomas 2001). Now, not only can
product speciation for polyatomic species be measured, but also the product
states for small systems, especially diatomic molecules. Very recently,
measurements of both cross sections and product distributions for vibration-
ally and electronically excited species have been made (Hellberg et al 2003,
Petrignani et al 2004). This is extremely important since theoretical
calculations of dissociative recombination kinetics are very difficult and
often fail to match experiment, although the agreement is improving for
small systems. In this section, recent work done in storage rings is empha-
sized since those experiments yield the most detailed information.
--- Page 184 ---
Recombination in Atmospheric-Pressure Air Plasmas
169
4.5.1 Theory
Guberman (2003a) has recently reviewed the important mechanisms for
dissociative recombination. Historically, two mechanisms are usually
described. They have been termed direct and indirect (McGowan and
Mitchell 1984). Direct recombination was originally proposed by Bates
and Massey (1947) to explain the almost complete disappearance of the iono-
sphere at night. Indirect processes were first attributed to Bardsley (1968).
Dissociation is efficient when there is a repulsive state of the neutral molecule
in the vicinity of the ionic state, although mechanisms presently exist for which
there is no curve crossing. Figure 4.15 illustrates the direct and indirect
processes for a particular channel of ot recombination (Guberman and
Giusti-Suzor 1991). Here the lI;t state of O2 intersects the X 2IIg state of
Ot. In the direct mechanism shown in figure 4.15, an electron with energy c;
is captured from ot (v = 1) into the 1 I;t dissociative state of the neutral
and the dissociation occurs directly on the repulsive potential. This type of
process is rapid if the neutral state crosses near a turning point of a vibrational
level of the ion so that the Franck-Condon factor between the states is large.
The nuclei separate rapidly on the repulsive curve if the auto-ionization life-
times are smaller than those for dissociation. Direct recombination leads to
cross sections that vary as E- 1 (McGowan and Mitchell 1984).
The indirect mechanism involves the electron being captured into a
vibrationally excited Rydberg state. In figure 4.15, an electron of energy c;'
is captured into the v = 5 level of the 1 I;t Rydberg state. Either vibronic
-0.62
8,"
-0.64
6'
c» ... ...
+ -0.66
81 I!
1::
IU -0.68
e.
>
~
:
w -0.70
z
( .....
W
1
+
-0.72
RYDBERG LJl
1
+
-0.74
VALENCE LJl
1.7
1.9
2.1
2.3
2.5
2.7
INTERNUCLEAR DISTANCE (Bohr)
Figure 4.15. Potential energy curves involved in at dissociative recombination. Terms are
defined in the text (Guberman and Giusti-Suzor 1991).
--- Page 185 ---
170
Air Plasma Chemistry
or electronic coupling leads to predissociation on the repulsive curve. Since
the Rydberg levels are discrete, indirect recombination results in resonances.
For ions with many atoms, the resonances are usually not detectable except
that the cross section changes with energy differently than E- 1•
4.5.2 oj +e-
Dissociative recombination of oj can proceed to produce two 0 atoms in a
variety of states. They are listed below in order of decreasing exothermicity,
Ot(X 2IIg) + e-
Oe P) + Oe P) + 6.54eV
(4.5.2a)
Oe P) + OeD) + 4.9geV
(4.5.2b)
OeD) + OeD) + 3.02eV
(4.5.2c)
Oe P) + OeS) + 2.77eV
(4.5.2d)
OeS) + OeD) + 0.8eV.
(4.5.2e)
Both excited states of 0 are known to fluoresce in the atmosphere, the
Oe D) .. -
Oe S) transition leads to what is referred to as the green line (at
5577 A.) (Guberman 1977, Kella et a11997, Peverall et aI2000), a prominent
component of atmospheric and auroral airglows. Red emissions (6300 and
6364A.) are obtained from the Oe PJ) -
Oe D) transitions (Guberman
1988). Due to the importance of these atmospheric emissions, much effort
has gone into studying the dissociative recombination of oj, both experi-
mentally and theoretically. Recent progress in experimental techniques has
allowed not only for cross section and branching ratio data to be measured
for the ground state but also for vibrationally excited states.
Rate constants for this ot recombination have been measured versus
temperature and kinetic energy decades ago. The early work has been
summarized (McGowan and Mitchell 1984, Mitchell and McGowan 1983)
and the rate constant can be expressed as 1.9 x 10-17 (300/Te)O.5 cm3 S-I,
where Te is the electron temperature. More recent work has resulted in
very detailed cross sections as a function of energy (Kella et a11997, Peverall
et aI2001). In the Peverall et al (2001) experiment only ground state ot was
present. Figure 4.16 shows cross sections versus collision energy from that
work. Resonances were found at 0.01, 0.2, 0.25, 1.4, and 1.8 eV, but do
not show well on this graph covering several orders of magnitude in cross
section. Such data should be used for non-equilibrium plasmas, otherwise
the thermal rate expression above should be used.
A measurement of the quantum yield of the reaction versus collision
energy was reported by Peverall et al (2001). At most energies, OeD) is
the most abundant product followed closely by oe P). This indicates that
channel b is dominant, followed by c and a. While the Oe S) yield is small,
--- Page 186 ---
Recombination in Atmospheric-Pressure Air Plasmas
171
10-6 :'. fh- -_
10-8 :-
1E-3
tams
'1
'if--
'~.'"I,--
'1
...
...
. -.. -
.. ~.:
,I
,I
.1
0.01
0,1
1
Collision energy (eV)
Figure 4.16. Rates constants for recombination of 01' as a function of kinetic energy
(Peverall e t at 2001).
it is important since it is the source for the green airglow line (Guberman
1977, Guberman and Giusti-Suzor 1991, Peverall et al 2000). Its quantum
yield decreases with energy at low energy and increases at high energy. The
production of the 0(' S) and 0(' D) states has been discussed theoretically
(Guberman 1977, 1987, 1988, Guberman and Giusti-Suzor 1991, Peverall
et aI2000).
The most recent work on this reaction reports the vibrational level
dependence for the cross sections and branching ratios at near OeV collision
energy (Petrignani et al 2004). Vibrational excitation of the ion has been
postulated to explain the abundance of the green airglow (Peverall et al
2000). The relative cross sections for v = 0, 1, and 2 are 14.9,3.7, and 12.4
at ca. 0 e V (2 me V FWHM). It is interesting that the cross section for
v = 1 is much smaller than for v = 0 or 2. Some of the resonances are
enhanced with vibrational excitation, but the cross section versus energy
data have not been derived as yet from the raw data. The branching data
versus vibrational state are listed in table 4.7. The production of 0(' S)
increases with vibrational level, which indicates that the vibrational distribu-
tion of ot will be critical in determining airglow as has been predicted.
NO+ is another important ion in air plasmas and excellent new studies have
yielded detailed information on numerous aspects of the dissociative recom-
bination reaction. Recombination of the ground state (X 1 E+) can lead to
three channels and seven more channels are possible for NO+(a 3E+), a
long-lived metastable species, or for high energy collisions. The channels
--- Page 187 ---
172
Air Plasma Chemistry
Table 4.7. Branching percentage for various channels as a function of vibrational state for
ot dissociative recombination (from Petrignani et a12004)
Channel
v=O
v=1
v=2
OCD) + oCS)
4.7 ± 2.5
19.9 ± 10.5
10.7 ± 5.9
OCD)+OCD)
23.9 ± 12.0
28.8 ± 24.1
8.3 ± 7.6
Oep) +OCD)
47.9 ± 23.7
28.1 ± 36.7
63.4 ± 38.6
Oep) +oep)
23.4 ± 11.7
23.3 ± 30.4
17.6 ± 20.5
and associated energetics for the ground state are
NO+(XI~+) +e--- Oe P) + N(4S) + 2.70eV
(4.5.3a)
OeD) + N(4s) + 0.80eV
(4.5.3b)
Oe P) + NeD) + 0.38eV
(4.5.3c)
Oe P) + Ne P) - 0.81 eV
(4.5.3d)
Oe S) + N(4S) - 1.42eV
(4.5.3e)
OeD) + NeD) - l.5geV
( 4.5.3f)
OeD) + Nep) - l.5geV
(4.5.3g)
OeS) + NeD) - 3.81 eV
(4.5.3h)
OeS) + Nep) - 5.00eV
( 4.5.3i)
O( S) + N(4 S) - 6.38 eV.
( 4.5.3j)
Production of Oe D) from this reaction is another source for the red airglow
and the N(4 S) ... -
NeD) radiation is responsible for the 5200 A airglow line
(Jursa 1985). As for ot, rate constants for the sum of all channels have been
known for years. The recommended rate from swarm experiments is
4.3 x 10-7 (300/Te)O.37 cm3 S-I, where Te is the electron temperature
(McGowan and Mitchell 1984, Mitchell and McGowan 1983). More recent
work has yielded product state distributions and detailed cross section
measurements for both the ground (X 1 ~+) state at several energies and
for the a 3~+ state at low energy (Hellberg et al 2003).
Table 4.8 gives the branching fractions for reaction (4.5.3) for several
energies for the ground state and also for the metastable. At low energy,
channel c accounts for nearly 100% of the reactivity and remains dominant
at 1.25 eV collision energy, although kinetic energy is seen to drive channel d.
At 5.6 eV collision energy, many other channels also become important with
channel fbeing the most abundant. Finally, results for the NO+(a3~+) state
--- Page 188 ---
Recombination in Atmospheric-Pressure Air Plasmas
173
Table 4.8. Branching percentage for various channels as a function of energy and state for
NO+ dissociative recombination. Both experimental and statistical theoretical
results are shown. Blanks indicate that the state is not accessible and a dash ('-')
indicates that channel was not able to be derived experimentally (Hellberg et al
2003).
NO+(Xl~+),
NO+(Xl~+),
NO+(Xl~+),
NO+(a3~+),
OeV
1.25eV
5.6eV
OeV
Channel
Exp't
Theory
Exp't
Theory
Exp't
Theory
Exp't
Theory
(4.5.3a)
5
17
10
11
3
3
6
(4.5.3b)
0
0
10
0
0
0
12
7
(4.5.3c)
95
83
70
57
15
20
23
32
(4.5.3d)
10
32
11
11
18
19
(4.5.3e)
0
0
4
(4.5.3f)
31
32
11
17
(4.5.3g)
21
20
7
10
(4.5.3h)
9
12
10
3
(4.5.3i)
10
3
13
2
(4.5.3j)
2
at low collision energy is included. Numerous channels are open and most are
observed with channel c again being the most abundant, although only
slightly.
Also included in table 4.8 are the results for a simple statistical model
calculation. The model includes two effects. (1) The number of states
connected to a dissociation limit determines its probability. For instance
for channel a, one takes the product of spin and angular momentum
multiplicities, i.e. (3 x 3 x 4 x I) = 36. Doing this for each open channel
and then normalizing yields the probability for that channel. (2) The results
are corrected so that spin-forbidden channels are not allowed, e.g. channel b.
The agreement is quite good, especially considering the difficulty of doing
detailed calculations.
4.5.4 Nt +e-
The final diatomic ion to be discussed is Nt. Again rate constants have long
been measured and can be represented as 1.8 x 10-7 (300/Te)o.39 cm3 S-I,
where Te is the electron temperature. Thus, all the atmospherically important
ions recombine at approximately the same rate and have about the same
dependence on electron temperature. Details of this reaction have been
studied recently in storage rings (Kella et a11996, Peterson et al 1998) and
theoretically (Guberman 2003b). The reaction can proceed by several
--- Page 189 ---
174
Air Plasma Chemistry
channels:
N(4S) + N(4S) + 5.82eV
N(4S) + NeD) + 3.44eV
N(4S) + Nep) + 2.25eV
NeD) + NeD) + 1.06eV
NeD) + Nep) - 0.13eV.
(4.5.3a)
(4.5.3b)
(4.5.3c)
(4.5.3d)
(4.5.3e)
The last channel is endothermic but is accessible for v = 1 and higher.
The recombination of Nt produces airg10w at 5200, 3466, and 10 400 A,
the latter two from Ne P). The large exothermicity combined with the
mass difference causes isotopic fractionation in the Mars atmosphere (Fox
1993). The lighter mass neutral, 14N, can escape at the maximum energy
allowed, but not 15N.
The storage ring experiments found that rate constants are in good
agreement with the early measurements and that vibrational excitation
decreased the rate slightly, although they could not quantify the reduction
for individual states (Peterson et al 1998). At an electron temperature of
300 K, Guberman calculated rate constants for v = 0, 1, and 2 to be
2.1 x 10-7,2.9 X 10-7, and 1.1 x 1O-7cm3s-1, respectively. Sincethev= 1
rate is calculated to increase and the v = 2 to decrease, the relatively insensi-
tive nature of the experimental value to vibrational excitation could be a
cancellation of the two effects.
Channel a, the lowest energy pathway, was found not to occur. The
branching for the other channels for v = 0 are (b) 37 ± 8%, (c) 11 ± 6%,
and (d) 52 ± 4% when the coldest source was used. For a higher temperature
source, more of channel (c) was observed at the expense of the other two
channels. The probability of producing the endothermic channel was
found to increase with rotational quantum number.
4.5.5 H30+(H20)n
In wet atmospheres, production of H30+ and its hydrates are likely. From
80 km and below in the atmosphere, these are either the dominant ions or
an important intermediary in the production of other clusters (Viggiano
and Arnold 1995). Since these molecules are polyatomic the detailed state
information on the dissociative recombination process is not available, but
complete product distributions are known.
The rate constants for dissociative recombination for these ions
are extremely rapid. H30+ rate constants can be expressed at 6.3 x
1O-7(300/Te)0.5cm3s-1 for Te < 1000K and 7.53 x 1O-7(800/Te)O.5cm3s-1
for Te > 1000 K (McGowan and Mitchell 1984). The rate constants for
--- Page 190 ---
Acknowledgments
175
the clusters are even faster. Johnsen gives the rate constants as
(0.5 + 2n)(300/T)o.s x 10-6 cm3 s-1 for n = 1-4 (Johnsen 1993). Thus, in
wet atmospheres, it is very hard to maintain a plasma unless negative ions
are formed.
H30+ can dissociate four ways. The pathways and the percentage of
each channel are listed below for both Hand D (Neau et al 2000),
H20 + H + 6.4eV (H: 18 ± 5%)(D: 17 ± 5%)
HO + H2 + 5.7 eV
(H: 11 ± 5%)(D: 13 ± 3%)
OH + 2H + 1.3 eV
(H: 67 ± 6%)(D: 70 ± 6%)
0+ H2 + H + 1.4eV (H: 4 ± 6%)(D: 0 ± 4%).
(4.5.4a)
(4.5.4b)
(4.5.4c)
( 4.5.4d)
No statistical difference was observed between the two isotopes. At the time
of the measurements the preponderance of the channel producing three
neutrals was surprising. This can obviously be an important source of
radicals.
H30+(H20) can dissociate into a variety of pathways. The channel
producing 2H20 + H is by far the dominant channel (94 ± 4%) (Nagard
et al 2002). The experiment was performed with deuterium for better
separation of the channels. The only other channel definitely produced
within error is the channel producing H20, OH + H2 (4 ± 2%).
4.5.6 High pressure recombination
The above discussion refers to dissociative recombination in the low-pressure
limit. At high pressures, heavy-body collisions occur while an electron is
within the orbiting capture radius. This obviously can change the energy
of the collision and lead to different kinetics. It has been shown that larger
rate constants are found with increasing pressure. At pressures greater
than an atmosphere, rate constants of 10-4 cm3 S-1 have been measured
(Armstrong et a11982, Cao and Johnsen 1991, Morgan 1984, Warman et al
1979). Theoretical examinations have been made to explain the increase
(Bates 1980, 1981, Morgan and Bardsley 1983). However, the number of
such processes that has been studied is limited and at present no information
is known about how pressure would effect product distributions. It may be
expected that high pressure would result in less fragmentation, especially if
the three-body fragmentation is sequential.
Acknowledgments
KB and MS would like to acknowledge invaluable discussion with and help
from U. Kogelschatz. SW, AAV, and RD thank numerous colleagues who
--- Page 191 ---
176
Air Plasma Chemistry
have contributed to sections 4.3, 4.4, and 4.5 of this chapter: John Paulson,
Robert Morris, Thomas Miller, Jeff Friedman, Peter Hied, Itzhak Dotan,
Me1ani Menendez-Barreto, John Seeley, John Williamson, Fred Dale, Paul
Mundis, Susan Arnold, Tony Midey, Jane Van Doren, Svetoza Popovic,
Yu-Hui Chiu, Dale Levandier and Michael Berman. The authors thank
Dick Zare, Scott Anderson, and Steve Leone for helpful discussions.
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--- Page 198 ---
Chapter 5
Modeling
Osamu Ishihara, Graham Candler, Christophe 0 Laux,
A P Napartovich, L C Pitchford, J P Boeuf
and John Verhoncoeur
5.1
Introduction
This chapter deals with the state-of-the-art in computer modeling of the
theoretical formulations that were presented in the previous two chapters.
Air plasmas are inherently complex, a situation made worse by the presence
of molecular ions and electro-negative species. The air plasma consists of a
high-temperature mixture of nitrogen and oxygen. With higher gas tempera-
ture, dissociation and recombination of N2 and O2 will produce more
neutrals like N, 0 and NO. Further increase of the temperature prompts
the ionization process to take place, producing electron population in the
air. The resulting ionic species include Nt, N+, ot, 0+ and NO+, while
electro-negative species are negligibly small in the amount relative to the
concentration of electrons for sufficiently high temperature. Detailed
mechanisms of ionization and recombination in atmospheric pressure air
plasmas are yet to be fully understood. The thermal state of the air plasma
may not be straightforward to describe because of the variety of populations
of atoms, molecules, and diatomic molecules involved. The energy of the
particles is characterized by their modes of motion, i.e. translation, vibration
and rotation. The thermal state may be well described by the electron
temperature and separate independent temperatures for heavy particles,
since free electrons are heated rapidly by external means while heavy particles
are much slower in changing their energy. A combination of computer
modeling in conjunction with experiments is expected to play an essential
role in filling in the gaps of our understanding and thereby lay the ground-
work for our eventual mastery over air plasmas.
The specific topics included in this chapter span the gamut of numerical
techniques used for the modeling of everything from glow discharges, to
183
--- Page 199 ---
184
Modeling
diffuse discharges, multi-dimensional flow, Trichel pulses, dielectric barrier
discharges, and the initial air breakdown.
It is worth mentioning that the determination of the electron energy
distribution function is important since the ionization source term and trans-
port coefficients are derived from this function. A model with the assumption
of a Maxwell-Boltzmann distribution for electrons provides an accurate
description of collisional air plasmas where it is possible to parameterize
the electron energy distribution as a function of the local reduced field
strength or the electron average energy. The models without the assumption
of a Maxwell-Boltzmann distribution for electrons, although applied only to
the electron-ion non-thermal plasma, are described in sections 5.4 and 5.5.
Full kinetic models, while harder to apply to the complexity of the air
plasma, offer the advantage of providing the electron energy distribution
function as a function of space and time. A description of a full kinetic
model and a novel application to gas breakdown (although limited in species)
in certain geometries is given in section 5.6. The self-consistent calculation of
the space charge electric field in the modeling is a challenging task in the air
plasma. The electrical properties of the discharges depend on the cathode
region where the charge neutrality fails to fulfill. The models described in
sections 5.2 and 5.3 are focused on the air plasma without boundary effect
and neglecting the coupling of the non-equilibrium plasma chemistry to
the flowing air stream, while latter sections, although limited in ion species,
concern the effect of boundaries.
Section 5.2, by G. V. Candler, deals with non-equilibrium air discharges
and discusses approximations and numerical solutions to the governing
equations. As a basis for modeling the atmospheric-pressure plasma, the
governing equations are described in detail. Those are conservations of
mass, momentum, and energy, supplemented by equations of vibration-
electron energy and electron translational energy. The model involves 11
species air plasma, including five neutral species (N2, N, O2 , 0, NO), five
ionic species (Nt, N+, ot, 0+, NO+), and the electrons, with finite-rate
chemical reactions and coupling between the energy modes and transport
processes. A numerical technique based on finite-volume computational
fluid dynamics is introduced.
Section 5.3, prepared by C. Laux, describes the modeling of dc glow
discharges in atmospheric pressure air. The air plasma is modeled by two
temperatures: electron temperature Te and gas temperature Tg . The numer-
ical solution of the two-temperature chemical kinetic model with 40 reactions
of the 11 species, where the electron temperature is elevated with respect to
the gas temperature, is studied. This section includes a brief description of
experiments conducted to validate the modeled mechanism of ionization in
two-temperature atmospheric pressure air plasmas.
Section 5.4, written by A. P. Napartovich, addresses the challenging
problem of modeling Trichel pulses characterized by regular current pulses
--- Page 200 ---
Multi-dimensional Nonequilibrium Air Plasmas
185
in a negative corona for pin-to-plane configurations. The proposed multi-
dimensional model is found to be essential in demonstrating the regular
current oscillations that are observed in Trichel pulses.
Section 5.5, contributed by L. C. Pitchford and J. P. Boeuf, provides an
overview of electrical models of plasmas created in gas discharges such as
dielectric barrier discharges (DBDs) and microdischarges associated with
the study of non-thermal, atmospheric pressure plasmas. The state-of-the-
art in modeling DBDs is advanced, but relatively few of the previous
works have dealt with DBDs in air. However, the formulation of a suitable
model and the understanding of the evolution of the plasma in DBDs is
independent of gas mixture, and conclusions derived from model results
are reviewed in this section. Models have helped us understand the different
modes observed in DBDs and have clarified the underlying physical nature of
atmospheric pressure glow discharges. Modeling of discharges in small
geometries is now under way, and further work in this area should soon
lead to a better understanding of scaling issues.
The final section, authored by J. Verboncoeur, then discusses a model
for the initiation of breakdown in a surface-discharge-type PDP (plasma
display panel) cell in which a gas mixture is ionized. The modified particle-
in-cell (PIC) Monte Carlo (known collectively by the acronym, 'PIC-MC')
collision model is described and a technique to measure Paschen-like
curves is proposed.
5.2
Computational Methods for Multi-dimensional
Nonequilibrium Air Plasmas
5.2.1
Introduction
There has been considerable interest in recent years in finding methods for
reducing the power budget required to generate large volumes of atmos-
pheric pressure air plasmas at temperatures below 2000 K with electron
number densities of the order of 1013 cm -3. These reactive air plasmas poten-
tially have numerous applications. In order to increase the electron density
without significantly heating the gas, the energy must be added in a targeted
fashion. One method is to add energy to the free electrons with a dc
discharge. This approach was successfully demonstrated at Stanford Univer-
sity in a series of experiments in atmospheric pressure air at temperatures
between 1800 and 3000 K. The experiments showed that it is possible to
obtain stable diffuse glow discharges with electron number densities of up
to 2 x 1012 cm-3 from a 250mA power supply, which is up to six orders of
magnitude higher than in the absence of the discharge. In principle, the
--- Page 201 ---
186
Modeling
electron number density could be increased to higher values with a power
supply capable of delivering more current. No significant degree of gas
heating was observed, as the measured gas temperature remained within a
few hundred Kelvin of its value without the discharge applied.
In this section, we present a computational approach for simulation of
this type of non-equilibrium air plasma. First, we present the multi-
dimensional governing equations that describe the atmospheric-pressure
plasma generated in the Stanford experiments. We then describe how to
solve the equations with a finite-volume computational fluid dynamics
approach. The model presented assumes a three-temperature, II-species
air plasma. Finite-rate chemical reactions and coupling between the
energy modes and all of the relevant transport processes are included.
Such an approach may be extended to model many multi-dimensional air
discharges.
5.2.2 Basic assumptions
The thermal state of the gas is assumed to be described by separate and
independent temperatures. The energy in the translational mode of all the
heavy particles is assumed to be characterized by a single translational
temperature. The rotational state of the diatomic molecules is taken to be
equilibrated with the translational temperature.
The vibration-electronic state of the gas is described by a separate
vibration-electronic temperature. This approach is taken by Gnoffo et at
(1989), and is based on the rapid equilibration of the vibrational mode of
molecular nitrogen and the electronic states of heavy particles. The transla-
tional energy of the free electrons is characterized by a separate electron
temperature, Te. This implies that the translational energies of free electrons
can be characterized by a Maxwell-Boltzmann distribution at that tempera-
ture. Additional specific assumptions are made and these will be discussed in
conjunction with the derivation of the governing equations.
5.2.3 The conservation equations
The flow within the plasma experiment test-section is described by the
Navier-Stokes equations that have been extended to include the effects of
non-equilibrium thermo-chemistry. In this section the individual species'
mass, momentum and the energy conservation equations are discussed.
The mass conservation equation for chemical species s is given by
Bps
(_)
at + V'. PsUs = w.,
where Ps is the species mass density, Us is the species velocity vector and Ws
represents the generation rate of species s. We define the mass-averaged
--- Page 202 ---
Multi-dimensional Nonequilibrium Air Plasmas
187
velocity, U, as
n
- "p-
u= ~-us
s=1 Ps
where the sum is over the n species present in the plasma. The total mass
density, p, is
Then we define the diffusion velocity, V" to be the difference between the
species velocity and the mass-averaged velocity, Vs = Us - U. The species
mass conservation equation becomes
~: + V . (Psu) = -V· (Psvs) + Ws
where the first term on the right hand side is the flux due to diffusion.
The electron conservation equation is more commonly written as
one
-;'
7it+ V 'le = We
where We is the rate of formation of electrons by ionization reactions. The
electron number flux, le, is obtained from the electron momentum equation
by neglecting inertia. This gives
~
--:
~
De
neve = le = -ne/LeE - -
V(neTe)
Te
where De is the electron diffusion coefficient and /Le is the electron mobility.
These are given by
D _ /LekTe
e-
e
Now, for numerical reasons (Hammond et al 2002), it is more convenient
to write the electron velocity in terms of the logarithmic derivative of the
electron number density:
~
~
De
Ve = -/LeE -- VTe -DeV(lnne)·
Te
This form results in significantly less numerical error in regions where the
electron number density is changing rapidly.
The mass-averaged momentum equation is
a
n
_
at (pit) + V . (Psuit) + V P = - V . T + L NseZsE
s=1
where p is the pressure, and T is the shear stress tensor.
--- Page 203 ---
188
Modeling
The total energy conservation equation is the total energy equation for
the mixture,
~~ + V'. ((E + p)it)
n
= -V'. (q + qv-el + qe) - V' . (U . T) - V' . L NseZsE(il + vs)·
s=l
The heat conduction vector, q + qv-el + qe, has been expressed in component
form, where each term is due to gradients of the different temperatures.
In addition to the total energy equation, we require an equation for each
independent energy mode. The vibration-electronic energy of a given species
is defined to be the difference between that species' internal energy computed
from the Gordon-McBride (1994) data and the sum of its translational-
rotational energy and heat of formation. For example, for a diatomic
molecule the specific vibration-electronic energy at the vibration-electronic
temperature Tv-e1 is given by
ev-el,s(Tv-e1 ) = es(Tv-e1) -
~RsTv-el -
h~
where es is the species specific internal energy, Rs = R/ Ms is the specific heat,
and h~ is the heat of formation. For atoms the translational energy is
removed from the enthalpy.
The vibration-electronic energy equation is similar to the total energy
equation, and may be written as
aEv_e1 + V' . (E
-)
at
v-el U
n
n
= -V'. L vsEv-e1,s - V'. qv-el + QT-v-el + Qe-v-el + L wsev_el'
s=l
s=l
The various energy transfer mechanisms to the vibrational energy modes
have been represented here. QT-v-el and Qe-v-el are the rates of translation-
vibration-electronic and electron-vibration-electronic energy exchange,
respectively.
The conservation of the electron translational energy, Ee = ~ nekTe' can
be written as
%t GnekTe) + V' . GnekTeve) = -neeE . ve -
QT-e - WeI - V' . fie
where QT-e is the translation-electron energy exchange rate. The term WeI is
due to the loss of electron energy due to ionization, where the ionization
energy is I.
These differential equations describe the flow of a time-dependent,
multi-component, multi-temperature gas. The solution of these equations
yields the dynamics of the conserved quantities of mass, momentum, and
--- Page 204 ---
Multi-dimensional Nonequilibrium Air Plasmas
189
energy. A detailed description of the applied electric field and the conserva-
tion of the current is given below.
5.2.4 Equations of state
Equations of state are required to derive the required non-conserved quanti-
ties of pressure and the temperatures. The total energy, E, is made up of the
separate components of energy, namely the kinetic energy and the internal
modes of energy constituting the thermal energy. It is written as
n
1 n
n
E = L
PSCyS T + 2" L
Psil . i1 + E y _e1 + Ee + L
Psh~.
s#e
s#e
s#e
This expression may be inverted to yield the energy in the translational-
rotational modes, and consequently T. The constants of specific heat at
constant volume, CyS ' are the sum of the specific heat of translation and the
specific heat of rotation. Thus, for diatomic molecules CyS = 5R/2Ms and
for atoms CyS = 3R/2Ms• The vibration-electronic temperature is computed
using a Newton method to find the root of the expression given above for
the vibrational-electronic energy. The electron temperature is determined
by simply inverting the relation between the electron energy, Ee, and the
energy contained in the electron thermal energy
Ee = PecyeTe = ~nekTe.
The total pressure is the sum of the partial pressures
n
n
R
R
P = LPs + Pe = L
Ps M T + Pe M Te·
s#e
s#e
s
e
5.2.5 Electrodynamic equations
The electric field can be computed from the Poisson equation for the electric
potential:
E = -\7</>,
However, we choose to take advantage of the experimental geometry,
and assume that the field only varies in the direction along the axis of the
flow. In this case, there is no forced diffusion in the radial direction, which
simplifies the implementation of the numerical method outlined above. In
addition, we can determine the local electric field from the known total
current of the discharge. Fundamentally, we know
. J
J (
De aTe
{)In ne)
1=-
A eneVex dA = A ene J-LeEx + Te ax + De ----a;- dA
--- Page 205 ---
190
Modeling
where A is the cross-sectional area of the discharge and Vex is the axial
electron velocity. Now, since the total current is a parameter set by the
experimental conditions, we can compute the electric field at each axialloca-
tion from the above equation. This ensures that the discharge carries the
correct current at every location in the discharge. This concept is supported
by previous work cited in Raizer (1997).
5.2.6 Transport properties
5.2.6.1
Shear stresses and heat fluxes
The shear stresses are assumed to be proportional to the first derivative of the
mass-averaged velocities and the Stokes assumption for the bulk viscosity is
made. This results in the conventional expression for the shear stress tensor.
The heat conduction vectors are given by the Fourier heat law
where Ibt , Ibv, and Ibe are the translational-rotational, vibration-electronic
and the electron translational conductivities.
5.2.6.2
Viscosity and thermal conductivity
The plasma flow is far from chemical equilibrium and properties based on
local thermodynamic equilibrium cannot be used. Thus a general multi-
component approach for transport properties is necessary. The collision
cross section method of Gupta et al (1990) accounts for the transfer of
momentum and energy by collision by means of a non-dimensional factor,
which is a function of the molecular weights of the species pairs, as well as
the collision cross sections.
5.2.6.3
Collision cross section method
The collision cross section method was developed for high temperature non-
equilibrium conditions. It permits efficient computation in the numerical flow
field and provides accurate non-equilibrium properties. The average collision
cross sections O,~/ and 0,;;2 are evaluated per species from the Chapman-
Enskog first approximation formulas and curve fits as a function of
temperatures. Here it must be pointed out that if one of the colliding partners
is an electron, the electron temperature Te must be used in the curve fits.
Viscosity for the gas mixture is given below, where 6.~;) is a function of
the collision cross sections evaluated at the appropriate temperatures
--- Page 206 ---
Multi-dimensional Nonequilibrium Air Plasmas
191
The thermal conductivity components, translational thermal conductivity
/'i,tn rotational thermal conductivity /'i,rot' and vibrational thermal conduc-
tivity are defined as follows:
15
n
X
/'i,tr = 4 k L
s
(2)
sole Lr#e arsXr~rs
n
X
/'i,rot = k L
s
(1)
s=mol Lr#e arsXr~rs
n
X
/'i,v-el = k L
s
(I)'
sole Lr#e arsXr~rs
Here ars are functions of the collision cross sections,
(1 - Z:) (
0.45 - 2.54 ~)
ars = 1 +
2
(l+~)
and
~
(I) = ~ J2Mrs [21,1
rs
3
7fkT rs'
~(2) = 16 J2Mrs [22,2
rs
5
7fkT rs'
The electron thermal conductivity /'i,e is given by
15
Xe
/'i,e =4 k
(2)'
Lr 1.45Xr~er
5.2.6.4
Electrical conductivity
The electrical conductivity is defined using the electron mobility, Me' In the
discharge region, the charged particles are acted upon by the electric field.
The electrons and ions move in opposite directions under the influence of
the electric field. The force acting on the electrons due to collisions with
other particles can be given as
where ve is the diffusion velocity of the electrons. Here it has been assumed
that the average collision frequency of electrons with ions is negligible
compared with that of electrons with all heavy particles, VeH' The electron
diffusion velocity can now be given by
--- Page 207 ---
192
Modeling
The electron current density le, defined as the average flux density of electron
charge, is
where
is the electron electrical conductivity.
5.2.6.5
Ordinary diffusion
Ramshaw's (1990) method is the basis of the multi-temperature multi-
component ordinary mass diffusion modeling in this work. Recent compar-
isons (see Desilets and Proulx 1995) between an exact method, with effective
binary, linear and Ramshaw's approximations show that only Ramshaw's
method is adequate to model diffusion fluxes in the context of plasma
flows with temperature gradients. Since the energy transfer between
components is much slower than momentum transfer, a multi-temperature
diffusion formulation is needed.
Correct treatment of ordinary diffusion in multi-component gas
mixtures requires the solution of a linear system of equations for the diffusive
mass fluxes relative to the mass-averaged velocity of the mixture. However,
their solution presents unwelcome and costly complications in many situa-
tions, particularly in the present multi-dimensional numerical simulation
where the diffusional fluxes are required at each mesh point and at every
time step in the calculation. For this reason effective binary diffusion approx-
imations are often used to avoid solving these equations. However, most
formulations suffer from lack of mass conservation. Ramshaw (1990)
correctly identified the origin of this inconsistency and developed a rational
procedure for self-consistently removing it. Thus, Ramshaw's self-consistent
effective binary diffusion approximation is used to model the ordinary
diffusion fluxes. The reader is referred to the work of Ramshaw (1990) and
Ramshaw and Chang (1991, 1993) for further details.
5.2.6.6 Energy exchange mechanisms
The energy exchange mechanisms that appear on the right hand side of the
internal energy equations must be modeled. The models that have been
proposed are simplifications of the complicated energy exchange processes
that occur on a molecular level. The models used in this work are outlined
below.
--- Page 208 ---
Multi-dimensional Nonequilibrium Air Plasmas
193
Translation-vibration electronic energy exchange. The rate of energy exchange
between the vibration-electronic and translational modes is well described by
the Landau-Teller formulation where it is assumed that the vibration-
electronic level of a molecule can change by only one quantum level at a
time. In this work we use the relaxation rates of Millikan and White (1963).
Translation and vibration-electron energy exchanges. The energy transfer
rate between the heavy-particle and electron translational modes, QT-e, was
originally derived by Appleton and Bray (1964).
QT-e = ne L 3k(Te - T) me VeH'
h
mh
Appleton and Bray modeled the energy exchange for elastic collisions
between electrons and atoms and between electrons and ions. However,
the heating of electrons by interactions with the vibrational energy modes
is important under the present conditions. This exchange is modeled using
the inelastic energy factor Deh :
Qe-v-el = ne L 3k( Te - Te-v-e1) me (Deh - I) veH'
h
mh
Expressions for veH and Deb are taken from the work of Laux et at (1999).
5.2.7 Chemical kinetics
As the plasma exits the torch and flows through the nozzle and discharge
regions, chemical reactions occur and mass transfer between species takes
place. As the characteristic times for the chemical reactions and fluid
motion are far apart, equilibrium predictions cannot be used to determine
the individual species concentrations. As a consequence, finite rate chemistry
is introduced to determine individual species concentrations.
The plasma consists of a high-temperature mixture of nitrogen and
oxygen. The species considered in the flow are the neutral species (N2' O2,
NO, N, 0), the ionic species (Nt, Ot, NO+, N+, 0+), and the electrons,
e-. A 38 reaction finite-rate chemical kinetics model (Laux et al 1999) is
employed to describe the chemistry in the flow. Backward reaction rates in
the law of mass action are computed from the equilibrium constants obtained
from the Gordon-McBride (1994) data.
5.2.8 Numerical method
The electron number density varies by many orders of magnitude in the flow
field, and therefore the numerical method must be designed to be stable and
accurate under these conditions. Hammond et at (2002) developed a numer-
ical method for glow discharges that reduces numerical error for this type of
--- Page 209 ---
194
Modeling
flow. In one dimension, the numerical representation of the electron conser-
vation equation is written as
n+ I
n
~t ( n
n
n
n
)
A
n
nei =nei-""A ne i+I/2Vei+I/2 -nei-I/2Vei-I/2 +utwei
,
'uX'
,
"
1
where ne,i+ 1/2 is the average electron number density, and ve,i+ 1/2 is
computed using the electron temperature and number density at grid
points i and i + 1. This approach is easily extended to multiple dimensions.
We use this approach for the electron conservation equation and a similar
approach for the electron energy conservation equation.
The most difficult part of simulating the discharge flows is the huge
range of time scales that govern the flow. The discharge energy relaxation
has a time scale of a nanosecond or less, while the total flow time through
the discharge region is of the order of 100 /ls. Therefore, the time integration
method must be designed to increase the stable time step size to the maximum
extent possible.
Under the conditions of the present dc discharge experiments, the
energy relaxation processes are very fast relative to the fluid motion time
scales and the chemical kinetic processes. To handle this large disparity in
characteristic time scales, we would usually use an implicit time integration
method. However, for this problem a complete linearization of the problem
is itself very expensive. (We solve 17 conservation equations, and the cost of
evaluating the Jacobians and inverting the system scales with the square of
the number of equations.) Therefore we linearize only those terms that are
relatively fast, which results in a simple and inexpensive semi-implicit
method that very substantially reduces the cost of the calculations.
The relatively fast terms are the internal energy relaxation and the Joule
heating terms in the source terms for the three energy equations. Therefore,
we split the source vector, W, into these terms, Wfast> and all of the other
terms, Wslow ' The conservation equations are then written as
aU of
1 orG
~
+ --.q- + - ----;;;- = Wfast + W s10w
ut
ux
r ur
where U is the vector of conserved variables, F is the axial direction flux
vector and G is the radial direction flux vector. We then linearize Wfast in time
Wfu~ I = W rast + Cfast 8Un + O(~p)
where Cfast is the Jacobian of Wfast with respect to U, and 8Un = Un+ 1 - Un.
Because of the form of Wfast> Cfast is a simple matrix that can be inverted
analytically. Then the solution is integrated in time using
8 n+1
(
A n )-1 (A (
)
(OF
1 orG))
U
= I - utCfast
ut Wfast + W s10w
-
~t ox + -;: or
.
--- Page 210 ---
Multi-dimensional Nonequilibrium Air Plasmas
195
This approach increases the stable time step by a factor of 50 compared to an
explicit Euler method. This results in a very large reduction in the computer
time required to obtain a steady-state solution.
A two-block grid is used to facilitate the implementation of the
boundary conditions. The first grid block represents the nozzle section,
and the second grid block represents the discharge region as well as a portion
of the open air which acts as a large constant-pressure exhaust reservoir at
one atmosphere.
The inflow boundary conditions are set by choosing the inflow static
pressure to give the experimental mass flow rate of 4.9 g/s. The inflow is
assumed to be in L TE at the measured temperature profile. This results in
a consistent representation of the inflow conditions. The boundary con-
ditions along the test-section surface are straightforward. The velocity is
zero at the surface, the temperature is specified, and the normal-direction
pressure gradient is zero. We assume that the metallic surface is highly catalytic
to ion recombination. Otherwise, the surface is assumed to be non-catalytic to
recombination for neutrals.
The computation is initialized as follows: first, the inflow conditions are
specified as above. Then the test-section and reservoir are all initialized at
atmospheric pressure, and at each axial location the temperature profiles
and chemical concentration profiles are set identical to the inflow boundary
profiles. Once a converged solution is obtained for the flow in LTE, the
discharge is ignited by injecting a flux of electrons at the cathode and
applying the Joule heating source term to the energy equations. Then a
steady-state solution for the dc discharge is obtained.
5.2.9 Simulation results
In this section we present numerical simulations of the dc discharge
experiment. Figure 5.2.1a shows the loglo of the electron number density
contours in the computational domain. The dc discharge region can be
observed in this figure. This is the bright region where the electron
number density is several orders of magnitude higher than in the region
upstream of the cathode where there is no discharge. It can be observed
that the electron number density is slightly higher than 1012 cm -3 in most
of the discharge region. This is in good agreement with the experimental
measurements for the electron number density. The electron number
density falls off gradually downstream of the anode region. The shape of
the discharge is similar to that observed in the experiments, which also
shows that the discharge is constricted at the cathode and diffuses
radially outward, away from the cathode. The simulations capture this
behavior.
Figure 5.2.1 b plots the electron temperature contours in the computa-
tional domain. It shows that the electron temperature is about 1~ 000 K in
--- Page 211 ---
196
Modeling
~III[JU[.]~
.lillIDL:::~
-.mlJULLIr:.
1500 1750 2000 2250 2500 2750 3000
2000
5250
8500 11750 15000
7
8.25
9.5 10.75
12
(a)
(b)
(c)
Figure 5.2.1. Log IO of (a) the electron number density, (b) the electron temperature and (c)
the translational temperature contours in the discharge region.
the discharge region. The computed electron temperatures are consistent
with the experimental predictions. Figure 5.2.1 b also shows that the electron
temperature drops off sharply just downstream of the anode because the
electrons rapidly equilibrate with the heavy particles due to their strong
coupling with the heavy species.
Figure 5.2.1c shows contours of the translational temperature in the
domain. It shows that the temperature in the discharge is about 3000 K in
the discharge region. The computed temperatures are generally higher than
the experimental measurements.
Figure 5.2.2 plots the axial variation of the centerline electron number
density and the temperatures along with the experimental values. This
figure quantitatively shows the variation of the electron concentration and
the three temperatures along the centerline of the discharge. From the
figure it can be seen that the electron number density remains slightly
above 1012 cm-3 in the discharge region. It falls off gradually downstream
of the anode. The computed electron temperature is very high in the cathode
region and falls to about 12000 K in most of the discharge region, which is
close to the two-temperature kinetic model prediction. As observed in the
contour plot for the electron temperature, the electron temperature falls
off abruptly in the region downstream of the anode. The translational
temperature increases from about 2200 K at the cathode to about 3000 K
in the discharge region. This is higher than the measured translational
temperature. However, the computed vibrational temperature is slightly
lower than the experimentally measured value.
--- Page 212 ---
Multi-dimensional Nonequilibrium Air Plasmas
197
16000
~
14000 ,---no
12000
sz
~10000
l!?
::s
~8000
&
E 6000
~
4000
2000
V
....
o 0
T.
~
.Tv . . .
•
• T •
•
•
•
Q)
"8
c: <
1 2 3
Distance from Centerline (cm) -
10'
Figure 5.2.2. Computed electron number density and temperatures along the dc discharge
centerline. Symbols denote experimentally measured values.
Figure 5.2.3 plots the radial profiles of the electron number density at
two locations in the discharge. Near the cathode it can be seen that the
diameter of the discharge is small and the electron number density is elevated
in a region which is nearly equal to that of the cathode area. Near the center
of the discharge the electron density is more diffuse and the diameter of the
discharge is about 4 mm, which compares well with the experimentally
observed diameter.
10"..-----------------,
c?'1012
E
.2-
~1011
UI
C
Gl
Cl
(fi 1010
.c
E
::s
Z 10'
c e
~ 10'
1 0~0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Distance from Centerline (cm)
Figure 5.2.3. Computed radial profiles of electron number density.
--- Page 213 ---
198
Modeling
5.2.10 Conclusions
The present work and that presented in section 5.3 demonstrates that stable,
diffuse discharges with electron number densities approaching 1013 cm -3 at
gas temperatures below 2000 K can be produced in atmospheric pressure
air. This result stands in sharp contrast to the widespread belief that these
diffuse discharges cannot exist without arcing instabilities or high levels of
gas heating. A computational fluid dynamics code for the simulation of
flowing non-equilibrium air plasmas including the presence of a dc discharge
was developed and compared to the dc experiments conducted at Stanford
University. The code uses a detailed two-temperature chemical kinetic
mechanism, along with appropriate internal energy relaxation mechanisms.
The discharge region was modeled by generalizing the channel model of
Steenbeck, and a new semi-implicit time integration method was developed
to reduce the computational cost. The computational results show good
agreement with the experimental data; however, the heat loss is more rapid
in the experiment than predicted by the computations.
Acknowledgments
This work was funded by the Director of Defense Research and Engineering
(DDR&E) within the Air Plasma Ramparts MURI program managed by the
Air Force Office of Scientific Research (AFOSR). Computer time was
provided by the Minnesota Supercomputing Institute.
References
Appleton J P and Bray K N C 1964 'The conservation equations for a nonequilibrium
plasma' J. Fluid Mech. 20 659-672
Gnoffo P A, Gupta R N and Shinn, J L 1989 'Conservation equations and physical
models for hypersonic air flows in thermal and chemical non-equilibrium' NASA
TP-2867
Gordon S and McBride B J 1994 'Computer program for calculation of complex chemical
equilibrium compositions and applications' NASA RP-1311
Gupta R N, Yos J M, Thompson RA and Lee K 1990 'A review of reaction rates and ther-
modynamic and transport properties for an II-species air model for chemical and
thermal non-equilibrium calculations to 30000 K' NASA RP-2953
Hammond E P, Mahesh K and Moin P 2002 'A numerical method to simulate radio-
frequency plasma discharges' J. Computational Phys. 176402
Laux C, Pierrot L, Gessman R and Kruger C H 1999 'Ionization mechanisms of two-
temperature plasmas' AIAA Paper No. 99-3476
Laux C 0, Yu L, Packan D M, Gessman R J, Pierrot L and Kruger C H 1999 'Ionization
mechanisms in two-temperature air plasmas' AIAA Paper 99-3476
Millikan R C and White DR 1963 'Systematics of vibrational relaxation' J. Chern. Phys.
393209
--- Page 214 ---
DC Glow Discharges in Atmospheric Pressure Air
199
Raizer Y P 1997 Gas Discharge Physics (Berlin: Springer) pp 275-287
Ramshaw J D 1990 'Self-consistent effective binary diffusion in multicomponent gas
mixtures' J. Non-Equilibrium Thermodynamics 15 295
Ramshaw J D 1993 'Hydrodynamic theory of mu1ticomponent diffusion and thermal
diffusion in multitemperature gas mixtures' J. Non-Equilibrium Thermodynamics
18121
Ramshaw J D and Chang C H 1991 'Ambipolar diffusion in multicomponent plasmas'
Plasma Chern. Plasma Proc. 11(3) 395
Ramshaw J D and Chang C H 1993 'Ambipolar diffusion in two-temperature multi-
component plasmas' Plasma Chern. Plasma Proc. 13(3) 489
Ramshaw J D and Chang C H 1996 'Friction-weighted self-consistent effective binary
diffusion approximation' J. Non-Equilibrium Thermodynamics 21
5.3 DC Glow Discharges in Atmospheric Pressure Air
5.3.1
Introduction
We present experimental and numerical investigations to determine whether
and to what extent the electron number density can be increased in air
plasmas by means of dc discharges. The strategy is to elevate the electron
temperature, Te, relative to the gas temperature, Tg, with an applied dc
electric field.
Section 5.3.2 describes numerical investigations of two-temperature
air plasma chemical kinetics. We present first a two-temperature kinetic
mechanism to predict electron number density in air at a given gas
temperature, as a function of the electron temperature. Close attention has
been paid to the influence of the electron temperature on the rate coefficients,
because collisions with energetic electrons can affect the vibrational
population distribution of molecules, thereby the rates of ionization and
dissociation.
Section 5.3.3 discusses the implications of this analysis for the genera-
tion of nonequilibrium air plasmas by means of electrical discharges. We
determine in section 5.3.3.1 the relation between electron number density
and current density, and between electron temperature and electric field.
This is accomplished with Ohm's law and the electron energy equation, as
discussed in section 5.3.3.2. A key quantity in the electron energy equation
is the rate of electron energy lost by inelastic collisions. To predict inelastic
losses in air plasmas, we have developed a detailed collisional-radiative
model. This model is presented in section 5.3.3.3.
Section 5.3.4 describes experiments with dc glow discharges in air. We
demonstrate that stable diffuse glow discharges with electron densities of
up to ",,2 x 1012cm-3 can be sustained in flowing preheated atmospheric
--- Page 215 ---
200
Modeling
pressure air. The electrical characteristics and thermodynamic parameters of
the glow discharges are measured.
Section 5.3.5 compares the measured electrical characteristics of dc
glow discharges in air with those obtained with the two-temperature and
collisional-radiative model. This comparison validates the two-temperature
model theoretical predictions. In addition, it enables us to establish the
power requirements of dc discharges in air plasmas. This fundamental
understanding forms the basis for the power budget reduction strategy
using repetitively pulsed discharges presented in chapter 7 section 7.4.
5.3.2 Two-temperature kinetic simulations
This section presents results of numerical investigations to determine
whether and to what extent electron number densities can be increased in
air plasmas by elevating the electron temperature, Te, relative to the gas
temperature, Tg • The two-temperature kinetic mechanism and rates used
for this work are presented in section 5.3.2.1. In section 5.3.2.2, the kinetic
model is used to predict the temporal evolution and steady-state species
concentrations in an atmospheric pressure air plasma with constant gas
temperature of 2000 K and with electron temperatures varied from 4000 to
18000 K. In section 5.3.2.3, the key reactions controlling ionization and
recombination processes are identified. An analytical model based on the
set of controlling reactions is then used to predict steady-state species
concentrations in two-temperature air. As will be seen, the analytical
model not only reproduces the CHEMKIN solution but also predicts an
additional range of steady-state electron number densities.
5.3.2.1
Two-temperature kinetic model
The rate coefficients required for the two-temperature kinetic model depend
on the relative velocities of collision partners (related to Tg for reactions
between heavy particles and to Te for electron-impact reactions) and on
the population distributions over internal energy levels of atoms and
molecules. Thus, these rate coefficients correspond to the weighted average
of elementary rates over internal energy states of atoms and molecules.
This forms the basis of the Weighted Rate Coefficient (WRC) method
described in references [1-4]. The method assumes that the internal energy
levels of atoms and molecules are populated according to Boltzmann distri-
butions at the electronic temperature Teb the vibrational temperature Tv, and
the rotational temperature Tr • Elementary rate coefficients are calculated
from cross-section data assuming Maxwellian velocity distribution functions
for electrons and heavy particles at Te and Tg , respectively. It is further
assumed that Tel = Te and Tr = Tg• The remaining parameter, Tv, can
only be determined in the general case by solution of the master equation
--- Page 216 ---
DC Glow Discharges in Atmospheric Pressure Air
201
for all vibrational levels by means of a collisional-radiative (CR) model that
incorporates vibrationally specific state-to-state kinetics. We have recently
developed such a model for nitrogen plasmas [1, 4] that provides insight
into the relation between Tv and Tg and Te in atmospheric pressure plasmas.
The nitrogen CR model accounts for electron and heavy-particle impact ion-
ization (atoms and molecules) and dissociation (molecules), electron-impact
vibrational excitation, V-T and v-v transfer, radiation, and predissociation.
Through comparisons between the results of the CR model and of a two-
temperature kinetic model of nitrogen that assumed either Tv = Tg or
Tv = Te, we have shown [4, 5] for the case of a nitrogen plasma at
Tg = 2000 K that the steady-state species concentrations determined with
the two-temperature kinetic model are in close agreement with the CR
model predictions if one assumes (1) that Tv = Tg for electron temperatures
Te ::; 9500K and electron number densities ne ::; ""lOll cm-3, and (2) that
Tv = Te or Tv = Tg for Te > 9500 K and ne ;::: "" 1015 cm -3 (in the latter
range, best agreement is obtained with Tv = Te but assuming Tv = Tg
leads to electron number densities that are underestimated by at worse a
factor of 5). It should be noted that the often-used assumption Tv = Te
produces steady-state electron number densities that are several orders of
magnitude greater than those obtained with the CR model for electron
temperatures Te ::; 9500K and electron number densities ne ::; ""lOll cm-3.
We extend these results to atmospheric pressure air by calculating all
WRC rate coefficients with the assumption Tv = Tg.
The full II-species (02, N2, NO, 0, N, oT, NT, NO+, N+, 0+, and elec-
trons), 40-reaction mechanism and rate coefficients for the case Tg = 2000 K
are summarized in table 5.3.1. Electron attachment reactions can be
neglected in atmospheric pressure air at temperature> 1500 K because the
equilibrium concentrations of O2 or 0- are negligibly small relative to the
concentration of electrons above ",,1500K (figure 5.3.1). For reactions
between nitrogen species, the rate coefficients are taken from Yu [5]. This
set is supplemented by two-temperature rate coefficients determined using
the WRC method for electron-impact dissociation and ionization of O2
and NO. For electron-impact ionization of 0, we adopt the two-temperature
rate
of Lieberman
and
Lichtenberg
[6].
Rate
coefficients
for
0+ + N2 {:} NO+ + Nand 0+ + O2 {:} oT + 0 are taken from Hierl
et al [7], and the rate coefficient of the charge transfer reaction between 0+
and NO is calculated using the experimental cross-section reported by
Dotan and Viggiano [8]. The remaining reactions involve collisions between
heavy particles and thus mostly depend on the gas kinetic temperature (as we
assume Tr = Tv = Tg). For these reactions, the rate coefficients of Park [9,
10] are employed.
The two-temperature kinetic calculations presented in the rest of this
section were made with the CHEMKIN solver [11] modified [12] so as to
allow a different temperature (Te) to be specified for the rates of particular
--- Page 217 ---
202
Modeling
Table 5.3.1. Two-temperature kinetic model of air plasmas. The temperature entering the
Arrhenius-type expressions is either the gas (Tg) or the electron (Te) tempera-
ture, as indicated in columns kr (forward rate) and kr (reverse rate). The
present mechanism is for gas temperatures greater than 1500 K.
Reaction
Temperature
Rate coefficient,
Ref.
dependence
k = ATb exp( -E/ RT)
(see
foot-
kr
kr
A
b
E/R
notes)
(mole cm s)
(K)
O2 Dissociation/recombination
1.
O2 + O2 = 20 + O2
Tg
Tg
2.00 X 1021
-1.5
59500 a
2.
O2 +NO= O+O+NO
Tg
Tg
2.00 X 1021
-1.5
59500 a
3.
O2 + N2 = 0 + 0 + N2
Tg
Tg
2.00 X 1021
-1.5
59500 a
4.
O2+0=0+0+0
Tg
Tg
1.00 X 1022
-1.5
59500 a
5.
02+ N =0+0+N
Tg
Tg
1.00 X 1022
-1.5
59500 a
6f. O2 + e=}O + 0 + e
Te
2.85 X 1017
-0.6
59500 b
6b. O+O+e =} O2 +e
Te
4.03 X 1018
-004
0 b
NO dissociation/recombination
7.
NO + O2 = N + 0 + O2
Tg
Tg
5.00 X 1015
0.0
75500 a
8.
NO+NO =N +O+NO
Tg
Tg
1.10 X 1017
0.0
75500 a
9.
NO + N2 = N + 0 + N2
Tg
Tg
5.00 X 1015
0.0
75500 a
10.
NO+O=N+O+O
Tg
Tg
1.10 X 1017
0.0
75500 a
11. NO+N=N+O+N
Tg
Tg
1.10 X 1017
0.0
75500 a
12f. NO + e =} N + 0 + e
Te
3.54 X 1016
-0.2
75500 b
12b. N + 0 + e =} NO + e
Te
8042 X 1021
-1.1
0 b
N2 Dissociation/recombination
13.
N2 + O2 = N + N + O2
Tg
Tg
7.00 X 1021
-1.6
113 200 a
14.
N2 +NO =N +N +NO
Tg
Tg
7.00 X 1021
-1.6
113 200 a
15.
N2 + N2 = N + N + N2
Tg
Tg
7.00 X 1021
-1.6
113 200 a
16. N2+0=N+N+0
Tg
Tg
3.00 X 1022
-1.6
113 200 a
17. N2+N=N+N+N
Tg
Tg
3.00 X 1022
-1.6
113 200 a
18f. N2 + e =} N + N + e
Te
1.18 X 1018
-0.7
113 200 b
18b. N + N + e =} N2 + e
Te
1.36 X 1023
-1.3
0 b
Zeldovich reactions
19.
N2 +0 =NO+N
Tg
Tg
6040 X 1017
-1.0
38400 a
20.
NO+0=02+ N
Tg
Tg
8040 X 1012
0.0
19400 a
Associative ionization/dissociative recombination
21f. N +0 =} NO+ +e
Tg
8.80 x 10°8
1.0
31900 a
21b. NO+ +e =} N +0
Te
9.00 X 1018
-0.7
0 c
22f. N+N=}Ni+e
Tg
6.00 x 10°7
1.5
67500 b
22b. Ni + e =} N + N
Te
1.53 X 1018
-0.5
0 b
23f. 0+0 =}oi +e
Tg
7.10 x 10°2
2.7
80600 a
23b. Oi+e=}O+O
Te
1.50 X 1018
-0.5
0 c
--- Page 218 ---
DC Glow Discharges in Atmospheric Pressure Air
203
Table 5.3.1. (Continued)
Reaction
Temperature
dependence
kr
Rate coefficient,
k = ATb exp( -E/ RT)
A
b
(molecms)
E/R
(K)
Electron impact ionization/three-body recombination
24f. O+e ~ 0+ +e+e
Te
7.74 X 1012
0.7
157760
24b. 0+ + e + e ~ 0 + e
Te
2.19 X 1021
-0.8
0
25f. N+e~N++e+e
Te
5.06 X 1019
0.0
168200
25b. N+ +e+e ~ N +e
Te
5.75 X 1026
-1.3
0
26f. O2 + e ~ oi + e + e
Te
5.03 X 1012
0.5
146160
26b. oi + e + e ~ O2 + e
Te
8.49 X 1023
-1.9
0
27f. N2 + e ~ Ni + e + e
Te
2.70 X 1017
-0.3
181000
27b. Ni +e+e ~ N2 +e
Te
2.05 X 1021
-0.8
0
28f. NO + e ~ NO+ + e + e
Te
2.20 X 1016
-0.3
107400
28b. NO+ + e + e ~ NO + e
Te
2.06 X 1025
-2.0
0
Charge exchange/charge transfer
29f. N++N2 ~ Ni+N
Tg
4.60 x 1011
0.5
12200
29b. Ni + N ~ N2 + N+
Tg = 2000 K
1.93 x 1013
0.0
0
30.
NO+ +0 = N+ +02
Tg
Tg
1.00 X 1012
0.5
77200
31.
NO + 0+ = N+ + 02
Tg
Tg
1.40 X 10°5
1.9
15300
32.
0+ + N2 = NO+ + N
Tg
Tg
4.40 X 1013
0.0
5664
33.
0+ +N2 =Ni +0
Tg
Tg
9.00 X 1011
0.4
22800
34.
NO+ +N = Ni +0
Tg
Tg
7.20 X 1013
0.0
35500
35. oi +N=N+ +02
Tg
Tg
8.70 X 1013
0.1
28600
36. oi + N2 = Ni + O2
Tg
Tg
9.90 X 1012
0.0
40700
37.
NO+ + O2 = oi + NO
Tg
Tg
2.40 X 1013
0.4
32600
38. No++o=oi+N
Tg
Tg
7.20 X 1012
0.3
48600
39.
0+ +02 =oi +0
Tg
Tg
3.26 X 1013
0.0
2064
40.
0+ + NO = NO+ + 0
Tg
Tg
2.42 X IOn
0.0
902
a. Park [10].
Ref.
(see
foot-
notes)
d
e
b
b
b
b
b
b
b
b
b
b
a
a
f
a
a
c
c
c
c
f
g
b. WRC [3, 4]. These rates were calculated at Tg = Tv = 2000 K. The present fitting formulas are
valid for 6000 K ::; Te ::; 20000 K
c. Park [9].
d. Lieberman [6].
e. Detailed balance
f. Hierl et at [7].
g. Dotan and Viggiano [8].
reactions. The extended code functions in a similar manner to CHEMKIN. For
thermal reactions, reverse rate coefficients are computed from equilibrium
thermodynamic functions (detailed balance). Reverse rate coefficients with a
dependence on Te were determined with the WRC model by detailed balance.
--- Page 219 ---
204
Modeling
~e' --8-NO'
--T- N' -><r- N"
4r~~~~~~~~ -e-rr -9-0"
10.5 lLL..L..I--'-.L.W..L..ILL.L..L..L..IL.Ll.L..L--'--"I~.L>......L....L.L..L...J
1000
2000
3000
4000
5000
6000
Temperature (K)
Figure 5.3.1. Charged species concentrations relative to the electron concentration in
equilibrium air (P = I atm).
5.3.2.2 Results
We consider first the case of an air plasma taken to be in equilibrium
(T~ = T~ = 2000 K, P = 1 atm) at time zero when an elevated electron
temperature is instantaneously prescribed, in an idealized way modeling an
electrical glow discharge in a reactor section. In the example shown in
figure 5.3.2 the gas temperature is held constant at 2000 K and the electron
1019
1016
"1'-'"
8
1013
<J
'-'
.e
~
~ 1010
... ... 1
Z
107
104
10-4
T =2000K
g
T = 13000K
•
P=latm
10'3
10'2
10'1
+
+
".---.-..... 0 2, N2
~_-<l--<J- 0+
10°
Time (ms)
Figure 5.3.2. Temporal evolution of species concentrations in atmospheric pressure air at
constant gas temperature (2000 K) and constant electron temperature (13000 K).
--- Page 220 ---
DC Glow Discharges in Atmospheric Pressure Air
205
1020
T. ~ 2000 K (f"lXed)
P~labn
40 reactions
T,(K)
20000
J-'---'-'" :~ggg
_
_
16800
Figure 5.3.3. Temporal evolution of the electron number density in a two-temperature air
plasma. Initial conditions are equilibrium air at 2000 K (n~t=O) = 3.3 x 106 cm-3).
temperature is increased to 13 000 K at time zero. The time evolution of
species concentrations computed with the two-temperature CHEMKIN
solver is shown in figure 5.3.2. The electron number density rises from its
initially low value of 3.3 x 106 cm-3
to a steady-state value of
,,-,4 x 1012 cm -3 in about 0.1 ms. The dissociation fraction of oxygen atoms
increases from ,,-,0.03 % at time zero to "-' 1 % at steady-state. NO+ is the
dominant ion at all times.
Additional calculations were made for various electron temperatures
while keeping the gas temperature constant at 2000 K. The predicted
temporal evolutions of the electron number density are shown in figure
5.3.3. Practically no increase in the electron number density is observed for
electron temperatures below a threshold value of Te ~ 6000 K, which
corresponds to the temperature where electron-impact ionization reactions
begin to dominate over heavy particle impact dissociation. As the electron
temperature is further increased, the steady-state electron concentration
increases significantly, with a very abrupt change at Te ~ 16800 K.
Figure 5.3.4 shows the steady-state electron number densities
predicted with CHEMKIN as a function of the electron temperature. At
Te = 16800 K where the predicted steady-state electron number density
suddenly increases from ",J 014 to "-' 1018 cm -3 over a few Kelvin. It is
interesting to examine the reverse case where steady-state electron concen-
trations are calculated for an initial composition given by the steady-state
solution corresponding to Tg = 2000 K and Te = 20 000 K (corresponding
to n~t=O) = 1.7 x 1018 cm-3). As can be seen from figure 5.3.5 in this case
the predicted steady-state electron number densities start by decreasing
--- Page 221 ---
206
Modeling
10000
12000
14000
16000
18000
20000
22000
Electron Temperature, T. (K)
Figure 5.3.4. Steady-state electron number density predicted by CHEMKIN for air at
Tg = 2000 K, as a function of Te. For each steady-state calculation, initial conditions
are equilibrium air at 2000 K.
along the same curve as in figure 5.3.4 but, instead of the abrupt decrease at
16800 K, continue their slow decrease until the electron temperature reaches
rv 14300 K. When the electron temperature is further decreased, the steady-
state electron number density abruptly decreases to the level of the curve
l~LL~~~--~~~~~~~~--~~~-L~~
8000
10000
12000
14000
16000
18000
20000
22000
Electron Temperature, T. (K)
Figure 5.3.5. Steady-state electron number density predicted by CHEMKIN for air at
Tg = 2000 K, as a function of Te. For each steady-state calculation, the initial condition
corresponds to the steady-state composition predicted by CHEMKIN at Tg = 2000 K
and Te = 20000 K (n~t=O) = 1.7 x 1018 cm-3).
--- Page 222 ---
DC Glow Discharges in Atmospheric Pressure Air
207
of figure 5.3.4. Thus a hysteresis occurs as the electron temperature is
increased and decreased in a cyclical fashion.
5.3.2.3 Analysis of the ionization mechanisms
Through detailed examinations of the reactions and rates, we found that the
behavior in each of the two regions A and B of the curve in figure 5.3.4 can be
explained in terms of the following simplified reaction mechanisms:
( A) Ionization mechanism in region A
In region A, the initial rapid electron concentration rise (see figure 5.3.2 for
the case Te = 13 OOO,K) is the result of electron-impact ionization ofN2 and
O2 via three-body reactions:
O2 + e ::::} ot + e + e
N2 +e ::::} Nt +e+e
and via electron-impact dissociation of O2 followed by electron-impact
ionization of 0:
O2 +e ::::} O+O+e
O+e ::::} 0+ +e+e
The charged species produced by these processes undergo rapid charge
transfer to NO+, via
0++N2 ::::}NO++N
Nt + O2 ::::} N2 + ot
ot + NO ::::} NO+ + O2
The main path for electron recombination is the two-body dissociative
recombination reaction:
NO+ +e ::::} N +0
When the concentration of NO+ becomes sufficiently large, the rate of disso-
ciative recombination balances the rate of electron production and the
plasma reaches steady-state. Thus, in region A, the termination step for
the ionization process is the two-body recombination of a molecular ion.
(B)
Ionization mechanism in region B
An example of the temporal evolution of species concentrations in region B
is shown in figure 5.3.6 where the electron temperature is fixed at
Te = 18000 K. As in region A, the electron number density initially increases
--- Page 223 ---
208
Modeling
N,
1018
0,
1016
,.......
..... -._ ........
"1e
101'
u
'-'
T =2000K
NO·
.0
8
'r;;
1012
T, = 18000 K
o'
5
2
P= I attn
Cl
1010
... .,
.0
~
108
10'
10"
10.3
10-2
10-1
Time (ms)
Figure 5.3.6. Temporal evolution of species concentrations in atmospheric pressure air at
constant gas temperature (2000 K) and constant electron temperature (18000 K).
by electron-impact ionization of N2 and O2 via
O2 + e ::::} ot + e + e
N2 + e ::::} Nt + e + e
and via electron-impact dissociation of O2 followed by electron-impact
ionization of 0:
O2 +e ::::} O+O+e
O+e ::::} 0+ +e+e
The difference with region A is that the charge transfer reactions are not
fast enough to produce NO+ at a high enough rate. This is because these
reactions are controlled by the gas temperature, whereas electron impact
ionization reactions are controlled by Te. The critical electron temperature
that defines the limit between regions A and B corresponds approximately
to the electron temperature for which the rate of the transfer reaction
0+ + N2 ::::} NO+ + N is comparable with the rate of avalanche ionization
by electron impact. Above this critical electron temperature, the avalanche
ionization process continues until all molecular species are dissociated.
Eventually the rates of three-body electron recombination reactions balance
the rate of ionization, and steady-state is reached.
It is noted that, in region A, electron impact dissociation ofN2 (or NO)
is negligible because the dissociation energy of N2 (9.76eV) is much larger
than that of O2 (5.11 eV), and the concentration of NO is small relative to
the concentration of O2, It is only above the critical temperature that electron
impact dissociation of N2 starts having a noticeable effect.
--- Page 224 ---
DC Glow Discharges in Atmospheric Pressure Air
209
(C)
Analytical solution
The kinetics in regions A and B can be described with a simplified subset of
reactions that takes into account the dominant channels discussed in the
foregoing section. With this simplified mechanism, the steady-state concen-
trations of major species are obtained by solving the following system of
equations:
• Steady-state for e-:
O2 +e =} ot +e +e
N2 +e =} Nt + e+e
O+e {:} 0+ + e + e
NO++e =}N+O
• Steady-state for O2:
O2 + e=}O + 0 + e
O+O+M =} O2 +M,
with M = 02,N2,0
• Steady-state for NO+:
• Steady-state for 0+:
• Steady-state for Ot:
• Steady-state for Nt:
NO+ +e =} N +0
0+ + N2 =} NO+ + N
ot + NO =} NO+ + O2
o + e {:} 0+ + e + e
0+ + N2 =} NO+ + N
0+ + O2 =} ot + 0
O2 + e =} ot + e + e
Nt + O2 =} ot + N2
ot + NO =} NO+ + O2
N2 + e =} Nt + e + e
Nt + O2 =} ot + N2
In writing the corresponding steady-state relations, we make the approxima-
tion that the change of plasma volume due to the increase of the total number
--- Page 225 ---
210
Modeling
1019
1018
.r-
10"
~
~. 1016
C
10"
·Vi
5 1014
Cl
tl
10"
.0 e 1012
::I
Z
10"
I': i 1010
@
10"
108
8000
-- 10th order polynomial solution
... _ .•. _. CHEMKIN starting at n = 3xlOfi em-'
._-.... -_. CHEMKIN: starting at n: = 1.7xlO18 em-'
10000
12000
14000
16000
18000
20000
22000
Electron Temperature, T, (K)
Figure 5.3.7. Steady-state electron number densities predicted by CHEMKIN and by the
tenth-order polynomial analytical solution.
of moles at constant T and P is negligible, and that the concentration of N2
remains constant and equal to its initial value. Furthermore, we consider that
the dominant neutral species in the plasma are °2, 0, and N2.
By elimination of no, no2 , no+, no;, nN; and nNO+, we obtain a tenth-
degree polynomial in ne with coefficients that only depend on Tg, Te, noiO) ,
nN;O) and the rate coefficients. The roots of this polynomial were extracted
with the mathematical package MATLAB. The roots that give negative
values for no are omitted from the solution. The remaining roots of the
polynomial are plotted in figure 5.3.7 along with the CHEMKIN predictions
corresponding to the full mechanism of table 5.3.1. As can be seen from figure
5.3.7, the approximate solution obtained with the simplified mechanism is in
very good agreement with the CHEMKIN predictions in regions A and B.
The small discrepancy in region B is due to the neglecting in our simplified
model of nitrogen dissociation. Furthermore, the tenth-degree polynomial
exhibits an extra solution that could not be attained with CHEMKIN
(region C). The limits of region C are the turning points labeled (a) and (fJ)
in figure 5.3.7. If we initialize CHEMKIN with the plasma composition
corresponding to a point in region C of figure 5.3.7, CHEMKIN produces a
new steady-state electron number density located on either the lower (region
A) or upper (region B) limb of the steady-state curves. Thus region C of
figure 5.3.7 cannot be obtained by fixing the electron temperature.
Figure 5.3.8 shows the concentrations of dominant species as predicted
by the analytical model. We see that the concentration of NO+ increases up
to turning point (a), and then stays approximately constant as charge
transfer becomes slower than oxygen ionization. The concentration of
oxygen atoms steadily increases throughout regions A and C. Beyond
--- Page 226 ---
DC Glow Discharges in Atmospheric Pressure Air
211
1011
2/("")
no,
~
'" E
~ 1015
.c-
.;;;
c:
<1l
0
1013
I-<
<1l
..0 E
::s Z
1011
10000
12000
14000
16000
18000
20000
22000
Electron Temperature, T, (K)
Figure 5.3.8. Steady-state species concentrations at Tg = 2000 K, as predicted by the
analytical solution.
turning point (3, molecular oxygen is nearly fully dissociated. The electron
concentration is approximately equal to the concentration of NO+ in
region A and to the concentration of 0+ in regions Band C.
5.3.3
Predicted electric discharge characteristics
The electron number density and electron temperature can be related to the
current density and electric field, respectively, by means of Ohm's law and
the electron energy equation. The current density and electric field values
provide guidance for the design of non-equilibrium dc discharges, as well
as an estimate of the power requirements of such discharges.
5.3.3.1
Ohm's law
Ohm's law relates the current density j to the electric field E:
ni
j=aE=
e
E
me L:h Veh
(1)
where a is the electrical conductivity of the plasma, me the electron mass, and
Deh the average frequency of collisions between electrons and heavy particles.
The total collision frequency is the sum of the collision frequencies of
electrons with neutrals, n, and ions, i:
(2)
--- Page 227 ---
212
Modeling
The electron-neutral collision frequency Den can be expressed in terms of
the number densities of neutral species, nn' the electron velocity,
ge = J8kTe/7fme, and the energy-averaged momentum transfer cross-
sections Qen as
The energy-averaged electron-neutral momentum transfer collision cross-
sections Qen are calculated by:
Qen = ~ ;~ J~ e2 exp ( - ;e) Qen(e) de
(3)
where Te is the electron temperature, e is the electron impact energy, and
Qen (e) is the momentum collision cross-section. For N2, O2 and 0, these
cross-sections have been taken from Brown [13], Shkarofsky et al [14],
and Tsang et al [15]. The resulting average energy cross-sections Qen are
presented in figure 5.3.9.
In region A, where the dominant neutral species are N2 and °2, and
where ions have negligible concentrations, the total collision frequency is
well approximated by the electron-neutral collision frequency.
In region B, where the plasma is almost fully ionized, the total collision
cross-section is approximately equal to the electron-ion collision frequency,
2e-15 , ............ , ............ , ............. , ........................ .,.. .......... , ......... -........ _
.. , .. .
N~
E
~ 1.5e-15;-
c o
~ l g
1e-15 :
CD
~
~
e;
5e-16 ~
CD c
CD
electron temperature T. (K)
·-····1
~e-02
_____ e-O
-e-N2
Figure 5.3.9. Energy-averaged momentum transfer cross-sections for collisions between
electrons and N2 , O2 , O.
--- Page 228 ---
DC Glow Discharges in Atmospheric Pressure Air
213
which can be expressed as [ ]:
_
-6
InA
Vei = 3.64 x 10
ni 3[i
Te
(4)
where A represents the ratio of the Debye length to the impact parameter for
90° scattering and is approximately equal to 2.5 for electron number densities
of lOIS cm-3 (Mitchner and Kruger [16]).
5.3.3.2 Electron energy equation
( A) Introduction
For a stationary plasma in a dc electric field, the electron energy equation can
be written as
(5).
In equation (5), k is the Boltzmann constant and Th the kinetic temperatures
of heavy species (assumed to be the same for all heavy species and thus
equal to Tg). The term on the left hand side of equation (5) represents the
volumetric power for Joule heating of electrons by the electric field. The
first and second terms on the right-hand side represent the volumetric
power lost by free electrons through elastic and inelastic collisions, respec-
tively, and the last term on the right-hand side stands for volumetric radiative
losses.
In region A of the S-shaped curve, inelastic energy losses dominate the
elastic and radiation losses by at least two orders of magnitude. In region B,
however, inelastic losses are negligible relative to elastic and radiation losses.
In the rest of this analysis, we limit ourselves to the lower limb of the S-
shaped curve (region A), and therefore we neglect radiation losses.
The basis for calculations of inelastic losses in atmospheric pressure air
plasmas is summarized below. Electrons lose energy through the following
inelastic processes: vibrational excitation of molecular species (VE transfer),
ionization, electronic excitation, dissociation of molecules, electronic
excitation, and ionization of atoms. At electron temperatures below about
17000 K, the main channel for inelastic electron energy loss in air is via
electron impact vibrational excitation of nitrogen. This process is par-
ticularly important for the ground state of molecular nitrogen because
vibrational excitation by electron impact of this state occurs via resonant
transitions to the ground state of the unstable negative ion N2:
N2(X,v") +e ---. N2(X,v) ---. N 2(X,v') +e.
The net rate of energy lost by this process is:
Ev"v' = (Kvllv' [N2 (X, v"][e] - KV'v" [N2 (X, v')][e])~Evllv'
--- Page 229 ---
214
Modeling
where K v"'; and K';';I are the rate coefficients of electron-impact vibrational
excitation and de-excitation, and !:l.E,;lv' stands for the difference of energy
between the two vibrational levels. The net rate of inelastic losses is a func-
tion of the gas and electron temperatures, the electron number density,
and the vibrational population distribution of the ground state of N2. In
the limiting case where the vibrational level populations follow a Boltzmann
distribution at the electron temperature, the net rate of energy loss by VE
transfer is equal to zero because the energy lost by VE excitation reactions
is exactly balanced by the energy gained from de-excitation. In the other
limiting case where the vibrational levels follow a Boltzmann distribution
at the gas temperature, the rate of excitation is much larger than the rate
of de-excitation. In the general case, the vibrational population distribution
is intermediate between the two previous cases. The vibrational population
distribution is then governed by the relative importance of the rates of
vibrational excitation by electron impact, and the rates of de-excitation
which are mostly determined by collisions with heavy species. The dominant
de-excitation processes are vibrational-vibrational transfer between two N2
molecules (V-V transfer), vibrational-vibrational transfer between one N2
molecule and other molecular species such as O2 and NO (V-V' transfer),
and vibrational-translation (V-T) relaxation by collisions of N2 with other
heavy species (N2' O2, NO, Nand 0). Here the main relaxation processes
are V-T relaxation by 0 and N2. To calculate inelastic energy losses in air,
we must therefore predict the vibrational population distribution of the
nitrogen ground state by taking into account the aforementioned processes.
This is a complex calculation that requires the use of a vibrationally specific
collisional-radiative (CR) model. We have developed such a model for pure
nitrogen plasmas [1, 2, 4, 17] and have recently extended it to air plasmas [18].
( B)
Rate coefficients controlling the vibrational distribution of N2 levels
The rate coefficients for VE transfer are calculated [4] using the cross section
calculation method of Kazansky and Yelets [19]. This method reproduces
available experimental cross-sections relative to the low-lying vibrational
levels within about 10%.
For electron temperatures up to 17000 K (turning point a in the S-
shaped curve), the dominant N2 V-T, v-v and V-V' relaxation processes
are:
N2(Y,v+l)+Mr;N2(Y,v)+M
(6)
N2(X,v\ + 1) +AB(X,v2) r; N2(X,vd +AB(X,v2 + 1).
(7)
In equation (6), M represents the heavy particle collision partner M = N2,
O2, NO or 0 and in equation (7), AB is the diatomic molecule N2, O2 or NO.
To our knowledge, no experimental data have been reported for the V-T
relaxation of N2 by collisions with N. However, Kozlov et al [20] experi-
mentally determined an upper limit value of the V-T relaxation rate for
--- Page 230 ---
DC Glow Discharges in Atmospheric Pressure Air
215
v = 1 ---. v = O. They showed that for temperatures between 2500 and
4500 K, this rate is about one order of magnitude lower than the rate of
V-T relaxation of N2 by collisions with 0 atoms. Since for our conditions
the concentration of N atoms is at least four orders of magnitude lower
than the concentration of 0 atoms, we neglect the V-T relaxation of N2
by collisions with N atoms.
Most measured vibrational relaxation rate coefficients are for transitions
between vibrational levels v = 0 and v = 1. When available, experimental rates
have been preferred over theoretical ones. The existing experimental rates have
been compared and critically selected. Rates for transitions between higher
levels have been calculated using scaling functions derived from SSH theory,
which is a reasonable approximation when the gas temperature is below
3000 K. The reverse rates have been determined by application of the detailed
balance method.
For each V-T transfer process, the rates kl,o corresponding to transition
v = 1 ---. v = 0 have been calculated with the following analytical expression:
n
(
B C)[
( EIO)]-I
kl,o = ATg exp - Ti l3 + T;
1 - Dexp -
Tg
(8)
where kl,o is expressed in cm3 S-I, and Tg and EIO (energy of the N2 transition
v = 1 ---. v = 0) are expressed in Kelvin. The parameters A, B, C, D, m and n
were determined in reference [18] and are listed in table 5.3.2.
The rate coefficients kv+ I,v for transitions v + I ---. v between upper
vibrational levels have been calculated using appropriate scaling laws from
the measured klO rates:
kv+l,v = kl,oG(v+ 1).
(9)
Using SSH theory [21] and some approximations for the Morse oscillator
model [22], G( v + 1) can be expressed as
G(v+ 1) ':::' (v+ 1)(I- xe) F(Yv+l,v)
(10)
1-xe(v+ 1)
F(YI,o)
where Xe is the anharmonicity of the N2 molecule, and Yv+ I,v is given by
Yv+l,v = 0.32Ev+I,vL~
(11)
Table 5.3.2 Parameters for the V-T rates kl,o'
M=
A
B
C
D
m
n
0
1.07 x 10-10
69.9
0
0
0
0
N2, O2, NO
7.8 X 10-12
218
690
--- Page 231 ---
216
Modeling
where Ev+ I v is the energy of the v + 1 ---+ v transition in Kelvin, L is the
characteristic parameter of the short range repulsive potential in A, fL is
the reduced mass of the two colliding particles in atomic !1nits, and Tg
is the gas temperature in Kelvin. We have taken L = 0.25A for all V-T
processes.
The function F in equation (10) is given by [21]
{
F(y) = ~ [3 - exp ( - Y) ] exp ( - Y) for 0 ~ y ~ 20
F(y) = 8 (i y/2 //3 exp( -3i/3)
for y > 20.
(12)
The calculated forward and reverse rates are plotted in figure 5.3.10. The
rates for V-T relaxation of N 2(v) by collision with 0 atoms are between
two and three orders of magnitude higher than the rates of V-T relaxation
ofN2(v) by collision with N2 .
The rates k~'6 corresponding to the v-v and V-V' processes (7) with
VI = 0 and V2 = 0, are calculated using the following expression:
k0,l
n
(
B)
I,D = ATg exp
- 7:1/ 3
g
(13)
10-7
.. -r-... -.-,-.,..---..,......y----:--.......... ...,.........-r-.------,--~ .. "-~'-T ..... ~---~ --T ·,.-·:---···=--·....,....·r-r--r·~-·i·t.....,.· ..... -..,....-..-·'~-~.,-l
10-8
..., .... 1
........
j
10-9
*""",..,,'"
1
.,,"
~
,,"'"
1
..
10-'0
,*"..;"
.. II!
....-'
-1
E
.,. ...
....-
...- ....-
i
u
"
....-
1
10-11
.,,'"
....-
.5
.... ",
...-
1
'E
....- .--
",'"
.--
CD 10-'2
--
,
'0
/
--
II:
'"
/
1
I'
.----
/
....---
10-'3
I
--
i
CD
--
li!
--
-- M..o. forward rlJte
i
--
10-'4
...-
M=O. IlMIrse rate
!
--
--
j
/'
/'
-
M=N •• fQrward rate
1
/'
-- M .. N •• reverse rate
10-'5
/'
J
/
/
~J
10-'8
I
._. __ .'.
'~'_.l ...... ..:.....~_._ •... ~._ .......... ,-' .... , ..•. .1.. .......... ~ ........ ~ ... _ ..•.. ..t. .,J.. •• i. •.. I._._ ........... ' ••.. L_.I ...... _ ••• ~ ••• J.. •. L .... -I. ........ ',_.' ••
0
10
20
30
40
50
vibrational level V
Figure 5.3.10. Rate coefficient for V-T relaxation: N2(X,v) + M -> N2(X,V - I) + M,
with M = 0, N2 at Tg = 2000 K.
--- Page 232 ---
DC Glow Discharges in Atmospheric Pressure Air
217
Table 5.3.3. Parameters for the v-v and V-V' rates k~:~.
v-v or V-V' process
A
B
n
Nz-Nz
1.27 x 10- 17
0
1.483
Nz-Oz
1.23 x 10- 14
104
1
Nz-NO
4.22 x 10- 10
86.35
0
where the gas temperature Tg is expressed in Kelvin and the parameters A, B,
and n are listed in table 5.3.3.
Note that the rate of v-v transfer for Nr N 2 collisions was recently
measured by Ahn et al [23]. The measured rates are about one order of
magnitude lower than the values adopted here. However, this rate has
practically no influence on the results presented here.
The rate coefficients k~~'~\~v: for exothermic transitions between upper
vibrational levels have been calculated using the relation
kV2 ,v2 +1
ko,IG( + 1
+ 1)
v + I v = 10
VI
,V2
I
,1
,
(14)
where G( VI + 1, V2 + 1) is an appropriate function which can be expressed
using SSH theory [21] and some approximations for the Morse oscillator
model as
where Xel and Xe2 are the anharmonicities of the two molecules involved.
F(y) is given by equation (12) with y~2,+v2tvl defined as
1
,1
y~~'~\~v: = 0.32 [EVI + I -
EVI + EV2 - EV2 + dL if:
(16)
where Ev are the energies of the initial and final levels in Kelvin. We have
1
0
I
v v +1
taken L = 0.25 A for all v-v and v-v processes. Note that Yv~'+\Vl must
always be positive since we are considering the reaction in the exothermic
direction.
The calculated forward and reverse rates are plotted in figure 5.3.11 as a
function of the vibrational number VI for V2 = O. For the Nr 0 2 process, the
rates increase up to the resonance point at VI = 27, and decrease after this
value. We observe the same behavior for the NrNO process but the
resonance appears at a lower value of VI (VI = 16) because the spacing
between NO levels is larger than between O2 levels. For the Nr N 2 process,
the rates increase until VI = 5 and then decrease because of the increasing
vibrational energy gap between the two N2 molecules.
--- Page 233 ---
218
Modeling
10'"
o
10
20
30
40
50
vibrational level v,
Figure 5.3.11. Rate coefficients for v-v and V-V' exchange: N 2(X, VI + 1) + AB(X, 0) --->
N2(X,vIl + AB(X, 1), with AB = N2 , O2 and NO, at Tg = 2000K.
Three sections with results pertaining to section 5.3.3 were inadvertently
omitted from the manuscript. They have been added as an Appendix to the
book at the proof stage. The Editors.
5.3.4
Experimental dc glow discharges in atmospheric pressure air plasmas
5.3.4.1
Introduction
Experiments have been conducted to validate the mechanisms of ionization
in two-temperature atmospheric pressure air plasmas in which the electron
temperature is elevated with respect to the gas temperature. To test the
predicted S-shaped dependence of steady-state electron number density on
the electron temperature and its macroscopic interpretation in terms of
current density versus electric field, dc glow discharges have been produced
in flowing low temperature, atmospheric pressure air plasmas. The flow
velocity is around 400 mis, and the gas temperature is varied between 1800
and 2900 K. These experiments show that it is feasible to create stable diffuse
glow discharges with electron number densities in excess of 1012 cm -3 in
atmospheric pressure air plasmas. Electrical characteristics were measured
and the thermodynamic parameters of the discharge were obtained by spec-
troscopic measurements. The measured gas temperature is not noticeably
affected by whether or not the dc discharge is applied. The discharge area
was determined from spatially resolved optical measurements of plasma
--- Page 234 ---
DC Glow Discharges in Atmospheric Pressure Air
219
emission during discharge excitation. The measured discharge characteristics
are compared in section 5.3.5 with the predicted electrical characteristics.
5.3.4.2 DC discharge experimental set-up
The ionization process in the discharge region is accompanied by energy
transfer to the gas through collisions between electrons and heavy particles.
Electrons lose more than 99.9% of the energy gained from the electric field
to molecular N2 through vibrational excitation, and the vibrationally excited
N2 transfers energy to translational modes through vibrational relaxation.
Thus the degree of gas heating (~Tg) is a function of the volumetric power,
jE, deposited into the plasma by the discharge and the competition of the vibra-
tional relaxation time and the residence time T of the plasma in the discharge
region. To limit gas heating to acceptable levels for given volumetric power,
it is desirable to flow the plasma at high velocity through the discharge region.
The experimental set-up is shown schematically in figure 5.3.12. Atmos-
pheric pressure air is heated with a 50 kW rf inductively coupled plasma torch
operating at a frequency of 4 MHz. A 2 cm exit diameter nozzle is mounted at
the exit of the torch head. The flow rate injected in the torch was approxi-
mately 96 standard liters per minute (slpm) (64 slpm radial and 32 slpm
swirl) and the plate power settings were 8.9 kV x 4.1 A, with approximately
14kW of power deposited into the plasma. Under these conditions, the
temperature of the plasma at the exit of the 2 em diameter nozzle is about
5000 K and its velocity is '" 100 m/s.
The plasma then enters a quartz test-section where it is cooled to the
desired temperature by mixing with an adjustable amount of cold air injected
into the plasma stream through a radial mixing ring. The quartz test-section
length of 18 cm ensures that the flow residence time (approximately 1.6 ms
here) is greater than the characteristic time for chemical and thermal equili-
bration of the plasma «1 ms). Thus at the exit of the quartz test-section the
air flow is close to local thermodynamic equilibrium (LTE) conditions.
Finally, a 1 cm exit diameter converging water-cooled copper nozzle is
mounted at the exit of the mixing test-section. This nozzle is used to control
the velocity, hence the residence time, of the flow within the discharge region.
Two-dimensional computational fluid dynamics (CFD) calculations
performed at the University of Minnesota (see section 5.2 by Candler)
show that the axial velocity at the entrance of the discharge region is approxi-
mately 445 mls [24]. The discharge itself is produced between two platinum
pin electrodes of 0.5 mm diameter held along the axis of the air stream by
two water-cooled ic;inch (1.6mm) stainless-steel tubes placed crosswise to
the plasma flow. The bottom electrode is mounted on the copper nozzle
and the upper electrode is affixed to a Lucite ring, itself mounted on a vertical
translation stage in order to provide adjustable distance between electrodes.
The interelectrode distance was set to 3.5 cm.
--- Page 235 ---
220
Modeling
Anode
(Stainless-steel)-
3 -€E!!!!!9-
Voltage Pins 2 -Eiiiiiiiiiiil-
I -e:!!!;a-.
Cathode
(Stainless-steel)
Cooling
Water Inlet
Mixing Ring
Injector:_
0-210 slpm
Nozzle
(2 em exit
diameter)
R.F. coil
Gas Injectors:
64 slpm radial
32 slpm swirl
___
vI)i~~:harge Section:
Plasma Plume
R = 12 ill
Figure 5.3.12. Set-up (not to scale) for discharge experiments showing the torch head, the
injection ring, the 2cm diameter, 18cm long water-cooled quartz mixing test-section, the
2 -> I cm converging nozzle, electrodes, voltage pins, and electrical circuit.
The discharge was driven by a Del Electronics Model RHSVlO-2500R
power supply with reversible polarities, capable of operation in control
current or control voltage mode, with current and voltage outputs in the
ranges 0-250mA and O-lOkV, respectively. For the present experiments,
the cathode (bottom electrode) was biased to negative potentials with respect
to ground.
The electric field within the discharge region is measured from the poten-
tial on a high purity platinum wire (0.02 inch (0.5 mm) diameter) that extends
to the center of the discharge region. The platinum wire is held by a small
ceramic tube installed on a two-way (horizontal and vertical) translation
stage. Horizontal translation moves the pin into the discharge region for
electric field measurements, and out of the discharge during spectral emission
measurements. Vertical translation moves the pin along the discharge axis to
determine the electric field from potential measurements. Although pure
platinum melts at ",,2045 K, radiation cooling prevents melting of the
--- Page 236 ---
DC Glow Discharges in Atmospheric Pressure Air
221
platinum wires for plasma temperatures up to at least 3000 K. The voltage
measurements reported here were made with a Tektronix Model P6015A
high voltage (20kV dc, 40kV peak pulse) probe and a Hewlett-Packard
Model 54510A digitizing oscilloscope. The current was measured from the
voltage drop across the 12 kO ballast resistor of the dc circuit.
The set-up for optical emission spectroscopy diagnostics includes a SPEX
model 750M, 0.75m monochromator fitted with a 12001ines/mm grating
blazed at 200 nm and a backthinned Spectrum One thermoelectrically cooled
charge-coupled device (CCD) camera. The 30 x 12mm CCD chip contains
2000 x 800 pixels of dimension 15 x 15 )lm. The dispersion of the optical
system is '" 1.1 nm/mm. The monochromator entrance slit width was set at
200 )lm, and 26 columns of 800 pixels were binned to produce an equivalent
exit slit width of 390 )lm. The spatial resolution was ",0.5 mm as determined
by the monochromator entrance slit width and the magnification of the optical
train (2.5 for two lenses of focal length 50 and 20 cm). Absolute spectral inten-
sity calibrations were obtained with an Optronics model OL550 tungsten
filament lamp and a 1 kW argon arcjet, with radiance calibrations traceable
to National Institute of Standards and Technology (NIST) standards.
5.3.4.3 Spectroscopic measurements
(A)
Measurements without dc discharge applied
The gas temperature (rotational temperature) without dc discharge applied
was measured by emission spectroscopy of the OH (A ---. X) transition.
The OH (A ---. X) transition is one of most intense emission systems in low
temperature (T:::; 4000 K) air plasmas containing even a small amount
(",1%) ofH2 or H20. In the present experiments, the water content of the
air injected into the torch was sufficient to produce intense OH radiation.
Rotational temperatures were obtained as described in chapter 8 section 8.5.
Line-of-sight OH emission spectra were recorded with the discharge off.
The amount of cold air mixing was adjusted to vary the temperature of the
preheated air. The measured OH spectra were later fitted with SPECAIR.
As shown in figure 5.3.13 the gas temperature can be varied from 1800 to
2900 K by adjusting the amount of cold air mixing.
It is expected that the plasma conditions are close to LTE at the entrance
of the discharge section for the 3000 K case. However, for the lowest
temperature cases (T close to 2000 K), the electron density may be elevated
with respect to LTE because electron recombination is small at these low
temperatures. Nevertheless, the electron density entering the discharge
section is expected in all cases to be less than 1010 cm -3.
( B )
Measurements with dc discharge applied
Emission spectra were also measured with the discharge applied (discharge
current of 150 rnA). A typical spectrum is shown in figure 5.3.14. As can
--- Page 237 ---
222
Modeling
mixing
t .8
-
68 slpm, T.=2900 K
-- 130 slpm, T.=2300 K
~
195s1pm, T.=1800K
1.0
]
0.6
~ I
0.4
0.2
0.0 ,cr> ... nA,"-~~--"--"~~-'---c~ ~~~~~----'
306
308
310
312
314
Wavelength (mn)
Figure 5.3.13. Measured OH A ---> X emission spectra without discharge applied as a
function of the amount of cold air mixing.
be seen in the figure, a factor of", 1 04 enhancement of the emission due to NO
gamma (A ~ X) and a factor of", 105 enhancement of the emission due to N2
(C ~ B) bands were observed. Figure 5.3.14 also shows that the N2 second
positive system (C ~ B) bands overlap the OR (A ~ X) feature around
308 nm. This overlap precludes accurate measurements of the rotational
temperature from OR (A ~ X) transition. Therefore the gas temperature
(rotational temperature) was measured by means of emission spectroscopy
of the (0,0) band of the N2 second positive system-the N2 (C ~ B) transi-
tion. Line-of-sight N2 emission spectra were recorded along lateral chords of
the plasma. The spectra were fitted with SPECAIR to obtain the rotational
temperature Tr and the vibrational temperature Tv of the C state ofN2. The
NO system
--Measured
(Discharge on, 1= ISO rnA)
N2(C- B)
Wavelength (nm)
Figure 5.3.14. Line-of-sight emission spectra measured at a discharge current I = 150 rnA.
--- Page 238 ---
DC Glow Discharges in Atmospheric Pressure Air
223
mixing,
T ,
T,
1.0 ____ 115 slprn, 2500 K, 3700K
__ 145 slprn, 2200 K, 3300K
.~ 0.8 -0--195 slprn, 1800 K, 3000K
~
_ 0.6
"0
~
~ 0.4
e
~ 0.2
364
368
372
376
Wavelength (mn)
380
Figure 5.3.15. Measured N2 second positive (C --> B) bands with discharge as a function of
the amount of cold air mixing (l = ISO rnA).
analysis procedure is described in chapter 8 section 8.5. Finally, the absolute
intensity of the spectrum was used to determine the population of the N2 C
electronic state.
Additional discharge experiments were conducted with different gas
temperatures. Figure 5.3.15 shows the measured N2 second positive system
spectra and the rotational and vibrational temperatures at a discharge
current of 150 rnA, as a function of the amount of mixing air. It can be
seen in the figure that both the rotational and vibrational temperatures are
lower with a higher amount of mixing cold air. Figure 5.3.16 shows the
measured spectrum as a function of the discharge current for 145 slpm of
mixing air. As can be seen from the figure, the rotational temperature
-
I=(i) rnA, T,=2200 K, T ,=2800 K
1.0 --- 1=150 rnA, T,=2200 K, T,=3150 K
---0-- 1=220 rnA, T,=2200 K, T,=3500 K
364
368
372
376
Wavelength (mn)
380
Figure 5.3.16. Measured N2 second positive (C --> B) bands with discharge as a function of
discharge current for the case of 145 slpm cold air mixing.
--- Page 239 ---
224
Modeling
Q' 2100
'-"
<I.)
~ ..
~ 1800
~
~
d
1500
~ 4
~
0
246
Radius (mm)
Figure 5.3.17. Rotational temperature profiles with and without the applied dc discharge
at l.5 cm downstream of the bottom electrode. The temperature profile without the
discharge was measured from rotational lines of the OH (A --4 X) transition. With the
discharge applied, the rotational temperature was measured from lines of the N2
(C --4 B) transition in the ultraviolet.
remains the same at all currents, but the vibrational temperature increases
with increasing discharge current.
Radial rotational temperature profiles with and without the discharge
applied were measured along chords of the plasma from Abel-inverted N2
second positive system emission spectra and OH emission spectrum, respec-
tively. Figure 5.3.17 shows the measured radial temperature profiles at a
distance of 1.5 cm downstream of the cathode (i.e. midway between the
two electrodes). As can be seen from the figure, the applied discharge does
not noticeably increase the rotational temperature of the plasma at this loca-
tion. Figure 5.3.18 shows the radial N2 C state electronic and vibrational
temperature profiles. On the axis of the discharge, the electronic temperature
of the N2 C state reaches about 5000 K, and the vibrational temperature is
about 3000 K.
Figure 5.3.19a shows a photograph of the air plasma plume at a
temperature of approximately 2200 K in the region between the two elec-
trodes without the discharge applied. Figure 5.3.19b shows the same
region when a dc discharge of 5.2 kV and 200 rnA is applied between the
two electrodes. In these experiments, the distance between electrodes is
3.5 cm. The bright region in figure 5.3.19b corresponds to the discharge-
excited plasma. Thus the plasma plume without discharge applied appears
to be homogeneous over a larger diameter than the plasma plume with the
discharge applied. However, figure 5.3.17 showed that the gas temperature
profile is practically the same as in the discharge applied case. The increased
brightness in figure 5.3.19b is due to the emission of excited electronic states
of molecular NO and N2 (see figure 5.3.18). Thus the applied discharge
--- Page 240 ---
DC Glow Discharges in Atmospheric Pressure Air
225
5000
.....---.-----e_
./
~
4500
~ Di~h~geOn ~
g
1= 150mA
'-
4000
.,
--.-T
~
.~ (N2,C)
---D-T v.(N2.C)
1;l 3500
~T
....
r, (N2,C)
~
E' 3000
0-0-0-0-0-0-0
0-0-
-o-~
~
oCT
2500 rru
~-o
lK- x-·· to- ),.;.r
);, .. - . .(
..I.
X
;.1" •• '1<....=<
~ ··x-
x··
~.-i-
2000
-5
-4
-3
-2 -I
0
1
2
3
4
5
Radius (nun)
Figure 5.3.18. Electronic, vibrational and rotational temperature profiles of Nz estate
with an applied discharge current of 1= 150 rnA.
increases excited state populations without significantly increasing the gas
temperature.
5.3.4.4
Current density measurements
The current density at the center of the plasma was determined by
dividing the measured current by the effective discharge area A*, i.e.
j(r = 0) = 1/ A*. The effective discharge area is obtained from the following
relation:
A* = J: 27frj(r) dr /j(r = 0)
(17)
(a)
(b)
Figure 5.3.19. (a) Air plasma at 2000 K without electrical discharge. (b) Air plasma at
2000K with applied discharge (1.4kVjcm 200mA). Interelectrode distance, 3.5cm. The
measured electron number density in the bright discharge region is around 101Z cm -3.
--- Page 241 ---
226
Modeling
1.0
0.8
'"
=' 0.6
,e.
.€
rIl 0.4
j
0.2
-4
-2
0
2
4
Radius(mm)
Figure 5.3.20. Spatial extent of the plasma produced by the discharge.
where j(r) is the local current density. As shown in reference [12], j(r) is
approximately proportional to ne(r). Thus, A* can be calculated as
A*= (J: ne(r)27frdr)/ne(r=0).
(18)
In separate discharge experiments conducted with a nitrogen plasma [5], the
electron number density profile ne was measured using various techniques
(from Hf3 Stark broadening and N2 first-positive emission spectra) to
calculate A* using equation (18). The discharge area A* was also estimated
from the full width at half maximum (FWHM) of the N2 C --+ B (0,0) band-
head intensity profile. In these nitrogen discharge experiments, the effective
area A* obtained with equation (18) and the measured ne profile was found
to be close to the effective area obtained from the N2 C --+ B (0,0) emission
intensity measurement. Thus for the present air plasma discharge experi-
ments, we estimate the effective discharge area from the spatially resolved
optical measurements of N2 C state emission. Spectroscopic measurements
of N2 C --+ B (0,0) emission with the applied discharge are shown in figure
5.3.20. It can be seen from the figure that the diameter (FWHM) of the
discharge is approximately 3.2 mm. This diameter was monitored and
found to be constant for all discharge currents ranging from 5 to 250 rnA.
The discharge diameter was therefore taken to be 3.2 mm and assumed
constant along the axis of the discharge.
5.3.4.5 Electric field measurements
Electrode and pin potentials were measured as a function of the applied
discharge current which was varied from °
to 250 rnA. The cathode current
was measured from the voltage drop across the 12 kO ballast resistor
--- Page 242 ---
DC Glow Discharges in Atmospheric Pressure Air
227
o
-1000
~ -2000
t;l
.'8 -3000
~
~ -4000
-5000
Discharge Current:
.-1=5 rnA
.£
1=\OrnA
•
I=100rnA
···llf· 1=250 rnA
0.0 U5
1.0
1.5 20 25 3.0 3.5
Distance along Discharge Axis (cm)
Figure 5.3.21. Measured potentials as a function of applied current in the discharge
section.
placed in series with the discharge (see figure 5.3.12). There is a small differ-
ence of 7 rnA between the anode and the cathode currents that was found to
be due to a current leak through the water cooling circuit of the anode. All
results reported below are based on the measured cathode current, which
is not affected by current losses to the cooling circuit.
Figure 5.3.21 shows the measured pin voltage as a function of the
applied current along the axis of the discharge. The potential varies approxi-
mately linearly along the axis of the discharge, indicating that the electric
field is approximately uniform in the discharge region. The electric field
measurements reported here were determined from the slope of a linear fit
of the pin potentials. In the vicinity of the cathodes, voltage falls of up to
several hundred volts were observed. These values are typical of the cathode
fall voltage in glow discharges [25].
The total voltage across the discharge was also measured as a function
of electrode separation, by translating the top electrode (anode) vertically.
The voltage-length characteristic for a discharge current of 150 rnA is
shown in figure 5.3.22. The lowest voltage reading as the electrodes are
brought within less than 0.2 mm from one another provides an approxima-
tion to the discharge voltage at zero gap length [26, 27]. The value of this
voltage is found to be 285 V and is independent of the current in the current
range investigated (10-250 rnA). This value agrees with the cathode fall
voltage reported in the literature [6, 28] for glow discharges in air with a
platinum cathode. The voltage gradient in the positive column, given by
the slope of the voltage-length characteristic, is constant as the discharge
length is increased. For a discharge current of 150mA, the gradient is
about 1400V/cm (see figure 5.3.22) and is consistent with the electric field
value determined from the pin measurements.
--- Page 243 ---
228
M adeling
--
i: =~;:'85V -2~-
o
.,/
i2~ //
i5 1000 ___/111
•
,. ,
0 00
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Distance along Discharge Axis (cm)
Figure 5.3.22. Voltage-length characteristic in the discharge region.
5.3.5 Electrical characteristics and power requirements of dc discharges in air
The experimental discharge characteristics presented in section 5.3.4 for
plasma temperatures ranging from 1800 to 2900 K are shown in figure
5.3.23. They are also compared with the predicted characteristics at the
corresponding gas temperatures. The method employed to predict the
discharge characteristics was discussed in section 5.3.3. As can be seen
from figure 5.2.23, good agreement is obtained between the measured and
1800
~ : :
l"
1200
III
f
¥ 1000
u::
o j
III
Figure 5.3.23. Measured (symbols) and predicted (solid lines) electrical discharge charac-
teristics in atmospheric pressure air plasmas generated by dc electric discharges.
--- Page 244 ---
DC Glow Discharges in Atmospheric Pressure Air
229
predicted discharge characteristics over a range of experiments spanning over
three orders of magnitude in current density.
Figure 5.3.23 also shows (dashed curve) the resistive characteristic of
equilibrium air at 2900 K, given by the relation
j
E = ---'------
O"equilibrium, 2900 K
(19)
where O"equilibrium,2900K, the electrical conductivity of equilibrium air at
2900 K, is calculated as
nequilibrium, 2900 K e2
e
O"equilibrium,2900K = --=-------
meVe-air
(20)
where n~quilibrium,2900K = 4 x 1010 cm-3 and the collision frequency De-air is
well approximated by
De-air = (k~Jge(1.5 X 10-15 cm2)
(21 )
where p is the pressure (1 atm), Tg = 2900 K is the gas temperature, and
ge = J8kTe/7fme is the electron thermal velocity. For Tg = 2900 K, as can
be seen from figure 5.3.23 the predicted E versus j characteristic is close to
the resistive equilibrium characteristic for current densities below 0.2 AI
cm2 • In this current density range, the predicted electron temperature
remains below approximately 8000 K and electron-impact reactions are
inefficient in ionizing the plasma. Thus the electron number density increases
only by a few percent. As the electron temperature increases, the frequency of
collisions increases with ...rr;, resulting in a decrease of the electrical conduc-
tivity of the plasma. This explains why the E versus j characteristic is higher
than the resistive equilibrium characteristic for j below ",0.2 A/cm2• At
higher values of the current density, where the discharge produces a signifi-
cant increase in the electron density, the conductivity increases dramatically
and the slope of the E versus j characteristic decreases. Thus the region to the
right of the resistive equilibrium characteristic is where the discharge
increases the electron number density. The experimental data at Tg between
1800 and 2900 K all show the turning trends of the non-resistive discharge
characteristics. We note, however, that the predicted resistive part appears
to be shifted to lower current densities relative to the experimental curves.
This difference may be due to the fact that the electron number density
was slightly above the equilibrium value in the incoming air stream. We
recall that the 'equilibrium' air was produced by cooling of an air stream
initially heated to high temperatures. Slow electron recombination could
therefore explain the differences at low current densities.
Figure 5.3.23 also shows experimental data obtained by Stark and
Schoenbach [29] in an atmospheric pressure glow discharge in air. The
--- Page 245 ---
230
Modeling
10· : .......•.......... , ..... ,.,.,.,' ....... , ..... , .......• .,., ............... , ...... , ...•.. , .. ,·.·'·'T·········.·····,····,··,·,·.·,· ..... ····_,······.···r·.··'·,·,.,
l
10'
10.0
10"
10.2
1013
electron number density (cm""l
1
:1
1 I
Figure 5.3.24. Power required to produce an elevated electron density in atmospheric
pressure air at 2000 K by means of dc discharges.
discharge was produced between a microhollow cathode and a positively
biased electrode, as described in reference [29]. The gas temperature was
measured to be around 2000 K, and the center electron number density is
reported to be above 1012 cm-3 [29, 30]. This measurement adds further
support to the kinetic mechanism predictions.
We conclude this section with the power required to produce a given
electron density in air at 2000 K by means of dc glow discharges. The results
are shown in figure 5.3.24. We predict that the production of 1013 electron/
cm3 in air at 2000K requires about l4kW/cm3. The corresponding electric
field is rv1.35kV/cm, and the current density is rvlO.4A/cm2.
This level of Joule heating may not lead to significant overall gas heating
in small scale stationary dc discharges where conduction to ambient air and
to the electrodes is high. This was the case for instance in Gambling and
Edels's experiments [27] where the positive column was a few millimeters
in length and approximately 0.2 mm2 in area. In larger volume dc discharges,
however, it is necessary to control the effect of Joule heating of the gas, for
instance by flowing the gas through the discharge at high velocities. For
air at 2000 K flowing through a 1 cm diameter region of length 3.5 cm at a
velocity of 450 mis, the residence time is 78 j..lS. The vibrational relaxation
times T reported by Park [9] indicate that the fastest vibrational relaxation
rate of molecular N2 is through collisions with atomic oxygen. The rate
constant is given by POT = 10-6 atm s -I), where Po is the partial pressure of
--- Page 246 ---
DC Glow Discharges in Atmospheric Pressure Air
231
atomic oxygen. In the present discharge experiments, the atomic oxygen
mole fraction is less than 1 %, according to the two-temperature kinetic
model predictions. Thus, the vibrational relaxation time T (> 100 Jls) is
larger than the flow time (78 Jls). This is consistent with the observation
that little gas heating was observed in the experiments. To limit gas heating
to acceptable levels for a given volumetric power, it is desirable to flow the
plasma at high velocity through the discharge region.
5.3.6 Conclusions
Investigations have been made of the mechanisms of ionization in two-
temperature air plasmas with electron temperatures elevated with respect
to the gas temperature. Numerical simulations of these mechanisms yield
the notable result that the electron number density exhibits an S-shape
dependence on the electron temperature at fixed gas temperature. This S-
shaped behavior is caused by competing ionization and charge transfer
reactions. The characteristic of electric field versus current density also
exhibits a non-monotonic dependence.
Discharge experiments were conducted in air at atmospheric pressure
and temperatures ranging from 1800 to 3000 K. In these experiments, a dc
electric field was applied to flowing air plasmas with electron concentrations
initially close to equilibrium. These experiments have shown that it is
possible to obtain stable diffuse glow discharges in atmospheric pressure
air with electron number densities of up to 2.5 X 1012 cm-3, which is up to
six orders of magnitude higher than in the absence of the discharge. The
value of 2.5 x 1012 cm-3 corresponds to the maximum current that can be
drawn from the 250 rnA power supply used in these experiments. The diffuse
discharges are approximately 3.5cm in length and 3.2mm in diameter. No
significant degree of gas heating was noticed as the measured gas temperature
remained within a few hundred Kelvin of its value without the discharge
applied. Results from these experiments are in excellent agreement with the
predicted E versus j characteristics. Additional comparisons were made
with results from glow discharge experiments in atmospheric pressure
ambient air by Gambling and Edels .[27] and Stark and Schoenbach [29].
The measurements of these authors are also consistent with the predicted
E versus j characteristics. As these measurements were made in the reactive
region of the E versus j curve, they support our proposed mechanism of
ionization for two-temperature air.
As the power budget for dc electron heating is higher than desired for
the practical use of air plasmas in many applications, methods to reduce
the power budget are currently being explored in our laboratory. Based
on the predictions of our chemical kinetics and electrical discharge models,
we have found that a repetitively pulsed electron heating strategy can provide
power budget reductions of several orders of magnitude with respect to dc
--- Page 247 ---
232
Modeling
electron heating. Repetitively pulsed discharges are presented in chapter 7
section 7.4.
Acknowledgment
The authors would like to acknowledge the contributions of Lan Yu,
Denis Packan, Laurent Pierrot, Sophie Chauveau, J Daniel Kelley and
Charles Kruger.
References
[1] Pierrot L, Laux C 0 and Kruger C H 1998 'Vibrationally-specific collisional-radiative
model for non-equilibrium nitrogen plasmas' Proc. 29th AIAA Plasmadynamics
and Lasers Conference, AIAA 98-2664, Albuquerque, NM
[2] Pierrot L, Laux C 0 and Kruger C H 1998 'Consistent calculation of electron-impact
electronic and vibrational rate coefficients in nitrogen plasmas' Proc. 5th
International Thermal Plasma Processing Conference (Begell House, New York),
pp 153-160, St. Petersburg, Russia
[3] Yu L, Pierrot L, Laux C 0 and Kruger C H 1999 'Effects of vibrational non-
equilibrium on the chemistry of two-temperature nitrogen plasmas' Proc. 14th
International Symposium on Plasma Chemistry, Prague, Czech Republic
[4] Pierrot L, Yu L, Gessman RJ, Laux C 0 and Kruger C H 1999 'Collisional-Radiative
Modeling of Nonequilibrium Effects in Nitrogen Plasmas' Proc. 30th AIAA
Plasmadynamics and Lasers Conference, AIAA 99-3478, Norfolk, VA
[5] Yu L 2001 'Nonequilibrium effects in two-temperature atmospheric pressure air and
nitrogen plasmas' PhD Thesis, Stanford University
[6] Lieberman M A and Lichtenberg A J 1994 Principles of Plasma Discharges and
Materials Processing (New York: John Wiley)
[7] Hierl P M, Dotan I, Seeley J V, Van Doren J M, Morris R A and Viggiano A A 1997
'Rate Constants for the reaction of 0+ with N2 and O2 as a function of temperature
(300-1800K), J. Chern. Phys. 1063540-3544
[8] Dotan I and Viggiano A A 1999 'Rate constants for the reaction of 0+ with NO as a
function of temperature (300-1400 K)' J. Chern. Phys. 1104730-4733
[9] Park C 1989 Nonequilibrium Hypersonic Aerothermodynamics (New York: Wiley)
[10] Park C 1993 'Review of Chemical-Kinetic Problems of Future NASA Missions, I:
Earth Entries' J. Thermophysics and Heat Transfer 7 385-398
[11] Kee R J, Rupley F M and Miller J A 1989 'Chemkin-II: A Fortran chemical kinetics
package for the analysis of gas phase chemical kinetics' Sandia National
Laboratories, Report No. SAND89-8009
[12] Laux C 0, Yu L, Packan D M, Gessman R J, Pierrot L, Kruger CHand Zare R N
1999 'Ionization Mechanisms in Two-Temperature Air Plasmas' Proc. 30th AIAA
Plasmadynamics and Lasers Conference, AIAA 99-3476, Norfolk, VA
[13] Brown S C 1966 Basic Data of Plasma Physics (MIT Press)
[14] Shkarofsky I P, Johnston T Wand Bachynski M P 1966 The Particle Kinetics of
Plasmas (Addison-Wesley)
--- Page 248 ---
Multidimensional Modeling of Trichel Pulses
233
[15] Tsang Wand Herron J T 1991 'Chemical kinetic database for propellant combustion.
1. Reactions involving NO, N02, HNO, HN02 , HCN and N20' J. Phys. Chern.
Ref Data 20 609-663
[16] Mitchner M and Kruger C H 1973 Partially Ionized Gases (New York: John Wiley)
[17] Pierrot L 1999 'Chemical kinetics and vibrationally-specific collisional-radiative
models for non-equilibrium nitrogen plasmas' Stanford University, Thermo-
sciences Division
[18] Chauveau S M, Laux C 0, Kelley J D and Kruger C H 2002 'Vibrationally specific
collisional-radiative model for non-equilibrium air plasmas' Proc. 33rd AIAA
Plasrnadynarnics and Lasers Conference, AIAA 2002-2229, Maui, Hawaii
[l9] Kazansky Y K and Yelets I S 1984 The semiclassical approximation in the local
theory of resonance inelastic interaction of slow electrons with molecules' J.
Phys. B 17 4767-4783
[20] Kozlov P V, Makarov V N, Pavlov V A, Uvarov A V and Shatalov ° P 1996 'Use of
CARS spectroscopy to study excitation and deactivation of nitrogen molecular
vibrations in a supersonic gas stream' Tech. Phys. 41 882-889
[21] Bray K N C 1968 'Vibrational relaxation of anharmonic oscillator molecules:
relaxation under isothermal conditions' J. Phys. B 1 705-717
[22] Keck J and Carrier G 1965 'Diffusion theory of non-equilibrium dissociation and
recombination' J. Chern. Phys. 43 2284-2298
[23] Ahn T, Adamovich I V and Lempert W R 2003 'Stimulated Raman Scattering
Measurements of Nitrogen V-V Transfer' Proc. 41st Aerospace Sciences Meeting
and Exhibit, AlA A 2003-132, Reno, NV
[24] Nagulapally M, Candler G V, Laux C 0, Yu L, Packan D M, Kruger C H, Stark R
and Schoen bach K H 2000 'Experiments and simulations of dc and pulsed
discharges in air plasmas' Proc. 31st AIAA Plasrnadynarnics and Lasers
Conference, AIAA 2000-2417, Denver, CO
[25] Raizer, Y P 1991 Gas Discharge Physics (Berlin: Springer)
[26] Thoma Hand Heer L 1932 Z. Tech. Phys. (Leipzig) 13 464
[27] Gambling W A and Edels H 1953 'The high-pressure glow discharge in air' Br. J. Appl.
Phys. 5 36--39
[28] Von Engel A 1965 Ionized Gases (Oxford: Oxford University Press)
[29] Stark R Hand Schoenbach K H 1999 'Direct current high-pressure glow discharges'
J. Appl. Phys. 85 2075-2080
[30] Leipold F, Stark R H, EI-Habachi A and Schoenbach K H 2000 'Electron density
measurements in an atmospheric pressure air plasma by means of infrared
heterodyne interferometry' J. Phys. D 33 2268-2273
5.4 Multidimensional Modeling of Trichel Pulses in Negative
Pin-to-Plane Corona in Air
5.4.1
Introduction
Negative corona-low current discharge between a cathode (a wire or a
point) and a plane anode-is a quite common object widely used in industry.
--- Page 249 ---
234
Modeling
While studying the negative point-to-plane corona in air, Trichel (1938)
revealed the presence of regular relaxation pulses. Qualitative explanation
given by him included some really important features like shielding effect
produced by a positive ion cloud in the vicinity of the cathode. The role of
negative ions was practically ignored. In the following work (Loeb et at
1941) it was stated that the Trichel pulses exist only in electronegative
gases, and a particular emphasis was put on the processes of electron
avalanche triggering. It was stressed also that, usually, the time of the nega-
tive ion drift to the anode is much longer than the pulse period. More detailed
measurements of the Trichel pulse shape demonstrated that the rise time of
the pulse in air may be as short as 1.3 ns (Zentner 1970a) and a step on a
leading edge of the pulse was observed (Zentner 1970b). Later, the systematic
study of the electrical characteristics of the Trichel pulses was undertaken
(Lama and Gallo 1974), and some empirical relationships were found for
the pulse repetition frequency, a charge per pulse and so on.
Among attempts to give theoretical explanation for discussed
phenomena the work of Morrow (1985) is most known, where the preceding
theories are reviewed also. Continuity equations for electrons and positive
and negative ions in a one-dimensional form were numerically solved
together with the Poisson equation computed by the method of disks. It
was supposed that the electrical charges occupy the cylinder of a given
radius. One of electrodes, cathode, was spherical. The negative corona in
oxygen at a pressure 50 torr was numerically simulated. Only the first pulse
was computed, and extension of calculations on longer times showed only
continuing decay of the current. In Morrow (1985a) the shape of the pulse
was explained while practically ignoring the ion-secondary electron emission.
In the following paper (Morrow 1985b) the step on the leading edge of the
pulse was attributed to the input of the photon secondary emission, and
the main peak was explained in terms of the ion-secondary emission.
In Napartovich et at (1997a) a so-called 1.5-dimensional model of the pin-
to-plane negative corona in air was formulated, theoretically reproducing, for
the first time, periodical Trichel pulses. Predictions of parameter dependences
within l.5-dimensional model were in good agreement with experiments and
allow for achieving some insight into the origin of the pulse mode. A two-
peak shape of the regular pulse was predicted and associated with formation
of a cathode-directed ionization wave in the vicinity of the point. However,
to derive equations of this 1.5-dimensional model it was necessary to make
some assumptions, the validity of which cannot be proved within the formu-
lated theory. Moreover, most probably these assumptions (preservation of
the current channel shape in time; slow variation of the current cross section
area in space) are strictly false, and one could only rely on anticipated
secondary role of these effects in the formation of Trichel pulses. Evidently,
a more accurate description of Trichel pulses requires that a three-dimensional
model be developed. Taking into account the circular symmetry of the corona
--- Page 250 ---
Multidimensional Modeling of Trichel Pulses
235
geometry, it is sufficient to make a model in two spatial variables: a distance
along the discharge axis, x, and a radius, r. Such a model was developed by
Napartovich et al (1997b). Later, results of numerical studies on Trichel
pulses dynamics in ambient air for pin-to-plane configuration with usage of
the three-dimensional model were reported in Akishev et al (2002a) and
published in Akishev et al (2002b).
5.4.2 Numerical model
In literature much attention is paid to multi-dimensional numerical simula-
tions of streamer propagation, e.g. Dhali and Williams (1987), Vitello et al
(1993), Egli and Eliasson (1989), Pietsch et al (1993), Babaeva and Naidis
(2000), and Kulikovsky (1997a,b). In contrast to streamers formation and
propagation, Trichel pulses are induced by a strongly non-uniform electric
field in the vicinity of the pin tip. It means that the location where the
most important processes take place is known in advance. Moreover, sizes
of this area are small for the fine point. Thus, it seems natural in calculations
to use a non-uniform mesh with small cells only around the point, increasing
the size of the cell when moving away from the point. Pietsch et al (1993)
exploit a similar technique in modeling a single micro-discharge in a dielectric
barrier discharge. The specific feature of this problem is an overall small
dimension, which makes the problem of high spatial resolution easily
solvable. In the case of negative corona discharge, it is necessary to describe
the evolution of the discharge in a region of 1 cm x 1 cm x 1 cm sizes.
However, an even greater difference in micro-discharge (streamer)
computing and Trichel pulses computing is in range of physical time,
where essential processes happen. The typical duration of micro-discharge
or streamer propagation is on the order of tens of nanoseconds. A single
Trichel pulse has a similar duration. However, to understand the mechanism
of regular repetition of Trichel pulses it is necessary to simulate at least
several pulses until the negative ions fill up the discharge gap. For short-
gap coronas this time is on the order of tens of microseconds. The required
enormous number of time steps is available only for a code possessing a very
high calculation rate. The discussed differences in requirements to the
mathematical algorithms for description of seemingly similar phenomena
(streamers and Trichel pulses) dictate the necessity to develop new
algorithms for multi-dimensional simulations of Trichel pulses.
5.4.2.1
Basic equations and electrode configuration
To describe the pulse mode of the negative point-to-plane corona it is
sufficient to solve the known continuity equations for electrons:
(5.4.1)
--- Page 251 ---
236
Modeling
positive ions
negative ions
8nn/8t + div nn Wn = Vane - Vdnn
and Poisson's equation
( 5.4.2)
( 5.4.3)
( 5.4.4)
where the indexes e, p and n refer to electrons, positive and negative ions,
respectively, np ' ne and nn are the positive ion, electron and negative ion
number densities, wp ' We and Wn their drift velocities, Vi, Va, and Vd are the
ionization, attachment, and detachment frequencies, e is the electronic
charge, (3ei is the electron-ion dissociative recombination coefficient, co is
the permittivity of free space. The electron drift velocity generally can be
determined from solving the electron Boltzmann equation. However, in the
following it was taken to be proportional to the electric field; the ion drift
velocities were calculated using the known ion mobilities. The current in
the external circuit, I, is determined from the equation
v = Uo - RI
( 5.4.5)
where V and Uo are the discharge and power supply voltages, and R is the
ballast resistor.
Equations (1)-(4) should be accomplished by boundary conditions. The
boundary conditions for positive and negative ions are self-evident: their
number density is equal to zero at anode and cathode, respectively. For elec-
trons the boundary condition was formulated in terms of the ion secondary
emission coefficient, 'Y
( 5.4.6)
where ie = neWe' ip = npwp' and rs and Xs are space variables at the cathode
surface. In calculations the fixed value of'Y = 0.01 was used. An electrode
configuration was taken as in the experiments of Napartovich et al
(1997a): the cathode pin in a form of cylinder with radius 0.06mm ended
with a semi-sphere of the same radius, and cathode-anode spacing of
7 mm. Kinetic coefficients were taken correspondent to dry air.
5.4.2.2 Numerical algorithm
To combine the requirements of accurate discrete approximations with a high
calculation rate a good choice is to do these calculations on a non-uniform grid,
which should be well adjusted to the electrode configuration. Because the shape
of the cathode is rather complicated, it is desirable to apply some generator of a
grid automatically fitted to boundary conditions. The generated grid is to be
nearly orthogonal, with some pre-described accuracy. Generation of
--- Page 252 ---
Multidimensional Modeling of Trichel Pulses
237
0.9
0.8
0.7
0.6
;,.. 0.4
0.3
0.2
0.1
0.5
0.75
X (em)
Figure 5.4.1. General view of the computational region and numerical grid. The minimum
cell size in the cathode vicinity is 6 x 1O~5 cm.
boundary-fitted meshes for curvilinear coordinate systems is a separate
problem, and the details of its solving are omitted here. A differential mesh
generation was employed, which locates the mesh points by solving an elliptic
partial differential equation (Thompson et aI1985). The computation domain
was bounded by a pin oflength 2 mm, a flat anode 7 mm from the pin tip, and a
dielectric sphere with a radius of9 .06 mm. The calculated mesh for the electrode
configuration is shown in figure 5.4.1. An average deviation angle from ortho-
gonality for this mesh is 0.48 0 , which may be considered as satisfactorily small.
An important point of controlling accuracy in numerical domain is the
method of discretization of differential equations (1 )-(4). In particular,
certain geometric identities have to be satisfied accurately in the discrete
form as well as in the continuous domain. A finite-volume approach yields
more accurate conservative discrete approximations than the method
based on the finite-differences approach. Therefore, a finite-volume discreti-
zation method (FVM) has been used with a consistent approximation of the
geometric quantities in a curvilinear coordinate system. The global algorithm
of calculations has the following steps:
1. The sources in continuity equations for charged particles are computed in
cells, and drift fluxes are computed at the cell faces.
2. By virtue of the continuity equation solving the 'new' charged particle
number densities are computed and then the total plasma conductivity
is defined.
--- Page 253 ---
238
Modeling
3. The solution to the Poisson equation determines new magnitudes for the
potential.
4. The new total current is calculated by integration of its density over the
respective surfaces.
5. The new magnitude of the cathode voltage is calculated from equation (5).
6. The condition for iteration convergence is checked:
11'+1 - rl ::; CI1sC2
where CI is the relative error, C2 the absolute error, and s is the iteration
number. If this condition is still not satisfied, the iteration procedure is
repeated starting from the first step. Details of the numerical algorithm
developed can be found in Napartovich et al (l997b).
5.4.3 Results of numerical simulations
The equations above were solved in space and time giving evolution of a
negative corona structure from a moment of step-wise applied voltage.
This evolution will be analyzed in detail for the voltage applied (4.2 kV).
The total number of numerical cells was equal to 102 x 151. The time step
was variable and automatically selected to provide a good accuracy of calcu-
lations. Computing one period takes about 12 h of continuous operation on a
Pentium 4 computer.
Figure 5.4.2 demonstrates evolution of discharge pulses after the initial
voltage step 4.2 kV, and after the second step with amplitude 8.2 kV at the
moment 40 J..lS. The height of the first peak is more than ten times higher
than that of the following pulses. The regime with regular pulses at 4.2 kV
Rb = 100 kn, h = 0.7 em, R. = 0.006 em
1
101
"-' I
100
10-1
~
Uo = 4.2 kV
Uo=8.2 kV
'5
10-2
~
10-3
0
10
20
30
40
50
Time (J.ls)
Figure 5.4.2. Discharge current evolution induced by two sequential voltage steps.
--- Page 254 ---
Multidimensional Modeling of Trichel Pulses
239
1,2
4
0,8
Vo = 4.2 kV, l\ = 100 kn, h = 0.7 em
~
3
'-'
....
5
0,4
1
2
0,0
64,0
64,1
64,2
64,3
64,4
Time (/1s)
Figure 5.4.3. Fine structure of a regular pulse: I, minimum current; 2, D.lImax leading edge;
3, about D.5Imax leading edge; 4, peak of current pulse; 5, about D.5Imax trailing edge; 6,
D.lImax pulse trailing edge.
step is completely established to about the 25th pulse. The peak height stopped
changing after four pulses, the minimum current between pulses is stabilized to
about the 12th pulse, and the repetition period stabilizes about the 25th pulse.
In the regime of regular pulses the ratio of peak to minimum current is equal to
442. With voltage increase the evolution proceeds faster. The height of the
regular pulse is insensitive to the voltage applied, while the minimum current
increases strongly. Such behavior agrees with experiment.
Figure 5.4.3 shows one of regular Trichel pulses on a nanosecond scale
for the voltage applied (4.2 kV). The duration of a peak is about 12 ns, and
the pulse has a smooth single-peaked shape with a trailing edge of about
20 ns length. In contrast to the prediction of the 1.5-dimensional model
(Napartovich et aI1997a), there is no peculiarity in the pulse leading edge.
To give an idea about pulse development and the dynamics of electrical
current spatial distribution, a number of figures illustrate the behavior of
some physical quantities for the moments marked in figure 5.4.3 by numerals.
Most strong variations of spatial distributions of charged particles and
electric field happen in the immediate vicinity of the pin tip. To show deforma-
tion of electric field distribution induced by spatial charge and plasma
produced just near the tip, the viewing region was limited in size by about
0.27 mm in axial and radial directions. Figures 5.4.4 and 5.4.5 demonstrate
contour plots for the electric field strength at the moments corresponding to
the minimum (figure 5.4.4) and maximum current (figure 5.4.5). The
influence of the spatial charge remaining from the preceding pulse on the elec-
tric field is seen even at the minimum current. In the maximum, formation of a
layer with high fields is clearly seen. This region resembles a classical cathode
--- Page 255 ---
240
Modeling
0.225
0.22 I~
10
350
9
247
:~'\
8
174
0.215
7
122
6
86
5
61
0.21
4
43
'£'~~ ~
-
3
30
2
21
0.205
15
0.2
~
~
....
0
0.01
0.03
Figure 5.4.4. Electric field strength contour plot near the pin at the minimum current. The
electric field strength in the legend is in k V jcm.
layer with the maximum electric field strength as high as 300 kV jcm. The thick-
ness of this high-field region is about 7 j.lm. Near this high-field zone, a region
appears with rather low fields (on the order of a few hundreds of V jcm). Poten-
tial curve leveling off indicates this zone. The transformation of an axial profile
of electrical potential shown in figure 5.4.6 within an interval 40 j.lm from the
pin tip demonstrates that already at 0.1 of the peak current (curve 2) something
like a cathode layer is formed with a potential drop of about 180V. Then this
potential drop diminishes, approaching minimum at the current peak. It is
seen that this layer broadens in the trailing edge of the pulse rather quickly
(curves 5 and 6). Electron number density between pulses is lower than
108 cm-3 and approaches 4 x 1015 cm-3 at the pulse peak.
0.225
0.22
10
190
9
137
8
99
0.215
7
71
6
51
5
37
0.21
4
27
3
19
2
14
1
10
0.03
Figure 5.4.5. Electric field strength contour plot near the pin at the current peak. The elec-
tric field strength in the legend is in kVjcm.
--- Page 256 ---
Multidimensional Modeling of Trichel Pulses
241
300
200
100
O~--~-.--~--.---~~--~--.
0.206
0.207
0.20S
X (cm)
0.209
0.210
Figure 5.4.6. Electric potential distribution along the discharge axis in the vicinity of the
pin tip at moments indicated in figure 5.4.3.
Negative ion distribution varies only close to the pin tip, and on the
whole suffers only small changes. The contour plot for the negative ion
concentration in the whole area is shown in figure 5.4.7 at the minimum
current. The presented contour plots gave a rough idea about space-time
evolution of discharge structure in regular pulses.
0.9
o.s
0.7
0.6
,.-..
0.5
e
u
""
10
S.OE+10
'-'
:><
0.4
9
l.SE+10
S
4.SE+09
7
1.4E+09
6
4.1E+OS
5
1.2E+OS
4
3.7E+07
3
1.1E+07
2
3.3E+06
1
1.0E+06
Figure 5.4.7. Negative ion number density contour plot at the minimum current for the
computation region. Negative ion density in the legend is in cm -3.
--- Page 257 ---
242
Modeling
100
-
d~310-4cm
> -u
::J
50
I
::J
0,01
0,02
Lc (em)
Figure 5.4.8. Distribution over the cathode surface of the voltage drop across the sheath
adjacent to the cathode surface with thickness of 3 ~m
Actually, the generation zone is the place where self-oscillations of the
corona current are initiated. Therefore, it is of particular interest to look
at the evolution of electric current at the cathode surface. Dynamics of the
current distribution over the cathode is rather complicated. Generally,
evolution of the total current profile can be described as an expansion over
the cathode surface until the pulse peak with following fast contraction
around the discharge axis. This feature of discharge evolution near the
cathode is clearly seen in figure 5.4.8 drawn for the voltage drop across the
sheath adjacent to the cathode surface with thickness of 3 ~m. In the front
of the pulse, the profile of this voltage drop looks like a shoulder, whose
length grows and height goes down. In the trailing edge of the pulse,
evolution proceeds in the reverse direction.
A time-average current radial profile on the anode is well known
(Warburg 1899, 1927). Results of numerical simulations are compared with
the Warburg profile in figure 5.4.9. The calculated radial current profile is
narrowed against Warburg profile. It should be noted that, according to the
Warburg distribution, the current density at the computation region boundary
is about 0.1 of the maximum. This indicates that the dielectric spherical
boundary imposed in calculations to restrict the computational region may
influence the current distribution over the anode, and on the whole pulse
dynamics. Indeed, experiments (Akishev et a/1996) demonstrated that restric-
tion of the space occupied by the corona notably influences the amplitude of
Trichel pulses and their repetition frequency (see section 6.7 in this book).
Numerical simulations for the same corona geometry performed for
various voltages applied showed that the predicted charge per pulse is
about three times smaller than experimental values for similar conditions.
Theoretically predicted dependence of the pulse repetition period on the
--- Page 258 ---
1,0
0,8
€ 0,6
~-
....
"'"<
~
;::;-- 0,4
0,2
Multidimensional Modeling of Trichel Pulses
243
-.
O,O~----~----T-----r-----~~~-'~~--~----~-----r----~
0,0
0,2
0,4
0,6
0,8
1,0
Figure 5.4.9. Average current density distribution over the the anode surface. Solid line,
our simulations; dashed line, classical Warburg profile.
voltage applied in comparison with measurements (Akishev et al 2002a)
agrees well for voltages higher than 6 kV. At 4.2 kV the predicted period is
2.5 times shorter than the measured one.
It is instructive to compare predictions made by the present multi-
dimensional modeled Trichel pulses with the 1.5-dimensional model devel-
oped earlier (Napartovich et al 1997a). In the 1.5-dimensional model the
current channel shape was assumed to be independent of time. It was
taken corresponding on the whole to known experimental data, and depends
on some parameters which were fitted to achieve better agreement between
calculated and predicted characteristics of regular pulses. A specific feature
of the current channel shape was a narrow (0.06 mm radius) cylinder adjacent
to the cathode pin with length 0.2 mm. The present model free of fitting
parameters predicts that the region with large gradients of particle densities
and voltage is essentially shorter than assumed in the 1.5-dimensional model
(tens of 11m instead of hundreds of 11m). Besides, the multidimensional model
predicts strong variations of radial distributions. Nevertheless, the differ-
ences between the time histories of the integral quantities turned out to be
not so strong. There are some details different in the two models. The 1.5-
dimensional model predicts very fast propagation of a highly ionized
region to the cathode at the front of the pulse. Besides, it predicts the forma-
tion of a very sharp subsidiary peak just prior to the main current peak. The
present model predicts formation of a cathode layer (not coinciding with the
normal cathode layer of glow discharge) first at the axis with following
--- Page 259 ---
244
Modeling
expansion over the cathode surface. Since the present model is free of arbi-
trary assumptions inherent to the l.5-dimensional model, the scenario of
pulse evolution predicted by it should be more realistic. However, we have
to recognize that the problem of correct description of cathode layer forma-
tion still remains. Specifically, effects of non-locality of the electron energy
distribution function were ignored, which may result in increase of ionization
rate and lengthening of a region with significant ionization. The high ioniza-
tion degree predicted by numerical simulations (up to 10-4 or greater) will
influence the electron energy spectrum, too. Very high local power density
in the pulse may lead to numerous processes becoming important in enhan-
cing the ionization rate in low-field regions. All the listed effects can hardly be
adequately accounted for at the present state of the theory.
5.4.4 Conclusions
The three-dimensional model with axial symmetry effectively reduced to the
two-dimensional one is formulated and applied to numerical simulations of
pulse evolution in a negative corona with a cathode in the form of a cylinder
with a semi-spherical cap in dry air at atmospheric pressure. Calculations
demonstrated that current oscillations became perfect regular after about 25
pulses. Space-time evolution of electric field and charged species densities
within one cycle of regular pulses is described in detail. The model predicts
fast formation of a cathode layer at the discharge axis followed by its quick
expansion over the cathode surface at the leading edge of the current pulse.
For a higher power supply voltage, the peak current rises a little, while
the current between pulses grows substantially. The predicted charge per
pulse is about three times smaller than experimental values for similar
conditions. The pulse repetition period is close to that observed at higher
voltages, while it is shorter at a low voltage. In contrast to the simplified
l.5-dimensional model predicting a two-peak shape of a Trichel pulse, the
exact three-dimensional model predicts single-peaked pulses when ion-
induced secondary emission processes are included, and photo-emission is
neglected. On the anode surface, radial profiles of electric current averaged
over one cycle was calculated and compared with the experiments. Revealed
discrepancies between experimental data on typical charge per pulse and
current distribution over the anode clearly indicate the necessity to improve
the model. A weak point in the model presented above is the oversimplified
description of plasma kinetics formed near the cathode pin.
References
Akishev Yu S, Deryugin A A, Kochetov I V, Napartovich A P, Pan'kin M V and Trushkin
N I 1996 Hakone V Contr Papers (Czech Rep.: Milovy) p 122
--- Page 260 ---
Electrical Models of DBDs and Glow Discharges
245
Akishev Yu S, Kochetov I V, Loboiko A I and Napartovich A P 2002a Bulletin of the APS
4776
Akishev Yu S, Kochetov I V, Loboiko A 1 and Napartovich A P 2002b Plasma Phys. Rep.
281049
Babaeva N Yu and Naidis G V 2000 in van Veldhuizen E M (ed) Electrical Dischargesfor
Environmental Purposes: Fundamentals and Applications (New York: Nova Science
Publishers) pp 21-48
Dhali S K and Williams P F 1987 J. Appl. Phys. 62 4696
EgJi Wand Eliasson B 1989 Helv. Phys. Acta 62 302
Kulikovsky A A 1997a J. Phys. D: Appl. Phys. 30441
Kulikovsky A A 1997b J. Phys. D: Appl. Phys. 301515
Lama W L and Gallo C F 1974 J. Appl. Phys. 45103
Loeb L B, Kip A F, Hudson G G and Bennet W H 1941 Phys. Rev. 60 714
Morrow R 1985a Phys. Rev. A 32 1799
Morrow R 1985b Phys. Rev. A 32 3821
Napartovich A P, Akishev Yu S, Deryugin A A, Kochetov I V, Pan'kin M V and Trushkin
N I 1997a J. Phys. D: Appl. Phys. 30 2726
Napartovich A P, Akishev Yu S, Deryugin A A and Kochetov I V 1997b Final report to the
Contract between ABB Management Ltd. Corp. research, Baden, Switzerland and
TRINITI
Pietsch G J, Braun D and Gibalov V I 1993 in B M Penetrante and S E Schultheis (eds)
Non-thermal plasma techniques for pollution control, Part A, NATO ASI Series pp
273-286
Thompson J F, Warsi Z U A and Mastin W C 1985 Numerical Grid Generation (New York:
Elsevier)
Trichel G W 1938 Phys. Rev. 54 1078
Vitello P A, Penetrante B M and Bardsley J N 1993 in Penetrante B M and Schultheis S E
(eds) Non-thermal plasma techniques for pollution control, Part A, NATO ASI Series
pp 249-271
Warburg E 1899 Wied. Ann. 67 69
Warburg E 1927 'Charakteristik des Spitzenstormes' in Handbuch der Physik 4 (Berlin:
Springer) pp 154-155
Zentner R 1970a ETZ-A 91(5) 303
Zentner R 1970b Z. Angew. Phys. 29(5) 294
5.5
Electrical Models of DBDs and Glow Discharges in Small
Geometries
5.5.1
Introduction
The purposes of our discussion here are to provide an overview of electrical
models of plasmas created in gas discharges, to show how they have been used
to improve our understanding of dielectric barrier discharges (DBDs), and to
suggest where they could be used to help develop a better understanding of
--- Page 261 ---
246
Modeling
discharges in very small geometries (microdischarges). As discussed in
greater detail in sections 2.6, 6.2, and 6.4 of this book, DBDs and micro-
discharges are two approaches being investigated as means for producing
non-thermal, atmospheric pressure plasmas.
In section 5.5.2 we describe briefly a physical model of the initiation and
evolution of non-thermal plasmas in electrical discharges where the cathode
region has a determining influence on the properties of the system. We then
present a numerical model suitable for describing the electrical properties of
such glow discharges. The same type of model has been used for essentially
all studies on DBDs to date and for the few modeling studies of micro-
discharges that have been published. We then summarize how modeling
has contributed to our current understanding of DBDs and microdischarges
(sections 5.5.3 and 5.5.4, respectively), using previously published results in
oxygen and rare gas mixtures to illustrate the phenomena occurring during
the transient evolution glow discharges in DBDs in general. The few previous
modeling results on DBDs in air are discussed by Kogelschatz in section
6.2.3, and the conclusions from the studies in air are the same as those
discussed below. A few concluding remarks are presented in the final section.
It is worth noting that the physical situation described in this section is
different from those presented in sections 5.2 and 5.3. That is, for DBDs and
discharges in small geometries, quasi-neutrality cannot be assumed; the space
charge electric field must be calculated self-consistently with the charged
particle transport and generation rate. The strong coupling between the
space charge field distribution and the charged particle transport and genera-
tion is a major issue here.
5.5.2 Model of plasma initiation and evolution
The physical situation we aim to describe is plasma initiation and evolution
in an electrical discharge. The discharge geometry is arbitrary, although
cylindrical or rectangular symmetry is often assumed in order to reduce
the problem to two dimensions. A dc, pulsed or rfvoltage is applied between
two or more electrodes which mayor may not be covered by dielectrics. The
electrodes are separated by a gap filled with a gas at a pressure p and we are
mostly interested in conditions appropriate to the generation of non-thermal
plasmas at high pressure.
5.5.2.1
Physical model
For a sufficiently high applied voltage and gas pressure, free electrons in the
gas gap gain enough energy from the electric field to produce ionization
through collisions with neutral gas atoms or molecules. The ionization
cascade due to one initial electron and its progeny is called an 'avalanche'.
The electrons in each avalanche move rapidly to the anode and leave
--- Page 262 ---
Electrical Models of DBDs and Glow Discharges
247
behind the slower ions that were also produced in ionization or attachment
events. Gas breakdown [1] proceeds either via Townsend breakdown or via
streamer breakdown. Townsend breakdown occurs when, on the average,
each electron, before arriving at the anode, has produced enough ioniza-
tion/excitation in the volume to replace itself through secondary emission
processes at the cathode (e.g. via ion-induced secondary electron emission,
photoemission, etc.). In contrast, 'streamer' breakdown occurs when the
space charge in an avalanche produced by a single electron grows large
enough to be self-propagating so that no secondary emission is needed. As
shown below, the streamer breakdown mechanism is favored for large
values of pd (the product of gas pressure p and gap spacing d) and for
high overvoltage; therefore, for high electron multiplication conditions.
This mechanism leads to thin, highly conducting channels.
Following Townsend breakdown, a 'glow' or 'transient glow' discharge
results if the accumulated positive space-charge, resulting from successive
generations of avalanches created by cathode-emitted electrons, becomes
large enough in a given volume to trap the electrons there, thus forming a
plasma. This plasma expands very quickly toward the cathode, not because
of the transport of existing particles, since that would be too slow a process,
but rather because the ionization produced by the cathode-emitted electrons
is enhanced in the relatively higher electrical field on the cathode side of the
expanding plasma. For dc discharges at steady-state, almost all the potential
drop is squeezed into the cathode fall between the plasma and the cathode. In
DBDs, the axial expansion of the plasma is limited because of the charging of
the dielectric surfaces. The plasma then expands radially along the electrode
surfaces until the local electric field is no longer sufficient to maintain the
electron temperature needed for ionization. At that point, the discharge
filament extinguishes.
Glow discharges resulting from Townsend breakdown can be uniform
radially or filamentary, depending on the conditions. The discharge can be
filamentary even in the absence of thermal effects or stepwise ionization
which are usually associated with the onset of instabilities. As a general
rule, when the radial dimension R of the electrodes is much larger than the
radial extent, 8r, of one electron avalanche in the gas gap, the discharge
will tend to be filamentary. For typical discharge applications, RI8r is
much larger at higher pressure. This is the reason why the filamentary
mode of glow discharges is often observed at high pressure even when the
current can be limited, as in a dielectric barrier discharge.
Discharges resulting from streamer breakdown are filamentary in nature
and thus, for applications requiring a uniform plasma, streamer breakdown
must be avoided. Streamers tend to evolve into arcs due to the formation of
hot spots on the electrodes and resultant thermal plasma channel. This evolu-
tion of arcs can be inhibited if the current density is limited by, for example, a
dielectric coating on an electrode. Note that a high level of pre ionization can
--- Page 263 ---
248
Modeling
provide enough initial electrons for the streamers to overlap [2, 3]. This can
result in a uniform plasma, at least for a time less than the time needed for the
onset instabilities due to power loading of the gas.
5.5.2.2 Numerical model
The fundamental variables in a numerical model of plasma initiation and
evolution are the electron and ion densities and the electric field, or potential.
The equations for these variables, complemented by suitable boundary
conditions, are solved self-consistently to yield charged particle densities
and electric field distribution as functions of time and space. From these
results, we can calculate most other quantities of interest.
The following equations provide a mathematical description charged
particle and electric field evolution.
• Electron and ion continuity equations:
one
[ -l
8t+ V'. neve = se
(1)
an· 0/ + V' . [niVil = Si
(2)
where Ve and Vi represent the mean velocity for electrons and ions respec-
tively and Se(r, t) and Si(r, t) are the production rates for electrons and
ions respectively. Each ion species is described with an equation in the
form of equation (2).
• Equations for conservation of momentum for electrons and ions of sign, s, in
the drift-diffusion approximation:
(3)
(4)
where Me (i) is the electron (ion) mobility and De (i) is the electron (ion) free
diffusion coefficient.
• The continuity and momentum transfer equations are coupled to Poisson's
equation:
(5)
where c is the permittivity (in general a function of x to include the
dielectric volumes), e is the unit charge, n+ is the total positive charge
density and n- is the total negative charge density (volume and surface
charge density). At the interface between the gas and any dielectric
surface the charge density is calculated by integrating the charged
particle current to the surface, during the evolution of each discharge
pulse. Thus the spreading of the surface charge along a dielectric surface,
--- Page 264 ---
Electrical Models of DBDs and Glow Discharges
249
due to radial field induced by the previous surface charge, can be taken
into account.
The electric field, E, is calculated from the potential as
E = -V'V.
(6)
With the assumption of rectangular or cylindrical symmetry, the problem
becomes two-dimensional.
The system of equations (1)-(5) must be closed by some assumptions
about the transport coefficients and source terms. In many models of
high pressure discharges, the mobility, diffusion coefficients and ionization
coefficient are assumed to be functions of the local reduced electric field.
This is logically referred to as the 'local field approximation'. Often, the
diffusion coefficients are assumed to be constant. This limits the occurrence
of numerical instabilities. This local field approximation allows a simple
and often realistic description of the discharge. However, a description of
the electrons involving the first three moments of the Boltzmann equation
(the electron energy equation in addition to the continuity and momentum
conservation equations) is more satisfactory not only for a better quantita-
tive description of the discharge but also, in some cases, for a better qualita-
tive representation of the physical phenomena. When an energy equation is
used, the electron mobility, diffusion coefficient, and ionization frequency are
assumed to depend on the local mean electron energy. A good example of a
high pressure dielectric barrier discharge model for plasma display panels
(PDPs) can be found in Hagelaar et al [4].
Finally, the electron current leaving the cathode is related to the incident
ion current and through the secondary electron emission coefficient, 'Yb as
follows:
'Pe(cathode) = L 'Yk'Pk(cathode)
(7)
k
where the sum is over all ion species, 'Yk is the secondary electron emission
coefficient due to the kth type of ion incident on the cathode, and 'Pk is the
flux of the kth type of ion to the cathode.
Note that photons and metastable atom bombardment of the cathode
can also lead to secondary electron emission [5], and desorption of electrons
from the dielectric layer has been proposed to account for some observations
[6]. We return to this point below; however, it is important to emphasize now
that the identification and quantification of the electron emission processes
from the cathode are unresolved modeling issues.
To the extent that the degree of excitation is too low to influence the
net rate of generation of charged particles, it is possible to neglect plasma
chemistry in the electrical model. As the power deposited in the gas increases,
two-step ionization (electron impact ionization of excited states) and
--- Page 265 ---
250
Modeling
associative or Penning ionization can start to playa role, in which cases a
model of the plasma chemistry must be solved self-consistently with the
electrical model. Gas heating is another consideration because the local
value of E / N is high, and thus the ionization rate is high, where the gas
temperature is high.
5.5.2.3
Numerical methods
Starting from the known or assumed initial conditions, equations (1)-(5) are
integrated in time to yield the charged particle densities and the electric field
as functions of space and time. Numerical methods for solutions of these
equations are discussed, for example, by Kurata [7]. Nevertheless, there
remain the following two particular numerical difficulties encountered in
the modeling of high pressure plasmas.
1. For dc or transient glow discharges (radially uniform or filamentary). The
simplest integration scheme for these equations is an explicit scheme in
which the charged particle transport and Poisson's equations are solved
sequentially. That is, Poisson's equation is solved at time l, and then
the charged particles are transported for a time tlt in the field calculated
at time l. Such an integration scheme is subject to the constraint that the
time step tlt must be smaller than the dielectric relaxation (Maxwell) time,
tltM' which is inversely proportional to the plasma density:
CO
tltM =
.
e(neMe + niMi)
(8)
Thus, for a plasma density of 1014 cm-3, the integration time step in an
explicit integration scheme is very approximately 10-12 sat 100 torr, and
this simple integration scheme leads to impractically long computational
times. Either semi-implicit [8] or fully implicit [7] schemes must be used.
2. For streamers. The modeling of streamer-type microdischarges is
difficult numerically because streamers have two very different spatial
scales that must be considered simultaneously, namely the streamer
front with steep gradients and the streamer body with a nearly uniform
plasma. Compounding this difficulty is that fact the streamer front
propagates. There have been a large number of publications presenting
results of modeling streamer formation and propagation (see, for
example, Dhali and Williams [9]). In the context of DBDs in oxygen, Li
and Dhali [10] have presented a method for solving these equations
using an adaptive grid where the resolution is highest in the region of
large density gradients.
In spite of the numerical complications, models have been developed that are
very efficient. As an example, models ofDBDs in typical PDP conditions [11]
take about several seconds, several minutes and several hours, respectively,
--- Page 266 ---
Electrical Models of DBDs and Glow Discharges
251
per pulse for one-, two-, or three-dimensional calculations using a
40 x 40 x 40 grid running on a 2 GHz personal computer.
5.5.3 Dielectric barrier discharges
Orders of magnitude estimates for some of the DBD discharge properties are
listed in table 5.5.1 for different operating modes at approximately atmos-
pheric pressure and for the conditions indicated. We will briefly summarize
results obtained from modeling these modes in the sections below, without
attempting to be exhaustive in the list of references.
5.5.3.1
Random filament mode
The common discharge mode in atmospheric pressure DBDs is the random
filament mode [14, 15] where as many as 106 Icm2 Is transient glow discharge
filaments occur at seemingly random locations, each being extinguished after
bridging the gap. The filaments are random in the sense that we cannot
predict where or when they will be initiated. We use this term to make explicit
the difference between this mode and the self-organization (pattern forma-
tion, see below) sometimes observed in DBDs as the voltage is decreased.
Most all of the modeling for this type of discharge mode has concen-
trated on simulating the evolution of a single, isolated current filament.
The early work of Eliasson et al [16] was developed to study the efficiency
of ozone production in DBDs. This was later coupled to a two-dimensional
electrical model consisting of plane parallel electrodes covered by dielectrics
in which many aspects of DBD behavior [17] were quantified. These aspects
include the spreading of the discharge along the dielectric surface due to
accumulated surface charges, the dependence of the current pulse width on
pressure and the total charge transferred per micro-discharge versus
Table 5.5.1
Conditions
Current pulse duration
Filament radius
Peak current density
Total charge transferred
Peak electron density
Electron energy
Random filament
mode [12]
I atm air/02
Imm
I-IOns/filament
~10011m
~100-1000A/cm2
0.1-1 nC/filament
~1014_1O15 cm-3
1-lOeV
PDP cells
[11]
560 torr, Xe/Ne
150 11m
50-lOOns
100 11m
IOA/cm2
30 pC/pulse
5 x 1013 cm-3
1-lOeV
Atmospheric
pressure glow
discharge
(APGD) [13]
I atm He
0.5cm
>ll1s
Uniform
~lmA/cm2
13nC/cm2
<lOll cm-3
1-lOeV
--- Page 267 ---
252
Modeling
pressure. These authors found good agreement between their numerical
results and experimental measurements of the latter two quantities. The
former quantity was not measured. Results from the two-dimensional
model were used to help define a simple model of the plasma chemistry in
oxygen DBDs and in rare-gas mixtures such as those used for the generation
of excimer radiation. Heating of the ions was identified by these authors as a
mechanism limiting the efficiency for ozone generation in DBDs.
Kogelschatz (see sections 2.6 and 6.2) argues that the filaments observed
in DBDs in this application are essentially transient high pressure glow
discharges and that the current density and electron density are what
would be expected based on j / i (ratio of current density to the pressure
squared) scaling of glow discharges to atmospheric pressure [18]. Note that
pt, the product of the gas pressure and time, is also a scaling parameter.
We assert that these scaling parameters cannot be applied to filaments
resulting from streamer breakdown because of higher current density and
narrower conducting channels following streamer breakdown, different
distribution of energy in excitation, ionization, and dissociation channels,
etc. Nevertheless, more work needs to be done to clearly identify the effects
of the breakdown mode (Townsend or streamer) on the plasma properties of
the filaments in DBDs.
Gibalov and Pietsch and their colleagues [19-21] have developed two-
dimensional models of DBDs in different configurations (volume, coplanar
and surface discharges) and for air/oxygen at atmospheric pressure. Braun
et al. [19] describe the evolution of an isolated filament in DBDs with
plane parallel electrodes, one of which is covered by a dielectric, in air for
pd = 76torrcm-1 and for a voltage near the breakdown voltage. These are
not streamer conditions in the sense defined above, and secondary electron
emission due to ion impact and as well as photo-ionization are considered
in the model. According to this work, 'the microdischarges behave like tran-
sient high pressure glow discharges'; a plasma forms first near the anode and
then expands towards the cathode. One could quibble with their persistent
use of the term 'cathode-directed streamer', and we suggest that 'transient
glow discharge filament' is a more appropriate term. Gibalov and Pietsch
[20] studied the efficiency of ozone generation in DBDs in planar and surface
discharge geometries. They modeled, for example, one dielectric-covered
electrode and either a bare parallel electrode a short distance away or a
bare perpendicular electrode touching the dielectric surface, respectively.
They found nearly the same efficiency for both. Gibalov et al [21] have
also studied DBDs in coplanar geometries and found reasonable agreement
with experiment, noting that 75% of the energy losses are due to heating of
the ions for the conditions of 100 !lm coplanar electrode spacing, 1 mm gas
gap, and 2 bar oxygen.
Results from the models of Gibalov and Pietsch and their colleagues in
planar DBD configurations are generally consistent with Eliasson et al [16].
--- Page 268 ---
Electrical Models of DBDs and Glow Discharges
253
The mlllimum thickness of the cathode sheath was found to be large
compared to a glow discharge. This was expected because the charging of
the dielectric layer prevents a fully developed glow discharge from forming.
The calculated discharge radius is about 200 /lm in the volume, but the area
covered by the surface charge is much larger than the channel diameter. This
arises because the electron surface charge spreads more than the ion surface
charge. At the peak value of the current, about 50% of the power is deposited
in the ions and the remaining energy is distributed almost homogeneously in
the electrons in the column. The increase in the mean gas temperature can be
high near the cathode, depending on the dielectric capacitance, but is only a
few Kelvin in the plasma column.
Other recent modeling work on single filaments in DBDs include that of
Steinle et al [22] who published results from a two-dimensional simulation of
filament evolution in DBDs in air at atmospheric pressure in a small gap with
high dc applied voltage. Conditions for streamer formation were satisfied for
the parameters chosen in this work, and the authors presented results
showing that the efficiency for ultraviolet generation, but not the efficiency
for generation of radicals, depends rather strongly on the applied voltage.
In this work, secondary electron emission produced via photoemission
from the cathode as well as photo-ionization in the volume are accounted
for in a rather detailed way, but the role played by secondary electrons
emitted from the cathode is not clear. Carman and Mildren [23] studied
pulse-excited DBDs in xenon and found that the efficiency for generation
of excimer radiation can be quite high in these conditions, namely greater
than 60%, consistent with the experiments of Vollkommer and Hitzschke
[24] who have developed a commercial lamp based on the concept of
pulse-excited DBDs and for which streamer conditions were avoided. Xu
and Kushner [25, 26] have reported one-dimensional radial calculations of
interacting filaments in DBDs in N2 and in N 2/02 mixtures at atmospheric
pressure. They find that filaments affect their neighbors mainly through the
charging of the dielectric and that the plasma chemistry in a given filament
is otherwise very little affected by the presence of its near neighbors.
Golubovskii et al [27], and more recently Boeuf [28], have been investi-
gating reasons for the formation of transient glow discharge filaments in
DBDs following Townsend breakdown. This is an interesting question
because Townsend breakdown can lead to either uniform or filamentary
discharges, and more work needs to be done to clearly identify reasons for
the occurrence of each.
5.5.3.2
Plasma display panels (PDPs)
Much modeling work has been done in dielectric barrier discharges for
plasma display panels (PDPs) where the discharge dimensions are on the
order of 100 /lm and the gas pressure is about 500 torr for mixtures of rare
--- Page 269 ---
254
Modeling
gases containing xenon, and the applied frequency is a square wave with a
frequency of 100kHz or more. Most PDPs today use a 'coplanar' geometry
where the main discharge occurs between parallel electrodes on the same
substrate, at a position selected by applying a suitable low voltage to the
third electrode (perpendicular) on the opposite substrate. 'Matrix' geome-
tries, in which the electrodes are perpendicular stripes on opposite substrates,
have also been studied for PDP applications.
The discharges in PDPs are at low values of pd (typically 5 torr cm -1)
that are typical of glow discharges but lower than for other DBD applica-
tions. The ability to control each discharge separately and the reproducibility
of the discharges are paramount in this application. In the sustaining mode,
the applied voltage is less than the breakdown voltage, and it is the surface
charge remaining from the discharge pulse on the last half cycle that
makes operation at this low voltage possible. The operation at an applied
voltage below breakdown is essential in the PDP application because it
allows bi-stability, namely, the coexistence of discharge cells in the ON
state and in the OFF state with the same sustaining voltage. To turn a
discharge cell from the OFF state to the ON state, one must first apply an
address-voltage pulse to the cell in order to deposit memory charges on the
cell walls. These memory charges create a voltage drop across the dielectric
layer that will add to the voltage across the electrodes when the sustaining
voltage is applied. During the sustaining period, the voltage rise time in
PDPs must be short enough that breakdown occurs during the plateau of
the square wave voltage. Using a sinusoidal voltage, as found in many
other DBD applications, does not allow adequate control of the voltage at
which breakdown actually occurs. In the driving scheme of a PDP there is
a period, called the 'priming period,' during which a very slowly rising
voltage is applied between the electrodes in each discharge cell. This gener-
ates a low current discharge that will provide seed electrons in order to mini-
mize the statistical time lag during addressing. The slowly rising voltage
allows one to operate in a low current Townsend (or 'dark') discharge
regime where the light emission is weak and does not significantly reduce
the contrast. This shows that the rise-time of the voltage is a very important
parameter and can help to control the discharge regime and the voltage at
which breakdown occurs in a DBD. Using a sinusoidal voltage does not
allow a simple control of the voltage rise-time because the only way to
change the rise-time is to change either or both the amplitude or/and the
frequency of the voltage waveform. There remains the need to study more
systematically, both in experiments and simulations, the effects of the voltage
wave-form on the properties of DBDs in general.
The first one-dimensional model published in 1978 [29] contained most
of the elements of DBD operation. Since then one-dimensional, two-
dimensional and recently three-dimensional fluid models have been used to
study PDPs in considerably more detail. These simulations are described in
--- Page 270 ---
Electrical Models of DBDs and Glow Discharges
255
the review of Boeuf [11]. State-of-the-art PIC-MC models have also been
used to check assumptions and study such purely kinetic effects [30, 31] as
the appearance of striations in the light intensity in the plasma spreading
along the dielectric surface. These models have been used to quantify the
characteristics of the plasmas produced in PDPs and, more recently as the
models have been improved, to help guide the experimental optimization
of these devices. Models were used to understand the reasons for the low
luminous efficacy which is due to the energy wasted in accelerating ions in
the sheath [32] and to suggest ways for improving efficiency such as modi-
fying the electrode geometry and/or increasing the length of the transient
positive column region [33-35]. For example, it has been seen that xenon is
efficiently excited in the low field region accompanying the spreading of
the discharge along the anode surface, and that enhancing this spreading
increases the efficiency [11]. Note, however, that the radial field at the
anode in ozonizers is not high enough to affect the desired chemistry and
thus leads to a decrease in the efficiency in that application [21]. The
addressing of individual cells in coplanar PDPs is accomplished by suitable
application of voltage pulses between the electrodes and on the third 'addres-
sing' electrode. Models have been used for parametric studies of different
addressing schemes. Excellent agreement has been obtained between
models and experiments of the electrical characteristics and with the space-
and time-dependence of the emission intensity. There is also generally
good agreement with available data for the efficiency for excitation of
xenon and in the space and time evolution of the emission features.
5.5.3.3 Atmospheric pressure glow discharge
DBDs at high pressure are normally filamentary [14], but, in a limited range
of conditions, it is possible to generate an atmospheric pressure glow
discharge (APGD) [13, 36]. As mentioned above, the conditions leading to
either a uniform plasma or filamentation in atmospheric pressure air are
not yet completely understood [27]. However, it seems that the properties
of any single filament which may arise are not very different from those of
the APGD plasmas.
Modeling has been an important tool in gaining an understanding of
the plasmas produced in APGDs. The models of Segur and Massines [37],
Tochikubo et al [38] and of Golubovskii and colleagues [6, 39] have been
used to calculate the charged particle density and electric field distributions
as functions of space (one-dimensional) and time in APGDs in helium and
nitrogen. From these results, the time variations of gap voltage, memory
voltage and current density have been obtained and compared with experi-
ment. Model predictions agreed quite well with measured current waveforms
and patterns of light emission intensity, although each found that the quan-
titative agreement required some additional ionization, which could be due
--- Page 271 ---
256
Modeling
to impurities or to the effects of metastables. Segur and Massines and Golu-
bovskii et at conclude that the uniform glow in nitrogen is in the Townsend
regime in that little or no space charge distortion of the geometrical field and
low charged particle densities are observed. However, they found higher
plasma densities in helium APGDs.
One can conclude from comparisons of models and experiment [13] that
the generation of an APGD depends on a slow growth of the avalanche, a
high enough electron density at the beginning of each half cycle, and a
high electron emission from the cathode. Essentially these same conclusions
have been derived by Golubovskii and colleagues who find that the rate of
voltage rise affects the discharge mode (see the discussion above for PDPs
in section 5.5.3.2). Specifically, for a slow rise time, breakdown occurs near
the Paschen minimum indicating a slow growth of the avalanche, and
favors a uniform glow mode [39]. Golubovskii and colleagues have proposed
a mechanism of desorption of electrons at the cathode to provide secondary
electrons between current pulses in order to reproduce experimental results
[6]. It is interesting to note that such additional electron emission was also
needed to describe PDP operation at low frequency where the plasma has
time to decay on each half cycle of the applied voltage [11]. Golubovskii
et at [40] have also looked at the question of photoemission as a mechanism
for discharge uniformity (photons strike the cathode at radial positions far
from the axis of their parent filament) and other mechanisms that could
lead to radial non-uniformities [27].
As emphasized by Aldea et at [41] and Tochikubo et at [38], the
discharge cannot be uniform if the breakdown process itself is filamentary
as indicated by streamer breakdown. Avoiding streamer formation is more
difficult at high values of pd and depends on the gas composition as shown
in figure 5.5.1. The minimum breakdown voltage, Vb, is plotted as a function
of pd, which, as stated previously, is the product of the gas pressure p and
gap spacing d in a parallel plate electrode geometry. The value of Vb can
be determined through the self-sustaining condition [42]
M = exp[a(Vb,pd) x d] = 1 + (111)
(9)
where the electron multiplication, M, is related to the net ionization rate
coefficient, a, which itself depends on Vb and pd, and 'Y is the secondary
electron emission coefficient. A rough estimate of the voltage required for
streamer formation, Vs, can be derived by supposing that streamers [43,
44] form when the electron multiplication in the gap exceeds 108. Using
ionization and attachment rate coefficients from the SIGLO database [45],
we calculated the ratio Vs/ Vb shown in figure 5.5.1 by assuming a secondary
electron emission coefficient of 0.3 in helium and 0.01 in air. Korolev and
Mesyats [46] point out that the boundary between Townsend and streamer
breakdown is not sharp, and thus the curves in figure 5.5.1 are only
qualitative. Nevertheless, the conclusion is clear: avoiding streamer
--- Page 272 ---
Electrical Models of DBDs and Glow Discharges
257
o
200
400
600
800
1000
pd (torr em)
Figure 5.5.1. Ratio of the voltage required for streamer formation to the minimum break-
down voltage versus pd for air and helium, calculated assuming streamers are formed when
the electron multiplication exceeds 108.
breakdown in air at high values of pd between parallel plate electrodes is
difficult and requires the careful control of operating conditions. It is rela-
tively easier to avoid streamer breakdown in helium. This simple comparison
of minimum breakdown and streamer formation voltages suggests an
explanation for the fact that APGDs in helium are so much easier to
obtain than those in air. Note also that preionization [2, 3] can impede
streamer formation and enhance discharge uniformity, and this may be
provided in DBDs by charges remaining from the previous half cycle.
Finally, it should be mentioned there is no guarantee that plasma
uniformity after breakdown can be maintained. Indeed there are numerical
examples where an initially uniform plasma eventually reaches a steady-
state where regular patterns appear (see section 5.5.3.4). Additional research
is also needed in this area.
5.5.3.4 Pattern formation
Observations of the formation of patterns of regularly spaced, quasi-
stationary filaments in DBDs have been summarized recently by Kogelschatz
[18]. In general, there is a transition from the random filament mode in DBDs
to a patterned discharge structure when the discharge voltage is decreased
[47]. Reasons for this behavior are not completely clear, but some indications
were obtained from a two-dimensional model [48] for a DBD in helium at
100 torr with a 0.5 mm gap spacing. It is interesting to note that thermal
effects, stepwise ionization or other well known causes of instabilities were
not included in these model calculations because they were not likely to be
--- Page 273 ---
258
M odeting
important under the simulated conditions. The model used periodic
boundary conditions in the transverse direction and assumed uniform initial
densities of the charged particles. A simple mathematical solution of the
problem was therefore a series of radially uniform transient glow discharges
at each half cycle of the applied voltage. However, the results showed that the
uniform solution was not stable and degenerated within several cycles of
the applied voltage into a non-uniform, filamentary solution very similar
to the observed patterned discharge structure. A conclusion of this work
was that if a local non-uniformity appears in the volume of the surface
charge density, breakdown occurs faster at the radial location where the
density is maximum. The charging of the surface occurs faster at this
radial location and spreading the charges induces a decrease in the gap
voltage around this location, resulting in the choking of the neighboring
plasma. This explanation of filament formation suggests that the slope of
the ionization coefficient as a function of the electric field is an important
parameter in this process. One can expect that the tendency to form a
filament will be smaller for conditions where the slope of the ionization
coefficient as a function of the electric field is smaller.
5.5.4 Micro-discharges: discharges in small geometries
A build-up of the internal excitation or kinetic energy of the gas corresponds
to an increase in the temperature of the gas and this can lead to instabilities
[42, 49). By 'instability' we mean that small perturbations or non-
uniformities in the plasma conductivity tend to grow catastrophically and,
if left unchecked, lead to a thermal plasma arc. Diffusion is a stabilizing
mechanism, damping small fluctuations in the plasma density at low
pressure. Since the diffusion rate decreases with gas pressure while rates
for mechanisms leading to instabilities tend to increase, maintaining a
stable non-thermal plasma is more difficult at high gas pressure. Concepts
for the generation of non-thermal atmospheric pressure plasmas have been
proposed recently which are based on the use of very small size geometries
such that the value of pd is about that of typical glow discharges (e.g. less
than about lOtorrcm-1) [50-53). Provided streamer conditions are avoided
at breakdown, a non-thermal plasma can be maintained in these 'micro-
discharge' configurations apparently because diffusion effectively dissipates
small fluctuations in the plasma density which could otherwise lead to
constrictions of the current carrying channel.
An open question at this time is the extent to which phenomena in high-
pressure microdischarges are the same as those in low pressure discharges
with the same value of pd. For example, it has been suggested that micro-
hollow cathode discharges are similar to those at low pressure [50, 52, 54]
with the same pd. That is, the structure in the measured V-I characteristic
is attributed to the classical hollow cathode effect, namely, the penetration
--- Page 274 ---
Electrical Models of DBDs and Glow Discharges
259
of the plasma into the hollow cathode cavity when the current density
exceeds a certain value. This interpretation of the structure in the V-I char-
acteristic is consistent with the calculations of Fiala et al [55] in similar
geometries but with a pressure of 1 torr. While this interpretation may
indeed be correct, more detailed analyses [56] including gas flow, thermal
effects and power loading in the gas are needed to develop a better under-
standing of the behavior of this and other [53] micro-hollow cathode
discharges.
Modeling work on discharges in very small geometries is under way.
Recent examples are the work of Wilson et al [57] who compare experiments
and model predictions in micro-hollow cathode discharges in nitrogen at
about 10 torr; Kushner [58] who discusses issues of scaling in very small
hollow cathode devices at 400-1000 torr; and Kothnur et al [59] examine
the structure of dc discharges in very small gaps using a fluid model. The
power density in the micro discharges can be quite high, and questions of
thermal balance and the glow-to-arc transition are important for under-
standing the behavior of single microdischarges or arrays of microdischarges.
More modeling and plasma diagnostics are needed to identify phenomena
specific to microdischarges, and this will undoubtedly be a developing area
in the coming years.
5.5.5 Conclusions
The purpose of our discussion here has been to provide an overview of electrical
models of plasma created in gas discharges and to illustrate their application to
DBDs and microdischarges. Over the past 20 years, modeling has proven to be
a very powerful and useful tool for helping to understand the basic physics and
for guiding the experimental optimization of different devices based on non-
thermal plasmas at low pressure. Modeling has also contributed greatly to
our current understanding of plasmas created in high pressure DBDs and
will certainly be used more in the future to help understand the generation of
non-thermal plasmas in micro-discharge configurations.
In all cases, models are most useful when used in combination with
experiments, and they are dependent on experiments for validation and for
determination of input data. Sophisticated diagnostic techniques are being
used to identify plasma parameters in DBDs and other micro-discharge
configurations. Examples of recent innovative applications of diagnostic
tools include the detailed measurements of the argon excited state densities,
plasma density and gas temperature in microdischarges [60] and detailed
imaging of single DBD filaments [61]. These and many other recent experi-
mental results give models valuable points for comparison with model
predictions. There is also a continuing need for more systematic results of
relatively simple electrical measurements and emission intensity measurements
for results over a wide range of conditions in DBDs and microdischarges.
--- Page 275 ---
260
M adeling
In conclusion, the following important issues can and should be
addressed through modeling .
• In the context of DBDs, modeling can help define conditions for the for-
mation of transient glow discharge filaments or for radially homogeneous
glow discharges. Modeling could also be used to help optimize the
excitation pulses for a given application. Volkommer and Hitzschke [24]
have shown that very high efficiencies for the generation of excimer radia-
tion can be obtained in DBDs in high pressure xenon with suitably tailored
voltage pulses and with values of pd such that streamer conditions are
avoided. Carman and Mildren [23] have addressed this problem through
modeling. Similar studies in DBDs in air have not been performed to our
knowledge. Through modeling it would also be possible to explore the
question of how the energy deposition in transient glow discharge filaments
in DBDs scales with operating conditions and how this scaling depends on
the breakdown mechanism.
• In the context of microdischarges, models could be used to help clarify the
physical mechanisms occurring in micro discharges operating at pressures
up to one atmosphere and to evaluate the role of physical processes
which are specific to high pressure/high power density conditions (e.g.
gas heating, stepwise ionization, etc.). This, in turn, could be used to
assess the validity or the range of validity of the usual similarity laws.
Finally, a better understanding of conditions leading to the glow-to-arc
transition due to hot spots on the electrodes or gas phase instabilities in
micro-discharge configurations is needed in order to evaluate the upper
limits on current density and plasma density possible in these devices.
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5.6 A Computational Model of Initial Breakdown in
Geometrically Complicated Ssystems
5.6.1 Introduction
In this section, a computational model for predicting the onset of breakdown
for electrodes in arbitrary geometric configurations is described. Although
the model described here is applied to a coplanar plasma display panel
configuration using a mixture of noble gases, the model can be extended to
many other configurations and gas chemistries in a straightforward manner.
Flat panel display technologies continue to increase in importance in the
consumer market as well as in the computer market. The active matrix liquid
crystal display (AM LCD) technology currently comprises the majority of fiat
panel displays at moderate sizes (6-19 inch (lS-48cm) diagonal measure-
ment). Despite recent increases in size and resolution, sizes required for
large screen applications such as high resolution computer monitors and
--- Page 278 ---
A Computational Model of Initial Breakdown
263
high definition television (HDTV) remain challenging for AMLCD tech-
nology. Viewing angle and update speed remain problematic for AMLCD,
although less severe than in the past. In addition, the brightness levels for
a transmissive screen such as an AMLCD panel are presently inadequate
for many applications and lighting conditions.
The emerging ac plasma display panel (PDP) technology provides a
number of advantages. In contrast to the stringent sub-micron feature sizes
of AMLCD panels, the PDP has super-micron features and can be manufac-
tured with relatively simple process technology. An important limit on
AM LCD size is the processing uniformity in manufacture, which drives
the price up rapidly at larger sizes due to lower yields. The PDP scales well
to large sizes (50 inches (127 cm) and up), and it is possible to build PDPs
larger than cathode ray tubes (CRT) can be practically manufactured.
PDPs are luminous devices, leading to higher brightness and contrast. The
viewing angle in the PDP is also similar to that of a conventional CRT,
and update speed is also comparable. Although the PDP is currently 3--4
times less efficient than the AMLCD, this is less important for HDTV and
computer applications. The efficiency and cost of PDPs is expected to
continue to decrease as production increases.
A typical three-electrode ac PDP is shown in figure 5.6.1. The panel
consists of a rear glass substrate, with trenches etched or barriers deposited
to separate neighboring pixels. The barriers are on the order of 10 /lm in
thickness, and the distance between barriers is on the order of 100 /lm.
Address electrodes are deposited in the bottom of the trenches, and covered
with a dielectric material of about 10/lm in thickness. The dielectric and
trench walls are then coated with phosphor, alternating red, green and
gO-~~~~~=;~~-r Yelectrode
Figure 5.6.1. Schematic coplanar ac plasma display panel.
--- Page 279 ---
264
Modeling
Figure 5.6.2. Schematic cross section of a coplanar PDP cell.
blue across rows. The top layer consists of a transparent glass substrate, with
pairs of electrodes deposited perpendicular to the direction of the address
electrodes. The upper electrodes, labeled X and Y in the figure, are the
sustain electrodes. The surface of the substrate, as well as the X and Y
electrodes, are then covered with a layer of dielectric on the order of 10 /lm
thick with dielectric constant typically about 10-15. The dielectric is
coated with a copious secondary emitter, such as magnesium oxide. The
region in the trenches is filled with a gas at a pressure of 300--700 torr,
often a mixture of neon, xenon, and possibly other inert gases including
helium and argon.
Cells are formed by the intersection of X-Y electrode pairs with address
electrodes. The cross section of a cell is shown in figure 5.6.2. In the figure, the
X and Y electrodes are perpendicular to the plane of the paper, while the
address electrode extends to the left and right. Discharges are generated by
various combinations of voltage applied to the X, Y, and A electrodes, as
well as voltage due to charge accumulated at the surface of the dielectric
from previous discharges.
The anatomy of a single discharge event is similar to that of a dc
discharge, except that the walls charge up and eventually extinguish the
discharge when the applied voltage is completely shielded by the wall
charge. Ions are attracted to the positively charged cathode, accelerating
through a non-neutral cathode fall region. Upon impact with the MgO-
coated dielectric material enclosing the cathode, the ions generate secondary
electrons. The secondary electrons accelerate through the cathode fall,
undergoing many collision events with the background gas. Elastic
scattering, electron impact ionization, and electron-neutral excitation, as
well as many other collisional events play an important role in shaping the
discharge. As the discharge current increases, charge builds up on the
dielectric surfaces, decreasing the gap voltage in the cell. When the cathode
fall no longer imparts sufficient energy to secondary electrons to generate
ionization events, the plasma behaves like a decaying glow discharge and
slowly extinguishes.
--- Page 280 ---
A Computational Model of Initial Breakdown
265
A priming pulse is applied to all cells in the PDP to initialize all cells with
a specified charge on the dielectric surface. The priming pulse typically
consists of a few hundred volts applied to the X and Y electrodes, and
often a supplemental voltage on the order of 100 V to the address electrode.
After all cells are primed, a refresh pulse continuously sweeps all cells. The
refresh pulse is applied to an entire row of cells which share the same X
and Y electrodes. The refresh pulse consists of a voltage difference applied
between the X and Y electrodes which is insufficient for breakdown. In
cells which discharged in the previous cycle, charge deposited on the walls
augments the applied voltage such that it is sufficient for breakdown. This
behavior, referred to as the 'memory effect', is a principal advantage of the
PDP since it obviates the need to address every cell during each refresh
cycle, leading to lower cost driving circuitry. In the PDP, only cells which
must undergo a change in state are addressed. The state of a cell is changed
by augmenting the X-Y voltage of the refresh pulse with a voltage on the
address electrode. For cells which were previously off, a write pulse is applied
which results in initiation of breakdown. For cells which were previously on,
an erase pulse drains the excess charge and returns the cell to it post-priming
pulse state.
In this work, the initiation of breakdown in a surface discharge type
PDP cell is examined. The breakdown may correspond to the priming
pulse, a refresh pulse in an activated cell, or a write pulse, depending on
the applied voltages and the wall charge configuration. Specifically, we
seek a spatial map of discharge current amplification, which indicates the
strength of the local breakdown process. This is analogous to constructing
a spatial map of the Paschen curve.
In section 5.6.2, the model for initial breakdown is described, including
the algorithm for the analysis of the initial breakdown. In section 5.6.3,
breakdown for specific configurations is described. In section 5.6.3.1, the
case of equally spaced electrodes and neighbor cells is discussed. In section
5.6.3.2, a case with large separation from neighbor cells is discussed. Finally,
conclusions are presented in section 5.6.4.
5.6.2 The numerical model
Consider the two-dimensional model shown in figure 5.6.2. Assume the gap,
d, is filled with a gas comprising neon and xenon at a pressure p. The spacing
between the sustain electrodes is gd' The dielectric thickness between the
sustain electrode and gap is given by d1, and the thickness of the dielectric
between the address electrode and the plasma gap is given by d2. The
width of the sustain electrodes is w, and the distance from the Y electrode
to the cell edge is gn/2. The cell is periodic in the length, L.
The PDP cell configuration is modeled using a modified version of the
XOOPIC particle-in-cell (PIC) code [1]. XOOPIC is a two-dimensional
--- Page 281 ---
266
Modeling
1010 ~-------------.---------------r--------------'
energy (eV)
Figure 5.6.3. Normalized collision frequency for electron-neon collisions.
PIC code which includes both electrostatic and electromagnetic models in
both axisymmetric and Cartesian coordinates. XOOPIC also includes a
Monte Carlo collision model which can handle non-interacting gas mixtures,
including elastic, excitation, ionization, and charge exchange collisions. For
the work here, XOOPIC is operated in electrostatic mode in Cartesian
coordinates.
The code includes a Monte Carlo collision (MCC) model including
electron-neutral elastic scattering, electron-neutral excitation, and elec-
tron-neutral impact ionization [2]. The electron-neon momentum transfer
cross section at low energies is from [3], and at high energies from [4]. The
electron-xenon momentum transfer cross section at low energies was taken
from [5], and at high energies from [6]. The electron-neon and electron-
xenon excitation cross sections are taken from [7], except the grouped neon
metastable level e
P2 and 3 Po) is taken from [8]. The electron-neon ionization
cross sections are from [9] at low energy and [10] at high energy. The
electron-xenon ionization cross sections are from [11]. Only direct ionization
of the ground state is modeled here. The normalized electron-neutral
collision frequencies in neon are shown in figure 5.6.3, and those for xenon
are shown in figure 5.6.4.
The usual PIC-MCC scheme was modified to perform the calculation
here, as illustrated in figure 5.6.5. First, Laplace's equation was solved for
the vacuum configuration with specified electrode potentials to obtain
--- Page 282 ---
A Computational Model of Initial Breakdown
267
10" r-------,--------,-------,
.......
.....
.
"t:'" 1 0 10
••••••••••••
• ••
o
r---~~-~~~~~---.~
... ~
.. ~~~---~
-.... -............... ..
I::
..... " ............ .
• .,.,. .. 1It ...... _
~
.t
~
.•..•.. ~
..!!!.
• • •• elastic
_ ........ - • - •
.e-1009
-
exc1
.. '
............ .
::':::.:.:.:~ .. -.... .
-.. -..... ::.: .
>
-exc2
_._. exc3
_ .. - .. exc4
•
•••••••• ionization ! : i
-total
':
10
100
1000
energy (eV)
Figure 5.6.4. Normalized collision frequency for electron-xenon collisions.
<I>(x,y). The resulting electric field, E(x,y) = -V'<I>(x,y), was held fixed.
Next, secondary electrons were released from a single point Xo along the
dielectric surface below the positively biased y electrode. The initial release
point was scanned across the surface bounded by the midpoint between
positively and negatively biased electrodes, Xl ~ Xo ~ x2, as shown in
x,
Xo
r------~---c--------~---x
y
emit secondaries
•
Figure 5.6.5. Schematic of a single coplanar PDP cell used for the initial breakdown
calculation.
--- Page 283 ---
268
Modeling
figure 5.6.5. The orbits were integrated for the released secondary electrons,
also applying the MCC model. However, the space charge of the electron
population was neglected during the calculation, since the density is low
during the onset of the discharge. The integration of the equations of
motion and MCC operation are performed until all the resulting particles
have been collected at the surface to obtain the transfer function fi(xo, x).
No further secondary electrons are generated, although electrons and ions
generated in ionization events are included in the calculation.
The ion distribution of species, fi, collected at x due to the initial
generation of secondary electron emission from Xo is
fJi,O(XO, x) = fi(xo, x).
(1)
We can write an approximate condition for breakdown when
(2)
where "ti is the secondary emission coefficient for impact of ion species, i, with
the wall.
When equation (2) is satisfied, each secondary electron emitted at Xo
generates sufficient return ion flux at Xo to emit more than one secondary
in the next generation, leading to net growth of the discharge current at
the point Xo. While satisfying equation (2) is sufficient to initiate breakdown,
it is not necessary; a more complete breakdown condition should include
not just the next generation, but all future generations in the secondary
electron-ionization-ion wall flux cycle.
For a secondary coefficient, "ti' the flux of the next generation of
secondaries at x due to an initial emission at Xo is
f\(xo,x) = L"tifJi,O(XO,x).
i
(3)
These electrons then accelerate through the cathode fall, generating
additional ionization events. The ions return to the dielectric surface, coating
the cathode, with a distribution corresponding to the point of emission. This
leads to the collection of the next generation of ions at the dielectric due to
emission from the initial point Xo returning back to the point x:
(4)
Similarly, the flux of the second generation of secondaries at x due to the
initial emission from Xo is given by
(5)
--- Page 284 ---
A Computational Model of Initial Breakdown
269
We can now generalize the nth generation of secondary electrons emitted at x
due to the initial emission from Xo:
fn(xo, x) = L 'Yif3i,n-l(XO,X).
(6)
Similarly, the nth generation of ions collected per secondary electron emitted
from Xo can be written
f3i,n(XO, x) = J
X
2 (L 'Yif3i,n-l (xo, X'))fi(X', x) dx'.
(7)
Xl
1
Breakdown occurs due to emission at Xo when successive generations of
secondary flux at Xo are increasing:
(8)
5.6.3 Simulation results
The initial breakdown model was first applied to coplanar ac plasma display
panel cells [12, 13]. Here we consider the initial breakdown in coplanar ac
plasma display panel cells with a narrow neighbor gap and a wide neighbor
gap. The geometric configuration of interest is the three-electrode cell, shown
schematically in figure 5.6.2. The addressing electrode is labeled A, while the
other electrodes are labeled x and y, respectively. The dimensions of the cell
are length L = 440 j.1m and height d = 110 j.1m. The dielectric coating on the
address electrode was taken to be d2 = 25 j.1m, with Cr = 7.9. The x and y
electrodes are embedded a distance d1 = 25 j.1m into a dielectric with
Cr = 11. The x and y electrodes are separated by a distance gd = 80 j.1m.
A Neumann boundary condition is used at the top edge of the cell, so at
the plane, y = D, the normal component of the electric field, Ey = O. The left
and right edges of the cell, x = 0 and x = L, are periodic. Between the top
boundary and the x and y electrodes is 25 j.1m of dielectric. The secondary
emission coefficients were taken to be 'YNe = 0.5 and 'YXe = 0.05.
The boundary condition at the bottom of the cell, y = 0 j.1m, is fixed by
the address electrode voltage. The neighbor gap, gn, was varied along with an
opposite variation in the electrode width w such that the cell size, L, remains
a constant. For the symmetric case, W/gd = 4.4 andgn/gd = 1, which leads to
equal spacing among all cells as shown in figure 5.6.6. For the asymmetric
Figure 5.6.6. Schematic of symmetric spacing of X and Y electrodes.
--- Page 285 ---
270
Modeling
Figure 5.6.7. Schematic of asymmetric spacing of X and Y electrodes.
case, W/gd = 2.9 and gn/gd = 4, which leads to the spacing shown schemati-
cally in figure 5.6.7. Arbitrary electrode widths and neighbor gap separations
can be studied using this technique. In both cases, the electrode voltages were
Vx = 160V, Vy = -160V, and VA = -80V.
First, the fields are solved for the initial (vacuum) condition to obtain
<I>(x,y); in this case the fields are fixed throughout the run. This assumption
is valid during the initial stages of breakdown, when the space charge is small.
The Monte Carlo simulation is run, with the initial condition of 104
secondary electrons emitted from the location Xo at cathode. These electrons
are advanced in the fixed (vacuum) fields, undergoing collisions using the
Monte Carlo algorithm. The electrons and ions created in ionizing collisions
are also followed. When ions are absorbed at the cathode, they do not emit
secondary electrons. Instead, the spatial distribution of the ion fluxes,
fi(xo, x), are collected along the dielectric surface beneath the cathode.
This process is repeated for initial emission points Xl ::::; Xo ::::; X2. Hence,
a map of the ion flux at the wall due to secondary electron emission from each
point along the surface is generated.
f(x,xO) Neon
100000
xo (arb. units)
x (arb. units)
135
100
Figure 5.6.8. Neon ion flux distribution on the surface for the symmetric case.
--- Page 286 ---
A Computational Model of Initial Breakdown
271
f(x,xO) Xenon
100000
xo (arb. units)
x (arb. units)
135
100
Figure 5.6.9. Xenon ion flux distribution on the surface for the symmetric case.
5.6.3.1
The case of symmetric gaps
The results of the Monte Carlo calculation for fi(xo, x) for the symmetric
case are shown in figures 5.6.8 and 5.6.9 for neon and xenon respectively.
The plots can be understood by considering slices for a constant xo, which
indicate the returning ion distribution for emission from Xo. The ratio of
(3\/(30 is shown for the symmetric case in figure 5.6.10. Note that, for the
specified conditions, the breakdown is initiated symmetrically at the edges
between the neighboring electrodes.
5.6.3.2
The case of asymmetric gaps
The results of the Monte Carlo calculation for fi(xo, x) for the asym-
metric case are shown in figures 5.6.11 and 5.6.12 for neon and xenon
respectively. As before, the plots can be understood by considering slices
for a constant xo, which indicate the returning ion distribution for emission
from Xo.
The ratio of (3\/(30 is shown for the asymmetric case in figure 5.6.13.
Note that, for the specified conditions, the breakdown is initiated between
the X and Y electrodes only, since the gaps between neighboring cells
effectively eliminate inter-cell breakdown.
--- Page 287 ---
272
0
~
....
c:r
Modeling
•
•
,
I
I
3
- - - ,- -,-.- - -
- - - -.- - - - - -
2 ------
1 -
o
100
-----~-
110
I
., .
, ., .,
,
--- -- - -,- - - - - -
,
-----~------,------
....
. ..
120
130
140
150
Xo (arbitrary units)
-neon
---- total
........ xenon
-T------
160
170
Figure 5.6.10. /3 ratio for the symmetric case. /3,//30 > 1 indicates that breakdown can be
initiated from the position Xo. The electrode is shown schematically to scale above the
figure.
10000
1000
100
, ,
I ....... .,.
,
145 140 135
130
125
xo (arb. units)
f(xO,x) Neon
0000
,
... - ,
,- .... I~ -
x (arb. units)
105
100
Figure 5.6.11. Neon ion flux distribution on the surface for the asymmetric case.
--- Page 288 ---
A Computational Model of Initial Breakdown
273
100000
10000
1000
100
.
__ 1
. . --
... ... i
xo (arb. units)
f(xO,x) Xenon
-,- ...
-.... .
105
100
100000
... .. .. ;-
,
... ... , .....
,
0000
,
,- ......
x (arb. units)
Figure 5.6.12. Xenon ion flux distribution on the surface for the asymmetric case.
CI
=. ...
cr
--neon
- - - - total
···· .. ··xenon
10
I
I
I
I
5
--------------------------------
o
100
110
,
,
120
130
140
xO (arbitrary units)
,
-------
.
150
160
170
Figure 5.6.13. (3 ratio for the asymmetric case.(31 / (30 > I indicates that breakdown can be
initiated from the position Xo. The electrode is shown schematically to scale above the
figure.
--- Page 289 ---
274
Modeling
5.6.4 Discussion
The results of this study indicate that the numerical modeling method
described above provides a rapid means of determining the location of
breakdown. The results indicate that breakdown is only possible over a
limited region of the electrodes, and is initiated most strongly near the
edges of the electrodes in the vicinity of strong field gradients.
Charging of the dielectrics during the discharge will cause expansion of
the discharge along the surface of the dielectric, but only within the region in
which the amplification factor exceeds the inverse of the secondary co-
efficient. Note that this result may be modified when sufficient space
charge and/or wall charge exists to alter <I> (x, y).
It is proposed to use this technique to measure Paschen-like curves for
particular electrode configurations, as well as to measure the regions eligible
for breakdown for a given configuration. These data can be used to optimize
gap spacing and voltage, including analysis of neighbor discharge. In
addition, the technique can be readily expanded to measure the breakdown
conditions for a cell with charge existing on the dielectric surface, as well
as fixed charge density in the cell volume.
The initial breakdown method described here can be extended to arbi-
trary geometric constructions as well as arbitrary gas chemistries. Extending
the initial breakdown model to an air plasma, for example, would require
adding a model for the air-plasma reactions which contribute to significant
electron and ion energy loss as well as ionization paths. Inclusion of the
full set of reactions is in principle possible, although the computation can
become significant compared to the present calculation which can be done
in less than an hour on a commodity computer.
5.6.5 Acknowledgments
This work supported in part by Hitachi Ltd. The author gratefully acknowl-
edges the advice and support of C K Birdsall, Y Ikeda, and P J Christenson.
References
[I] Verboncoeur J P, Langdon A B and Gladd N T 1995 'An object-oriented
electromagnetic PIC code' Computer Phys. Commun. 87 199
[2] Vahedi V and Surendra M 1995 'Monte Carlo collision model for particle-in-cell
method: Application to argon and oxygen discharges', Computer Phys. Commun.
87179
[3] Robertson A G 1972 J. Phys. B 5648
[4] Shimamura I 1989 Scientific Papers [nst. Phys. Chem. Res. 82
[5] Hunter S R, Carter J G and Christophorou L G 1988 Phys. Rev. A 38 5539
[6] Hayashi M 1983 J. Phys. D 16581
--- Page 290 ---
References
275
[7] Peuch V and Mizzi S 1991 J. Phys. D 24 1974
[8] Mason N J and Newell W R 1987 J. Phys. B 201357
[9] Wetzel R C, Baiocchi F A, Hayes T R and Freund R S 1987 Phys. Rev. A 35 559
[10] de Heer F J, Jansen R H J and van der Kaay W 1979 J. Phys. B 12 979
[11] Rapp D and Englander-Golden P 1965 J. Chern. Phys. 43 1464
[12] Verboncoeur J P, Christenson P J and Cartwright K L 1997 'Breakdown in a 3-
electrode ac plasma display panel'. Proc. 50th Annual Gaseous Electronics Con!
421739
[13] Verboncoeur J P 1998 'Initiation of breakdown in a 3-electrode plasma display panel
cell', 25th IEEE ICOPS, Raleigh, NC
--- Page 291 ---
Chapter 6
DC and Low Frequency Air Plasma
Sources
U Kogelschatz, Yu S Akishev, K H Becker, E E Kunhardt,
M Kogoma, S Kuo, M Laroussi, A P Napartovich, S Okazaki
and K H Schoenbach
6.1
Introduction
This chapter treats some more recent developments in the generation of non-
equilibrium plasmas. Section 6.2 (Kogelschatz), 6.3 (Kogoma, Okazaki) and
6.4 (Laroussi) are devoted to different aspects of barrier discharges. In
addition to the traditional dielectric barrier discharges with a seemingly
random distribution of microdischarges, regularly patterned and homo-
geneous dielectric barrier discharges are also addressed, as well as resistive
barrier discharges. The various novel applications in surface treatment, in
flat plasma display panels, ozone generation, excimer lamps and high
power CO2 lasers have attracted much interest and have led to a worldwide
increase in research activities in all kinds of barrier discharges.
Similar plasma conditions can also be obtained in microhollow cathode
discharges (MHCDs) and in a variety of discharges spatially confined in
small geometries (section 6.5 (Schoenbach, Becker, Kunhardt)). Of special
interest is the capillary plasma electrode discharge (CPED) which uses a
perforated dielectric with a large number of equally spaced holes.
Section 6.6 (Akishev, Napartovich) covers recent progress in the
generation, modeling and understanding of steady state corona glow
discharges. Section 6.7 (Kuo) describes a novel ac torch for the generation
of non-equilibrium plasmas.
Many of the discharge types described in this chapter can be used to
treat large surfaces or to generate large-volume atmospheric-pressure non-
equilibrium plasmas (Kunhardt 2000). Also combinations of different
discharge types like the barrier-torch discharge plasma source have been
276
--- Page 292 ---
Barrier Discharges
277
proposed (Hubicka et aI2002). Current research focuses on dielectric barrier
properties (surface structure, electron emission, surface and bulk conduc-
tivity) and on micro-structured electrodes, semiconductors or dielectrics to
obtain arrays of miniature non-equilibrium plasmas (Miclea et al 2001,
Park et aI2001).
References
Hubicka M, Cada, M. Sicha M, Churpita A, Pokorny P, Soukop Land Jastrabik L 2002
Plasma Sources Sci. Technol. 11195
Kunhardt E E 2000 IEEE Trans. Plasma Sci. 28 189
Mic1ea M, Kunze K, Musa G, Franzke J and Niemax K 2001 Spectrochim. Acta B 56 37
Park S-J, Chen J, Liu C and Eden J G 2001 Appl. Phys. Lett. 78419
6.2 Barrier Discharges
Based on experience with ozone research, the major application for many
decades, it was believed for a long time that dielectric-barrier discharges
always exhibit many discharge filaments or microdischarges. This multi-
filament discharge with a seemingly random distribution of micro discharges
is prevailing in atmospheric-pressure air or oxygen (Samoilovich et a11989,
1997, Eliasson and Kogelschatz 1991, Kogelschatz et al 1997, Kogelschatz
2003). Work performed in many different gases under various operating
conditions revealed that regularly patterned or diffuse barrier discharges
can also exist at atmospheric pressure. The formation of regular discharge
patterns, was observed for example by Boyers and Tiller (1982), Breazeal
et al (1995), Guikema et al (2000), Klein et al (2001), and Dong et al
(2003). The physical mechanism of pattern formation has been investigated
in a series of papers of the Purwins group at Munster University (Radehaus
et a11990, Ammelt et a11993, Brauer et a11999, MUller et aI1999a,b). In 1968
Bartnikas reported that ac discharges in helium can also manifest pulse-less
'glow' and 'pseudo-glow' regimes, apparently homogeneous diffuse volume
discharges, now often referred to as atmospheric pressure glow discharges
(APG/APGD). A few years later this work was extended to discharges in
nitrogen and air at atmospheric pressure (Bartnikas 1971). Early work on
polymer deposition in pulsed homogeneous barrier discharges in an ethy-
lene/helium mixture was reported by Donohoe and Wydeven (1979). Starting
in 1987 the group of S. Okazaki and M. Kogoma at Sophia University in
Tokyo (see section 6.3) reported on intensive investigations in homogeneous
dielectric-barrier discharges and their applications and proposed the term
--- Page 293 ---
278
DC and Low Frequency Air Plasma Sources
APG, short for atmospheric pressure glow discharge. The interesting
physical processes in these discharges and their large potential for industrial
applications have initiated experimental as well as theoretical studies in many
additional groups in France (Mas sines et al 1992, 1998), in the US (see
section 6.4), Canada (Nikonov et a1200l, Radu et aI2003a,b), in Germany
(Salge 1995, Kozlov et al 2001, Tepper et al 2002, Wagner et al 2003,
Brandenburg et al 2003, Foest et al 2003), in Russia (Akishev et al 2001,
Golubovskii et al 2002, 2003a,b), and in the Czech Republic (Trunec et al
1998, 2001), to name only the most important ones. Much of the work on
the physics of filamentary, regularly patterned and diffuse barrier discharges
was recently reviewed by Kogelschatz (2002).
6.2.1
Multifilament barrier discharges
The traditional appearance of the barrier discharge used for ozone
generation in dry air or oxygen (see section 9.3) or for surface modification
of polymer foils in atmospheric air is characterized by the presence of a
large number of current filaments or microdischarges (see also section 2.6).
Figure 6.2.1 shows a photograph of micro discharges in atmospheric-pressure
dry air taken through a transparent electrode.
Figure 6.2.1. End-on view of microdischarges in a 1 mm gap with atmospheric-pressure
dry air (original size: 6cm x 6cm, exposure time: 20ms).
--- Page 294 ---
Barrier Discharges
279
During the past decades important additional information was collected
on the nature of these filaments. Early image converter recordings of micro-
discharges in air and oxygen were obtained by Tanaka et al (1978). Precise
current measurements were performed on individual microdischarges
(Hirth 1981, Eliasson et a11987, Braun et aI199l). The transported charge
and its dependence on dielectric properties was determined over a wide
parameter range (Dfimal et al 1987, 1988, Gibalov et al 1991). Typically,
many microdischarges are observed per square cm of electrode area. Their
number density depends on the power dissipated in the discharge. For a
moderate power density of 83 m W /cm2 about 106 microdischarges were
counted per cm2 per second (Coogan and Sappey 1996). The influence of
humidity and that of ultraviolet radiation was investigated (Falkenstein
1997). In recent years spectroscopic diagnostics were refined to such a
degree that measurements of species concentrations and plasma parameters
inside individual microdischarges became feasible (Wendt and Lange 1998,
Kozlov et al 2001, Lukas et al 2001). For a given configuration and fixed
operating parameters all microdischarges are of similar nature. They are
initiated at a well defined breakdown voltage, and they are terminated
after a well defined current flow or charge transfer.
From all these investigations we conclude that each microdischarge
consists of a nearly cylindrical filament of high current density and approxi-
mately lOOl1m radius. At the dielectric surface(s) it spreads into a much
wider surface discharge. These are the bright spots shown in figure 6.2.1.
The duration of a microdischarge is limited to a few ns, because immediately
after ignition local charge build up at the dielectric reduces the electric field at
that location to such an extent that the current is choked. Each filament can be
considered a self-arresting discharge. It is terminated at an early stage of
discharge development, long before thermal effects become important and a
spark can form. The properties of the dielectric, together with the gas proper-
ties, limit the amount of charge or energy that goes into an individual micro-
discharge. Typical charges transported by individual microdischarges in a
1 mm gap are of the order 100 pC, typical energies are of the order 111J. The
plasma filament can be characterized as a transient glow discharge with an
extremely thin cathode fall region with high electric field and a positive
column of quasi-neutral plasma. The degree of ionization in the column is
low, typically about 10-4 . As a consequence of the minute energy dissipation
in a single microdischarge the local transient heating effect of the short current
pulse is low, in air typically less than 10 °C in narrow discharge gaps. The
average gas temperature in the discharge gap is determined by the accumulated
action of many microdischarges, i.e. the dissipated power, and the heat flow to
the wall(s) and from there to the cooling circuit. This way the gas temperature
can remain low, even close to room temperature, while the electron energy in
the microdischarges is a few eY. Major microdischarge properties of a DBD in
a 1 mm air gap are summarized in table 6.2.1.
--- Page 295 ---
280
DC and Low Frequency Air Plasma Sources
Table 6.2.1. Characteristic micro-discharge properties in a I mm gap in atmospheric-
pressure air.
Duration
Filament radius
Peak current
Current density
I-IOns
about 0.1 mm
0.1 A
100--1000 A cm-2
Total charge
Electron density
Electron energy
Gas temperature
0.1-1 nC
1014_10 15 cm-3
1-lOeV
Close to average gap
temperature
In addition to limiting the amount of charge and energy that goes into
an individual microdischarge, the dielectric barrier serves another important
function in DBDs. It distributes the microdischarges over the entire electrode
area. As a consequence of deposited surface charges the field has collapsed at
locations where microdischarges already occurred. As long as the external
voltage is rising, additional micro discharges will therefore preferentially
ignite in other areas where the field is high. If the peak voltage is high
enough, eventually the complete dielectric surface will be evenly covered
with footprints of microdischarges (surface charges). This is the ideal situa-
tion which leads to the almost perfect voltage charge parallelogram shown
in figure 2.6.4. The deposited charges constitute an important memory
effect that is an essential feature of all dielectric barrier discharges.
As far as applications are concerned each individual microdischarge can
be regarded as a miniature non-equilibrium plasma chemical reactor. Recent
research activities have focused on tailoring micro discharge characteristics
for a given application by making use of special gas properties, by adjusting
pressure and temperature, and by optimizing the electrode geometry as well
as the properties of the dielectric(s). Such investigations can be carried out in
small laboratory experiments equipped with advanced diagnostics. One of
the major advantages ofBDBs is that, contrary to most other gas discharges,
scaling up presents no major problems. Increasing the electrode area or
increasing the power density just means that more microdischarges are
initiated per unit of time and per unit of electrode area. In principle, indivi-
dual micro discharge properties are not altered during up-scaling. Efficient
and reliable power supplies are available ranging from a few hundred
watts in a plasma display panel, close to 100kW in an apparatus for high
speed surface modification of polymer foils to some MW in large ozone
generators.
6.2.2 Modeling of barrier discharges
Numerical modelling efforts have been devoted to describing the physical
processes and chemical reactions in a single filament, in adjacent filaments,
in a temporal sequence of many filaments and, more recently, in diffuse
dielectric-barrier discharges. The problem of modeling the initial phases of
--- Page 296 ---
Barrier Discharges
281
a single microdischarge has many similarities with that of treating break-
down. Depending on the external voltage, the gap width and the pressure,
breakdown can be accomplished either by the Townsend mechanism of
successive electron avalanches or by a much faster streamer breakdown
(see section 2.4). As soon as a conductive channel is formed and the current
in the microdischarge increases, the presence of the dielectric gains a strong
influence on further discharge development and on the termination of the
current flow. This necessitated the incorporation of additional boundary
conditions to adequately treat charge accumulation and distribution on the
dielectric surface(s). Early attempts were reported by Gibalov et al (1981).
With the development of refined numerical algorithms and the availability
of faster computers full two-dimensional treatment of a single micro-
discharges became possible (Egli and Eliasson 1989, Braun et al 1991,
1992, Li and Dhali 1997, Steinle et al 1999, Gibalov and Pietsch 2000). In
most cases the continuity equations for the major involved species are
solved simultaneously with Poisson's equation to determine the electric
field due to space charge (see also section 5.3). Secondary effects on the
cathode are normally included, in some cases also photo-ionization.
Nikonov et al (2001) suggested that in gaps wider than 0.02 cm the photo-
ionization contribution to the electron density becomes more significant in
comparison to the cathode photoemission. In many cases the role of
photo-ionization in numerical simulations is approximated by assuming
an equivalent density of seed electrons, about 107 to 108 cm -3, in the
background gas (Dhali and Williams 1987). Microdischarge simulations
could reproduce measured results about diameter, temporal current
variation and transferred charge. They also helped considerably improving
our understanding of the physical processes involved.
Steinle et al (1999) used a two-dimensional model to predict micro-
discharge development in a 0.35 mm wide gap bounded by a metal cathode
and a dielectric covered anode in atmospheric pressure air. Their current
pulse, reproduced in figure 6.2.2, clearly shows the different phases of the
discharge. At 0.54ns we already have a space charge dominated avalanche
phase followed by a streamer phase. The peak current of the micro discharge
is preceded by the formation of a cathode fall region, a process that takes
only a fraction of a nanosecond. After reaching the peak, within 0.3 ns, the
current is already reduced to half of its maximum value. This clearly
shows the strong current-choking action of the field reduction caused by
charges deposited on the dielectric surface. The development and the
radial extension of the cathode fall region was simulated in detail also
by Gibalov and Pietsch (2000). Its thickness is less than 20!lm and the
maximum field strength, according to this model, reaches over 4000 Td
(l Td = 10-21 V m2). Figure 6.2.3 shows the extension of the axial field
strength close to the cathode in air at atmospheric pressure. Cathode
fall voltage, thickness and current density roughly correspond to values
--- Page 297 ---
282
DC and Low Frequency Air Plasma Sources
S6
o
CIIlhocle n.1I
""A
I-
rMublbbcd
\
\
\
/
\
calhode~r
\
\ I
\.
• Ill'lll dIIII'!'8 \/
I\"~
1 .
.. 1 ..
.
o
0.5
1
I.S
Time(ns)
\
I~
1
2.S
Figure 6.2.2. Computed current pulse for a 0.35 mm gap in atmospheric pressure air
(Steinle et aI1999).
extrapolated from low-pressure discharges using the similarity laws of the
normal glow discharge described in section 2.4. This high current phase of
a microdischarge can be regarded as a quasi-stationary high-pressure glow
discharge. Such conditions are ideal to induce chemical changes, for example
ozone formation or air pollution control. It has also been attempted to model
the interaction of adjacent microdischarges (Xu and Kushner 1998).
In many papers the equations treating microdischarge dynamics have
been coupled with extensive chemical codes to follow chemical changes.
5000
;;-
4000
,.... ,
'-'
"0
3000
..
iZ
.S!
tl
Q.)
Ui
1000
Cathode
Figure 6.2.3. Numerical simulation of the cathode layer of a microdischarge in a I mm
atmospheric-pressure air gap (Gibalov and Pietsch 2000).
--- Page 298 ---
Barrier Discharges
283
Since chemical reactions may require longer time to approach equilibrium
than the typical duration of a microdischarge, this normally requires the
simulation of a large number of microdischarges with a given repetition
rate (Eliasson et at 1991, 1993, 1994, Gentile and Kushner 1996, Dorai
and Kushner 2001). With these tools it became feasible to correlate discharge
parameters and volume flow rate to the speed of chemical changes in the gas
flow. Recently it has also been attempted to compute the influence of small
additives (Niessen et at 1998, Dorai and Kushner 2000), of solid particles
(Dorai et al 2000) and of chemical changes on polymer surfaces (Dorai
and Kushner 2003).
With the important and somewhat unexpected experimental advances in
the control of diffuse barrier discharges (sections 6.3 and 6.4) one-dimensional
numerical modelling of these discharges became an important issue (Massines
et al 1998, Tochikubo et al 1999, Golubovskii et al 2002, 2003a). Concen-
trating mainly on He and N2 it was soon established that discharge modes
resembling a Townsend discharge as well as a glow discharge can be obtained.
The Townsend mode is characterized by extremely low current density,
negligible influence of space charge and the absence of a quasi-neutral
plasma. Typically the ion density is orders of magnitude higher than the
electron density, which shows exponential growth from cathode to anode.
The glow mode, on the other hand, reaches higher current densities (of the
order mA/cm2). It is influenced by space charge effects leading to a high
field region at the cathode, a Faraday dark space with vanishing field and a
column of quasi-neutral plasma at current maximum.
These one-dimensional fluid models for atmospheric-pressure discharges
bounded by dielectric barriers could produce some of the experimental results,
e.g. that the glow-like mode can preferentially be obtained if the gap is suffi-
ciently wide and the barrier is thin or of high dielectric constant. Also the
experimental findings of obtaining one current pulse or multiple current
pulses per half wave of the feeding voltage can be reproduced by relatively
simple models (Akishev et al 2001, Golubovskii et al 2003a). To exactly
reproduce details of measured current pulses it was necessary to introduce
additional processes. For example it was found that computations using
the ionization coefficient of pure He were not able to reproduce the
experimental results. Some low level impurities like Ar (Massines et al
1998) or N2 (Golubovskii et al 2003a) had to be introduced to get a better
match. Molecular ions Hei, Het, Nt had to be considered to get faster
recombination. It was also established that there must be a mechanism
releasing electrons from the dielectric surface stored in the previous voltage
half wave. Models assuming a constant electron desorption rate (Golu-
bovskii et al 2003a) or introducing a large "( cOl!fficient ("( = 0.5) for
secondary electron emission by impinging metastables (Khamphan et al
2003) achieved better agreement with experimental results. It is apparent
that knowledge is still lacking about the fundamental physical processes at
--- Page 299 ---
284
DC and Low Frequency Air Plasma Sources
dielectric surfaces, namely emission, desorption and recombination of
charged particles. Going to two-dimensional models it could be shown
that the Townsend discharge in DBDs is immune to filamentation while
the glow discharge is inherently unstable (Golubosvkii et al 2003b). The
situation is comparable to that investigated by Kudryavtsev and Tsendin
(2002) between metal electrodes. They could show that a glow discharge
operated to the right of the Paschen minimum is inherently unstable. It
should be pointed out that the current densities so far reached in diffuse
discharges between dielectric barriers are still much lower than those
expected for a normal glow discharge at atmospheric pressure (roughly
2 A/cm2 in He and 200 A/cm2 in N2). To reach those values much thinner
dielectrics with higher dielectric constants and/or higher voltage rise times
dU /dt are required. With fast pulsing techniques this should be possible.
References
Akishev Yu S, Dem'yanov A V, Karal'nik V B, Pan'kin M V and Trushkin N I 2001
Plasma Phys. Rep. 27 164
Ammelt E, Schweng D and Purwins H-G 1993 Phys. Lett. A 179348
Bartnikas R 1968 Brit. J. Appl. Phys. (J. Phys. D) Ser. 2 1 659
Bartnikas R 1969 J. Appl. Phys. 40 1974
Bartnikas R 1971 IEEE Trans. Electr. Insul. 6 63
Boyers D G and Tiller W A 1982 Appl. Phys. Lett. 41 28
Brandenburg R, Kozlov K V, Morozov A M, Wagner H-E and Michel P 2003 Proc. 26th
Int. Conf. on Phenomena in Ionized Gases (XXVI ICPIG) (Greifswald, Germany)
http://www.icpig.uni-greifswald.de/
Brauer I, Punset C, Purwins H-G and Boeuf J P 1999 J. Appl. Phys. 85 7569
Braun D, Gibalov V and Pietsch G 1992 Plasma Sources Sci. Technol. 1 166
Braun D, Kuchler U and Pietsch G 1991 J. Phys. D: Appl. Phys. 24 564
Breazeal W, Flynn K M and Gwinn E G 1995 Phys. Rev. E 52 1503
Coogan J J and Sappey A D 1996 IEEE Trans. Plasma Sci. 2491
Dhali S K and Williams P F 1987 J. Appl. Phys. 624696
Dong L, Yin Z, Li X and Wang L 2003 Plasma Sources Sci. Technol. 12380
Donohoe K G and Wydeven T 1979 J. App/. Polymer Sci. 232591
Dorai R and Kushner M J 2000 J. Appl. Phys. 88 3739
Dorai R and Kushner M J 2001 J. Phys. D: Appl. Phys. 34 574
Dorai R and Kushner M J 2003 J. Phys. D: App/. Phys. 36 666
Dorai R, Hassouni K and Kushner M J 2000 J. App/. Phys. 88 6060
Dfimal J, Gibalov V I and Samoilovich V G 1987 Czech. J. Phys. B 37 1248
Dfimal J, Kozlov K V, Gibalov V I and Samoylovich V G 1988 Czech. J. Phys. B 38159
Egli Wand Eliasson B 1989 Helvet. Phys. Acta 62 302
Eliasson Band Kogelschatz U 1991 IEEE Trans. Plasma Sci. 19309
Eliasson B, Hirth M and Kogelschatz U 1987 J. Phys. D: Applied Phys. 20 1421
Eliasson B, Simon F-G and Egli W 1993 Non-Thermal Plasma Techniques for Pollution
Control (Penetrante B M and Schultheis S E, eds), NATO ASI Series G: Ecological
Sciences, Vol. 34, Part B (Berlin: Springer) pp 321-337
--- Page 300 ---
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Falkenstein Z 1997 J. Appl. Phys. 815975
Foest R, Adler F, Sigeneger F and Schmidt M 2003 Surf Coat. Technol. 163/164323
Gentile A C and Kushner M J 1996 J. Appl. Phys. 79 3877
Gibalov V I and Pietsch G J 2000 J. Phys. D: Appl. Phys. 332618
Gibalov V I, Dfimal J, Wronski M and Samoilovich V G 1991 Contrib. Plasma Phys. 31 89
Gibalov V I, Samoilovich V G and Filippov Yu V 1981 Russ. J. Phys. Chem. 55471
Golubovskii Yu B, Maiorov V A, Behnke J and Behnke J F 2002 J. Phys. D: Appl. Phys. 35
751
Golubovskii Yu B, Maiorov V A, Behnke J and Behnke J F 2003a J. Phys. D: Appl. Phys.
3639
Golubovskii Yu B, Maiorov V A, Behnke J and Behnke J F 2003b J. Phys. D: Appl. Phys.
36975
Guikema J, Miller N, Niehof J, Klein M and Walhout M 2000 Phys. Rev. Lett. 85 3817
Hirth M 1981 Beitr. Plasmaphys. 21 I (in German)
Khamphan C, Segur P, Massines F, Bordage M C, Gherardi Nand Cesses Y 2003 Proc.
16th Int. Symp on Plasma Chem. (ISPC-16) (Taormina, Italy)
Klein M, Miller Nand Walhout M 2001 Phys. Rev. E 64026402-1
Kogelschatz U 2002 IEEE Trans. Plasma Sci. 30 1400
Kogelschatz U 2003 Plasma Chem. Plasma Process. 23 1
Kogelschatz U, Eliasson Band Egli W 1997 J. de Phys. IV (France) 7 C4-47
Kozlov K V, Wagner H-E, Brandenburg R and Michel P 2001 J. Phys. D: Appl. Phys. 34
3164
Kudryavtsev A A and Tsendin L D 2002 Tech. Phys. Lett. 28 1036
Li J and Dhali S K 1997 J. Appl. Phys. 82 4205
Lukas C, Spaan M, Schulz-von der Gathen V, Thomson M, Wegst R, Dobele H F and
Neiger M 2001 Plasma Sources Sci. Technol. 10445
Massines F, Mayoux C, Messaoudi R, Rabehi A and Segur P 1992 Proc. 10th Int. Conf
on Gas Discharges and Their Applications (GD-92) (Swansea) Williams W T Ed
730
Massines F, Rabehi A, Decomps P, Gadri R B, Segur P and Mayoux C 1998 J. Appl. Phys.
832950
Miiller I, Punset C, Ammelt E, Purwins H-G and Boeuf J-P 1999a IEEE Trans. Plasma Sci.
2720
Miiller I, Ammelt E and Purwins H-G 1999b Phys. Rev. Lett. 82 3428
Niessen W, Wolf 0, Schruft R and Neiger M 1998 J. Phys. D: Appl. Phys. 31542
Nikonov V, Bartnikas R and Wertheimer M R 2001 J. Phys. D: Appl. Phys. 34 2979
Radehaus C, Dohmen R, Willebrand Hand Niedernostheide F-J 1990 Phys. Rev. A 42
7426
Radu I, Bartnikas R and Wertheimer M R 2003a J. Phys. D: Appl. Phys. 36 1284
Radu I, Bartnikas R, Czeremuszkin G and Wertheimer M R 2003b IEEE Trans. Plasma
Sci. 31 411
Salge J 1995 J. de Phys. IV (France) 5 C5-583
Samoilovich V G, Gibalov V I and Kozlov K V 1997 Physical Chemistry of the Barrier
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Russian Edition, Moscow State University 1989
Steinle G, Neundorf D, Hiller Wand Pietralla M 1999 J. Phys. D: Appl. Phys. 32 1350
Tanaka M, Yagi Sand Tabata N 1978 Trans. lEE of Japan 98A 57
--- Page 301 ---
286
DC and Low Frequency Air Plasma Sources
Tepper J, Li P and Lindmayer M 2002 Proc. 14th Int. Con! on Gas Discharges and their
Applications (GD-2002) vol I (Liverpool: 2002) 175
Tochikubo F, Chiba T and Watanabe T 1999 Jpn. J. Appl. Phys. 38 Part I 5244
Trunec D, Brablec A, St'astny F and Bucha J 1998 Contrib. Plasma Phys. 38435
Trunec D, Brablec A and Buchta J 2001 J. Phys. D: Appl. Phys. 324 1697
Wagner H-E, Brandenburg R, Kozlov K Y, Sonnenfeld A, Michel P and Behnke J F 2003
Vacuum 71 417
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Xu X P and Kushner M J 1998 J. Appl. Phys. 84 4153
6.3 Atmospheric Pressure Glow Discharge Plasmas and
Atmospheric Pressure Townsend-like Discharge Plasmas
6.3.1
Introduction
In 1987, Okazaki and Kogoma (Kanazawa et al 1987) developed a new
plasma in He, which they referred to as atmospheric pressure glow (APG)
discharge plasma. However, Okazaki and Kogoma did not provide sufficient
evidence to prove that the plasma was really a glow discharge. Many
researchers had doubts about whether or not the plasma was in fact a
glow discharge plasma and have referred to this type of plasma by many
other names such as GSD (glow silent discharge), GDBD (glow dielectric
barrier discharge) at atmospheric pressure, APGD (atmospheric pressure
glow discharge), DBD diffuse barrier discharge and homogeneous barrier
discharges at atmospheric pressure (Massines et al 2003, Khamphan et al
2003, Trunec et al 2001, Brandenburg et al 2003, Tepper et al 2002).
Recently, Massines et al (2003) demonstrated that the glow-like plasma in
He in our discharge configuration was indeed a sub-normal glow discharge,
which is very similar to a normal glow discharge.
By contrast, Massines et al (2003) found that the same discharge in N2 is
Townsend-like and thus different from a normal glow discharge. Studies of
this Townsend-like discharge in nitrogen are continued with fine mesh
electrodes (Buchta et al 2000, Tepper et al 2002). Based on these findings,
it is justified to distinguish the discharge plasmas in the two gases, He
and N2, and call one an APG discharge plasma (He) and the other one an
atmospheric-pressure Townsend-like (APT) discharge plasma.
Since the semiconductor industry has achieved great success using
plasma processing, e.g. in the manufacture of microchips, research into
plasma processing has increased significantly worldwide. However, essen-
tially all plasmas used in semiconductor processing are low-pressure plasmas.
On the other hand, there are many applications where the vacuum enclosure.
required for a low-pressure plasma is an obstacle for its technological· use;
--- Page 302 ---
Atmospheric Pressure Glow Discharge Plasmas
287
For instance, the high-speed continuous treatment of sheet-like materials is
impossible using a low-pressure plasma. Similarly, materials with a high
vapor pressure cannot readily be exposed to a low-pressure plasma or a
long soft plastic tube may require plasma treatment of the inner surface,
but a low-pressure plasma cannot be generated in the interior of the soft
plastic tube. As a consequence, the development of glow discharges at atmos-
pheric pressure has become an urgent need in many areas. At the same time,
known discharges at atmospheric pressure (for example sparks, barrier
discharges, and arc discharges) could not be used for surface treatment,
because they are not homogeneous. The earliest account of a glow discharge
at atmospheric pressure is in a paper by von Engel et al (1933) where the
authors used cooled metal electrodes in hydrogen gas. Thus, atmospheric-
pressure glow discharges have been generated for some time, but the
principles of their generation and maintenance were never thoroughly
researched until recently.
Our group was among the first to develop a stable homogeneous glow
discharge at atmospheric pressure and our results are described in the
following sections.
6.3.2 Realization of an APG discharge plasma
6.3.2.1
Three conditions for stabilizing APG discharges
Three conditions (Yokoyama et al 1990) are generally needed to succeed in
producing a stable APG plasma.
(a) The presence of solid dielectric material between discharge electrodes.
(b) A suitable gas passing between the electrodes.
(c) The electric source frequency above 1 kHz.
However, there are situations where not all three conditions are needed.
(aJ
The first condition: dielectric material
The dielectric material assists pulse formation at low frequencies of the
applied voltage in the same way as in an ozone generator (ozonizer), in
which many fine filamentary discharges are generated on the dielectric
plate. In order to generate an APG discharge, the next two conditions
have to be met as well.
Figure 6.3.1 shows a system that has fine metal mesh electrodes. When
this mesh size is about 350-400 #, a stable discharge, which we believe to be
an APT discharge, will be generated even though the other two conditions
are not satisfied (Okazaki et al 1993). For example, in nitrogen, which is
not a gas included in the group of gases that satisfy the second condition
(see below), the mesh electrodes can generate a very stable, homogeneous
--- Page 303 ---
288
DC and Low Frequency Air Plasma Sources
Metal foil
Vinyl chloride
Ceramics, t=1.5 mm
Figure 6.3.1. Parallel plate type plasma generator with fine mesh electrodes.
glow plasma at atmospheric pressure and at 50 Hz applied voltage (which is
also outside the range of frequencies that meet the third condition), but the
gap distance between the two dielectric plates for stable operation is only
about 2-3 mm. When only one electrode is covered with a dielectric plate
and when the other electrode consists of many metal needles, an APG
discharge will be generated (Kanazawa et al 1988). This type of plasma
can be used at higher energy than is possible with dielectric plate electrodes
on both electrodes. However, the stability of an APG discharge with a multi-
needle electrode is lower than in that with conventional electrodes.
If a high frequency excitation source is used, pulse formation caused by
charging of the dielectric plate as in the case of a low-frequency source is not
important, but the presence of the dielectric plate prevents the build-up of
high concentration of discharges.
(b)
The second condition: a suitable choice of gas
The use of He as a feed gas, when the first condition is met (i.e. with a
dielectric plate inserted between the electrodes) and when the third condition
met (i.e. when a high frequency source above 1 kHz is used) will result in the
generation of an APG discharge (Yokoyama et at 1990, Kanazawa et al
1988). Other suitable gases such as Ar + ketone at ppm concentrations or
Ar+methane at ppm levels can also be used (Okazaki et aI199l). The use
of pure Ar gas with the first and third conditions met did not result in a
stable APG discharge. The plasma formed was a 'mixture' of a glow-like
plasma with a small number of filamentary discharges. However, the
addition of an extremely small concentration of any ketone changed this
plasma to a stable, uniform glow discharge plasma, whose stability was far
higher than that of a He plasma. However, ketones include oxygen atoms,
which are often undesirable. Thus, in order to remove oxygen completely
from the system, a mixture of methane and Ar was used. The stability of a
plasma using a mixture of methane and Ar is, however, lower than that of
a ketone-Ar mixture. It has been suggested that plasmas in mixtures
containing mostly noble gases are APG discharges (Massines et aI2003).
--- Page 304 ---
Atmospheric Pressure Glow Discharge Plasmas
289
( c)
The third condition: the electric source frequency
In addition to satisfying the first and second conditions, the third condition
regarding the frequency of the electric source originally stipulated that the
frequency be above 3 kHz. Subsequently, after 1990, we found that the
frequency limit could be lowered to I kHz. It is only under very special
circumstances that a stable APG plasma can be generated at low frequencies,
for example around 50-60 Hz, unless very fine mesh electrodes were used.
The APG discharge plasmas are generated in the form of very sharp and
narrow discharge current pulses because of the presence of the dielectric. In
particular, the APG plasma pulse is generated with a very high frequency,
which has no direct relationship to the frequencies of the applied electric
source. These discharge current pulses could be observed as a change of
charges which passed across the gap between the electrodes.
The use of very high frequency sources, for example a few hundred kHz,
can generate a stable APG or APT discharge plasma even in nitrogen without
mesh electrodes. The pulse-modulated high frequency discharge can create a
homogeneous glow style even from a very high-pressure system. This would
be a high-temperature plasma, but its duration is very short.
6.3.2.2 Discharge currents styles and discharge mechanisms
The existence of a dielectric barrier between the electrodes is a common feature
in the APG plasma (He), the APT plasma (N2' perhaps the same for O2 and
air), and in an ozone generator (02, air). When a low-frequency source is
applied, the form of the discharge current is quite different in terms of the
number of pulses per half cycle of the applied voltage and the pulse duration.
Figure 6.3.2 shows the current pulses in an APG discharge in pure Ar
and in an Ar-acetone mixture. It is interesting to note that we observed a
333 )!S
333 J.lS
Ar
Acetone/Ar
o
0.6
o
0.6
Figure 6.3.2. Pulse current of the APG discharge in pure Ar and acetone-Ar. 3 kHz, Ar
2000 slm, 2.0 kV (Ar), 1.0 kV (acetone-Ar).
--- Page 305 ---
290
DC and Low Frequency Air Plasma Sources
He, Ar, N2
4r---------------,
3
loscope
-1
0.2
0.4
0.6
0.8
Time/ms
Figure 6.3.3. Downstream plasma at atmospheric pressure: R: 50 n, 3 kHz, 1.8 kV, length
of plasma; 2 cm.
number of pulses in pure Ar, but only a single pulse per half cycle in the Ar-
acetone mixture. We characterize an APG discharge as a discharge having a
single pulse per half cycle. Using this criterion, the fine mesh electrode system
was shown to have this unique current pulse frequency in all gases at 50 Hz
(Okazaki et al 1993) and the plasmas generated are thus characterized as
APG or APT discharge plasmas. In spray-type plasma treatment, when the
outer electrode is located downstream as shown in figure 6.3.3, the current
pulse was also observed to be one pulse per half cycle thus classifying the
plasma as an APG or APT discharge plasma.
If a very high voltage is applied, the number of pulses per half cycle will
increase. If the frequency of the applied voltage is low, e.g. between 50 Hz
and 3 kHz, the analysis of the J-V characteristics of the discharge using a
Lissajous figure on an oscilloscope can be used to establish the nature of
the discharge.
The characteristic feature of APG and APT discharges of a single
current pulse per half cycle of the applied voltage suggests that these
discharges develop in a one shot from the entire surface of the dielectrics
in each half cycle. The repetitive formation of filamentary discharges as
seen in an ozone generator does not occur. This is a significant difference
from the silent electric discharge and allows for the possibility of using the
APG and the APT plasma for homogeneous surface treatment. A report
of Kekez et al (1970) concluded that the transition time from a glow
discharge to an arc discharge depends on the kind of gas, the gas pressure,
the discharge gap, and the amount of over-voltage applied. Their finding
--- Page 306 ---
Atmospheric Pressure Glow Discharge Plasmas
291
supported our conclusions regarding the formation of an APG discharge, in
particular the fact that a very short current pulse can produce a rapid succes-
sion of glow discharges.
Discharges using fine mesh electrodes were studied extensively by Trunec
et al (1998) and Tepper et al (2002), but the fundamental mechanisms that
generate and sustain the discharges are not yet completely clear and work in
this area is continuing (Golubovskii et al 2002). Applications of discharges
using mesh electrodes, which can generate a homogeneous glow in different
gases, are being pursued by many groups and some unexpected and
unexplained results have been reported. For example, it has been reported
that the mesh has no effect at higher frequencies and, after several hours of
operating an APG discharges, the discharge changes to a filamentary
discharges. This transition can be reversed by using a new mesh. It seems
there is a limit to the useful lifetime of the mesh electrodes (Buchta et aI2000).
6.3.3 Applications of APG discharge and APT discharge plasmas
Many technological applications of APG discharge plasmas have been
pursued. However, in most applications feed gases and gas mixtures other
than air have been used. Thus, these applications are outside the scope of
this book and we refer the reader to the original references for more details
on applications such as the surface modification of inner surfaces of tubes of
polyvinylchloride and surface polymerization applications (Babukutty et at
1999, Okazaki and Kogoma 1993, Rzanek-Borocha et al 2002, Sawada
et al 1995, Kojima et al 2001, Tanaka et al 2001), microwave heating of
powders (Sugiyama et a11998, Yamakawa et aI2003), exhaust gas treatment
(Hong et aI2002), adhesive strength control and surface analysis (Nakamura
et a1199l, Prat et at 1998), spray-type plasma applications at atmospheric
pressure (Nagata et al 1989, Okazaki and Kogoma 1993, Taniguchi et al
1997, Tanaka et al 1999, Tanaka and Kogoma 2001), powder coating
(Mori et al 1998, Nakajima et al 2001, Ogawa et al 2001), sterilization of
cavities and surfaces (Japan patent 1994), and surface treatment of woolen
fabrics (Okazaki and Kogoma 1999).
Perhaps the only application involving air is a marked improvement in
the efficiency of ozone generators using the APG discharge plasma concept.
The use of fine mesh metal electrodes in a dielectric barrier discharge
produced a glow discharge at atmospheric pressure, even though it showed
stability only for a very small gap distance of 2-3 mm, in air, N2, O2 and
other gases. This gap distance, however, is sufficient for an ozone generator.
The ozone formation efficiency in such a reactor was examined (Kogoma et al
1994) and an improvement in efficiency of about 20% over that of a conven-
tional ozone generator was found. These results were confirmed by Buchta
et al 2000 with respect to ozone formation concerning the use of the fine
mesh metal electrodes also by Trunec et a11998, Tepper et a11998.
--- Page 307 ---
292
DC and Low Frequency Air Plasma Sources
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the group
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Okazaki Sand Kogoma M 1993 J. Photopolymer Sci. Tech. 6 339
Okazaki Sand Kogoma M 1999 in Proc. XXIVth Int. Conference Phenomena in Ionized
Gases, Warsaw, Poland, vol I, pp 123-124
Okazaki S, Kogoma M and Uchiyama H 1991 in Proc. I!lrd Int. Symp. on High Pressure
Low Temperature Plasma Chern., Strasburg, France, pp. 101-107
Okazaki S, Kogoma M, Uehara M and Kimura Y 1993 J. Phys. D: Appl. Phys. 26 889
Prat R, Suwa T, Kogoma M and Okazaki S 1998 J. Adhesion 66 163
Rzanek-Borocha Z, Schmidt-Szalowski K, Janowska J, Dudzinski K, Szymanska A and
Misiak M 2002 in Proc. VI!lth Int. Symp. on High Pressure Low Temperature
Plasma Chern., Puhajarve, Estonia, vol 2, pp 415-419
Sawada Y Ogawa Sand Kogoma. M 1995 J. Phys. D: Appl. Phys. 28 1661
Sugiyama K, Kiyokawa K, Matsuoka H, Itoh A, Hasegawa K and Tsutsumi K 1998 Thin
Solid Films 316 117
--- Page 308 ---
Homogeneous Barrier Discharges
293
Tanaka K and Kogoma M 2001 Plasma and Polymers 6 27
Tanaka K, Inomata T and Kogoma M 1999 Plasmas and Polymers 4 269
Tanaka K, Inomata T and Kogoma M 2001 Thin Solid Films 386 217
Taniguchi K, Tanaka K, Inomata T and Kogoma M 1997 J. Photopolymer Sci. Tech. 10
113
Tepper J, Li P and Lindmayer M 2002 in Proc. XIVth Int. Conference on Gas Discharges
and their Applications, Liverpool, voll pp 175-178
Tepper J, Lindmayer M and Salge J 1998 in Proc. VIth Int. Symp. on High Pressure Low
Temperature Plasma Chem., Cork, Ireland, pp 123-127
Trunec D, Brablec A and Stastny F 1998 in Proc. VIth Int. Symp. on High Pressure Low
Temperature Plasma Chem., Cork, Ireland, pp 313-317
Trunec D, Brablec A and Buchta J 2001 J. Phys. D: Appl. Phys. 34 1697
Yamakawa K, Den S, Katagiri T, Hori M and Goto T 2003 in Proc. 16th Int. Symp. on
Plasma Chem., Taormina, Italy, p 832
Yokoyama T, Kogoma M, Moriwaki T and Okazaki S 1990 J. Phys. D: Appl. Phys. 23
1125
6.4 Homogeneous Barrier Discharges
Recently, research on material processing by non-equilibrium atmospheric
pressure plasmas witnessed a tremendous growth, both at the experimental
and simulation levels. This was motivated by the new technical possibilities
in generating relatively large volumes of non-equilibrium plasmas at or
near atmospheric pressure, in numerous gases and gas mixtures and at low
operating power budgets. Amongst the enabling technologies, the use of
'barrier discharges' has become very prevalent. this started with the use of
the 'dielectric barrier discharge' (DBD) which was developed and improved
upon over several decades (Bartnikas 1968, Donohoe 1976, Kogelschatz
1990, Kogelschatz et al 1997). DBDs use a dielectric material to cover at
least one of the electrodes. The electrodes are driven by voltages in the kV
range and at frequencies in the audio range (kHz). However, new methods
emerged which extended the frequency range down to the dc level. The
resistive barrier discharge (RBD) recently developed by Alexeff and Laroussi
is such an example (Alexeff et a11999, Laroussi et aI2002). The RBD uses a
high resistivity material to cover the surface of at least one of the electrodes.
It is capable of generating a large volume atmospheric pressure plasma with
dc and ac (60 Hz) driving voltages.
The limitations of barrier-based discharges have traditionally been their
non-homogeneous nature both in space and time. DBDs, for example,
exhibit a filamentary plasma structure, therefore leading to non-uniform
material treatment when used in surface modification applications. This
situation led some investigators to search for operating regimes under
--- Page 309 ---
294
DC and Low Frequency Air Plasma Sources
which diffuse and homogeneous discharges can be produced. In the late
1980s and early 1990s, Okazaki's group published a series of papers where
they presented their experimental findings regarding the conditions under
which a DBD-based reactor can produce homogenous plasma, at atmos-
pheric pressure (Okazaki et a11993, Yokoyama et a11990, Kanazawa et al
1988). Their work was soon followed by others (Massines et aI1992, 1996,
1998, Gherardi et al 2000, Roth et al 1992) who validated the fact that
non-filamentary plasmas can indeed be produced by DBDs, an outcome
not widely accepted by the research community active in this field at that
time.
In this section, description of the work of several investigators will be
presented. The electrical characteristics, ignition and extinction, stability,
and homogeneity of the discharges will be discussed.
6.4.1
DBD-based discharges at atmospheric pressure
6.4.1.1
Experimental set-up
The dielectric barrier discharge (DBD) consists basically of two planar elec-
trodes (sometimes co-axial or adjacent cylinders) made of two metallic plates
(or tubes) covered by a dielectric material and separated by a variable gap
(see figure 6.4.1). When operated at atmospheric pressure, the electrodes
are energized by a high voltage power supply with typical voltages in the
1-20kV range, at frequencies ranging from a few hundred Hz to a few
RF Amplif"rer
&
Impedance
Matching
RF Source
Figure 6.4.1. Dielectric barrier discharge (DBD) configuration.
Metal
Electrode
Dielectric
--- Page 310 ---
Homogeneous Barrier Discharges
295
Figure 6.4.2. Diffuse DBD in a helium/air mixture (photo courtesy: M Laroussi, Old
Dominion University).
kHz. To optImize the amount of power deposited in the plasma, an
impedance matching network may be introduced between the power
supply and the electrodes. The electrode arrangement is generally contained
within a vessel or enclosure to allow for the control of the gaseous mixture
used. The dielectric material covering the electrodes plays the crucial role
in keeping the non-equilibrium nature of the discharge. This is achieved as
follows. When a sufficiently high voltage is applied between the electrodes,
the gas breaks down (i.e. ionization occurs) and an electrical current starts
flowing in the gas. Immediately, electrical charges start accumulating on
the surface of the dielectric. These surface charges create an electrical
potential, which counteracts the externally applied voltage and therefore
limits the flow of current. This process inhibits the glow-to-arc transition.
Although traditionally DBDs produce filamentary-type plasmas, under
some conditions, which are discussed later in this section, homogeneous
plasmas can also be generated. Figure 6.4.2 is a photograph of a diffuse,
homogeneous plasma generated by a DBD in an atmosphere of helium
with a small admixture of air.
6.4.1.2
Current-voltage characteristics
Depending on the operating conditions (gas, gap distance, frequency,
voltage), the current waveform can exhibit multiple pulses per half cycle or
--- Page 311 ---
296
DC and Low Frequency Air Plasma Sources
80
8
-- Discharge current
60
................. Power supply voltage, V. 6
~
40
4
5 20
2
E
~
-<
0
c.>
0
0 i
."
bI)
<>
~ -20
-2 ~
..c::
c.> '" 0 -40
-4
-60
-6
-80
-8
0
20
40
60
80
100
Time (~s)
Figure 6.4.3. Current-voltage characteristics of a DBD in N2 (Gherardi et aI2000).
a single wide pulse per half cycle. The presence of multiple current pulses
per half cycle is usually taken as an indication that a filamentary discharge
is established in the gap between the electrodes. Figure 6.4.3 shows the
current and voltage waveforms of a filamentary DBD in nitrogen (Gherardi
et aI2000). On the other hand, diffuse and homogeneous discharges exhibit a
current waveform with a single pulse per half cycle, as shown in figure 6.4.4
8
6
4
~
2
CD
0
I
~ -2
-4
.e
-8
b
-- V.Power supply Voltag
........ Vg Gas voltage
1,0
0.8
0,6
(')
0,4 E;
~ a
0,2 0.
CD
::l
/,/ :~,;
-0.4 ~
...,:,'..J
-0.6
-0,8
+---....----,r----.----,---.----r---J -1.0
0
50
100
Time (!IS)
150
Figure 6.4.4. Current-voltage characteristics of a homogeneous DBD in N2 (Gherardi et al
2000).
--- Page 312 ---
Homogeneous Barrier Discharges
297
+
Figure 6.4.5. Ten nanoseconds (10 ns) exposure time photograph of a diffuse DBD in N2
(Gherardi et al2000).
(Gherardi et at 2000). However, a single pulse is not a sufficient test to
indicate the presence of homogeneous plasma. Indeed, if a very large
number of streamers are generated in a way that they spatially overlap and
if the measuring instrument is not capable of resolving the very narrow
current pulses, a wide single pulse can be displayed. Gherardi et at (2000)
used high-speed photography as a second diagnostic method to visually
inspect the structure of the discharge channel. Under conditions leading to
a homogeneous plasma, photographs taken with exposure times in the
order of streamers lifetime (1-10 ns) show a luminous region extending
uniformly over the whole electrode surface (see figure 6.4.5). In contrast,
when the plasma is filamentary, several localized discharges are clearly visible
(figure 6.4.6). Important physical differences between the characteristics of
the plasma in a streamer (or microdischarge) and that of a diffuse plasma
are to be noted (for details, see section 6.2). Of practical importance are
the electron number density, ne, and kinetic temperature, Te. In a streamer
ne and Te are in the 1014_10 15 cm-3 and 1-10 eV range, respectively, while
in a diffuse discharge ne and Te are in the 109_10 11 cm-3 and 0.2-5eV
range, respectively.
6.4.1.3 Discharge homogeneity conditions
The idea of using electrodes covered by a dielectric material to generate a
stable non-equilibrium plasma at high pressures is actually an old idea
dating from the time Siemens used a discharge to generate ozone (Siemens
1857). However, up until recently the plasma produced by DBDs was fila-
mentary in character, being made of a large number of streamers or micro-
discharges randomly distributed across the dielectric surface (Kogel schatz
et at 1997). However, Kanzawa et at (1988) showed that, under specific
+
Figure 6.4.6. Ten nanoseconds (10 ns) exposure time photograph of a filamentary DBD in
N2 (Gherardi et al 2000).
--- Page 313 ---
298
DC and Low Frequency Air Plasma Sources
conditions, the plasma could be homogeneous. These conditions are (1)
helium used as a dilution gas and (2) the frequency of the applied voltage
must be in the kHz range. These conclusions were purely empirical, based
on more or less experimental trial and error. Similarly, Roth et al (1992)
used helium and a low frequency rf source (kHz range) to produce a homo-
geneous discharge in their device, the 'one atmosphere uniform glow
discharge plasma' (OAUGDP). The OAUGDP is a DBD-based reactor.
They also concluded, based on experimental trials, that helium and the
frequency range are the critical parameters, which can lead to a homoge-
neous plasma at atmospheric pressure. Roth (1995) attempted to explain
the frequency range where the homogenous discharge could exist by what
he termed the 'ion trapping' mechanism. This idea is based on driving the
electrodes by high rf voltages, which induce an electrical field that oscillates
at a frequency that is high enough to trap the ions but not the electrons in the
space between the electrodes. The electrons ultimately reach the electrodes
where they recombine or form a space charge. This theory, however, is
different from what has been demonstrated by various modeling results
(Kogelschatz 2002). Another argument is the fact that in a highly collisional
regime one cannot trap charged particles by a single axially uniform electric
field (the axis normal to the plane of the electrodes in this case), even if it is
oscillating. Furthermore, collective effects were not taken into account. For
example if the ions were trapped and the electrons drifted towards the
electrodes, an ambipolar electric field would be established in such a way
as to repel the electrons away from the electrodes and towards the ions, a
mechanism not taken into account in the proposed analysis.
Massines et al (1998) presented a very different theory, which seems to
be well supported by experimental and modeling works. The main idea
behind Massines' theory is that since the plasma generated by a DBD is
actually a self-pulsed plasma, a breakdown of the gas under low electric
field between consecutive pulses is possible due to trapped electrons and
metastable atoms. These seed particles allow for a Townsend-type break-
down instead of a streamer-type, leading to continued discharge conditions
even when the electric field is small. In the case of helium, a density of seed
electrons greater than 106 cm -3 was found to be sufficient to keep the
plasma ignited under low field conditions (Gherardi et al 2000). The seed
electrons are electrons left over from the previous pulse and those generated
via Penning ionization emanating from metastable atoms. In the case of
nitrogen, Gherardi reported that the meta stables play the dominant role in
keeping the discharge ignited between pulses. Their concentration depends
strongly on the nature of the surface of the dielectric material, which is a
source of metastable-quencher species.
Using a one-dimensional fluid model, Massines calculated the distri-
butions of the electric field, the electron density, and the ion density, and
showed that the homogeneous DBD exhibits a structure identical to the
--- Page 314 ---
,.....,
=
~
>-
N 0 ......
'-"
"'0
Q)
~
(,)
'.6
(,)
<1)
~
Homogeneous Barrier Discharges
299
100
75
50
25
Positive column
-- Electric field
~
Ion density
---l>- Electron density
Negative
glow +
Faraday cathode
. dark space
fall
O.~~~~~~~~~~~~-L~
0,0
0,1
0,2
0,3
A
Position (cm)
20
15 i
a:
(11
fIl
10 ';:::
o o
Figure 6.4.7. Electric field, electron density, and ion density spatial distributions between
the anode and the cathode of a diffuse DBD in helium (Mas sines et aI1998).
normal glow discharge (positive column, Faraday dark space, negative glow,
etc.). Figure 6.4.7 shows such spatial distributions between the anode and
cathode of a homogeneous DBD (Mas sines et aI1998).
6.4.2 The resistive barrier discharge (RBD)
To extend the operating frequency range, a few methods were proposed.
Okazaki used a dielectric wire mesh electrode in a DBD to generate a glow
discharge at a frequency of 50 Hz (Okazaki et aI1993). Alexeff and Laroussi
(1999, 2002a,b) proposed what came to be known as the resistive barrier
discharge (RBD). The RBD can be operated with dc or ac (60 Hz) power
supplies. This discharge is based on the dielectric barrier (DB) configuration,
but instead of a dielectric material, a high resistivity (few MO·cm) sheet is
used to cover one or both of the electrodes (see figure 6.4.8). The high resis-
tivity sheet plays the role of a distributed resistive ballast which inhibits the
discharge from localizing and the current from reaching a high value, and
therefore prevents arcing. It was found that if helium was used as the ambient
gas between the electrodes and if the gap distance was not too large (5 cm and
below), a spatially diffuse plasma could be maintained for time durations of
several tens of minutes. Figure 6.4.9 shows the discharge structure when
helium was used. However, if air was mixed with helium (> 1 %) the discharge
formed filaments which randomly appeared within a background of more
diffuse plasma. This occurred even when the gap distance was small (Laroussi
et aI2002a).
--- Page 315 ---
300
DC and Low Frequency Air Plasma Sources
115
V
60Hz
Figure 6.4.8. The resistive barrier discharge (RBD) configuration.
6.4.2.1
Current-voltage characteristics
resistivity
material
The RBD can be operated under dc or ac modes. Even when operated in the
dc mode, the discharge current was found to be a series of pulses, suggesting
that, like the DBD, the RBD is also a self-pulsed discharge. Figure 6.4.10
shows the current waveform and the output signal of a photomultiplier
tube (PMT), when a dc voltage of 20 kV was applied. The current pulses
are a few microseconds wide and occur at a repetition rate of a few tens of
kHz. The PMT signal correlates very well with the current. The pulsed
nature of the discharge current can be explained by the combined resistive
and capacitive nature of the device. When the gas breaks down and a current
of sufficient magnitude flows, the equivalent capacitance of the electrodes
becomes charged to the point where most of the applied voltage starts
appearing across the resistive layer of the electrodes. The voltage across
the gas then becomes too small to maintain a discharge and the plasma
extinguishes. At this point, the equivalent capacitor discharges itself through
the resistive layer, hence lowering the voltage across the resistive layer and
increasing the voltage across the gas until a new breakdown occurs (Wang
et aI2003).
Figure 6.4.9. Photograph of a diffuse RBD in helium (Laroussi et at 2002a).
--- Page 316 ---
Homogeneous Barrier Discharges
301
Figure 6.4.10. RBD current waveform under dc excitation. Lower waveform is PMT
signal. Horizontal scale is 2llsjsquare.
The RBD offers a very practical solution to generate relatively large
volumes of low temperature plasma for processing applications and bio-
medical applications (Laroussi 2002). For homogeneity purposes, helium
was found to be necessary as the main component of the ambient gas mixture
between the electrodes. Introduction of air renders the discharge filamentary.
If only air is used, plasma can still be initiated for small gaps (millimeters).
However, in this case, the structure of the plasma is spatially non-uniform.
6.4.3 Diffuse discharges by means of water electrodes
Although the use of liquid cathodes (such as electrolytes) to generate a
discharge has been around for some time (Davies and Hickling 1952), only
recently have some investigators applied it to specifically producing diffuse
plasmas in air (Andre et at 2001, Laroussi et at 2002b). Andre used two
streams of water as electrodes. A non-equilibrium discharge was ignited
between the two streams (few millimeters apart) by means of a dc power
supply (applied dc voltage ",,3 kV). They reported a current density in the
--- Page 317 ---
302
DC and Low Frequency Air Plasma Sources
Water cooling
Metal electrode
Water-electrode
To power source
Figure 6.4.11. Discharge configuration with water as a lower electrode (Laroussi et al
2002b).
0.2-0.25 A cm -2 range. Laroussi used one water electrode (static or flowing
water) and as a second electrode a water-cooled metal disk (see figure
6.4.11). The discharge was ignited in the gap between the disk-shaped
electrode and the surface of the water by means of an ac power supply
(applied voltage ",,13 kV, frequency 60 Hz). The plasma generated by this
method is diffuse but not necessarily spatially uniform. Figure 6.4.12
Figure 6.4.12. Visual structure of the discharge. Water electrode is at the bottom (Laroussi
et al2002b).
--- Page 318 ---
Homogeneous Barrier Discharges
303
.....
:-, .
~"
2
Figure 6.4.13. Axial and radial distribution of light from the discharge (Laroussi et at
2003).
shows a typical visual structure of the plasma (Laroussi et aI2003). The top,
which is the location of the metal disk electrode, exhibits a more intense
region, whiter in color than the rest of the column. Next to the surface of
the water electrode (bottom), the plasma is more violet in color and rather
filamentary. This filamentation is due to the fact that, before breakdown
occurs, under the influence of the applied electric field, the water surface
develops a number of 'ripples'. These ripples offer sharp curvature points
with high electric fields at their tips, which ignite numerous local discharges
across the water surface. Figure 6.4.13 shows the axial distribution of light
intensity emitted by the discharge. The emission is most intense near the
metal electrode (located at z = 0 cm), exhibits a nearly constant plateau
along most of the gap, then a dark space at about 3 mm from the water
surface (located at z = 2 cm).
6.4.3.1
Temporal evolution of the plasma structure
In order to characterize the temporal evolution of the plasma structure, a high-
speed CCD camera was used to take pictures for different values of the
discharge current (Lu and Laroussi 2003). Figures 6.4.l4(a), (b) correspond
to the positive and negative peaks of the discharge current, respectively. The
--- Page 319 ---
304
DC and Low Frequency Air Plasma Sources
(a)
(b)
Figure 6.4.14. (a) Discharge structure in air (exposure time is 100/!s) when current is at
positive peak (water electrode is the cathode). Water electrode is the bottom electrode
(2). Gap distance is 1.3 cm (Lu and Laroussi 2003). (b) Discharge structure in air when
current is at negative peak (water electrode is the anode). Same conditions as in (a) (Lu
and Laroussi 2003).
exposure time is 100 ~s. Figure 6.4. 14(a) shows that when the water electrode is
the cathode the plasma takes the shape of a relatively wide column (about
9 mm wide) but is not visually bright. In contrast, when the water electrode
becomes the anode (during the second half cycle of the voltage, figure
6.4. 14(b)), the plasma appears as a brighter but narrower column (about
5 mm wide). Structures similar to the dc glow discharge, such as Faraday
dark space, negative glow, positive column, and anode dark space, are clearly
visible. The 'cathode fall' region is on the metal electrode side. However, when
the water electrode is the cathode (figure 6.4.l4(a)), the plasma exhibits multi-
contact points at the water surface with several localized discharges. These are
followed by a dark space, then a single wide bright region, and finally a dark
space near the anode (top electrode). The 'cathode fall' region is on the water
electrode side. Here, the electric field is high, contributing to the ignition of
several local discharges at the rippled surface of the water. It was also found
that the discharge always ignites at the water surface and propagates towards
the metal electrode at velocities approaching 1 km/s (Lu and Laroussi 2003).
This velocity is much smaller than that of streamer heads (",100 km/s) gener-
ated in DBDs, suggesting that the breakdown mechanism in this discharge is
not similar to the usual electron-driven avalanche.
6.4.3.2 Electron density and gas temperature measurements
The electron number density, ne , was estimated from the electrical par-
ameters of the discharge: the electric field E, the current density j, and
--- Page 320 ---
References
305
electron collision frequency Ve:
j = neiEjmeve
where e and me are the electronic charge and mass respectively. Under high
pressure and low temperature conditions the electron collision frequency is
dominated by electron-neutral collisions. Assuming that the collision
cross-section is weakly dependent on temperature, Ve is related to the electron
temperature as T~/2. For current densities in the range 0.01-1 A/cm2 ,
electron number densities 1010_1012 cm -3 were calculated.
In order to determine the background gas temperature, the simulated
spectra of the 0-0 band of the second positive system of nitrogen were
compared with experimentally measured spectra. Because of the low energies
needed for rotational excitation and the short transition times, molecules
in the rotational states and the neutral gas molecules are in equilibrium.
Consequently, the rotational temperature also provides the value of the
gas temperature. Using this method, Lu and Laroussi (2003) measured gas
temperatures in the 800-900 K range when the water electrode is the cathode,
and in the 1400-1500K range when the water electrode is the anode.
References
Alexeff I and Laroussi M 2002 'The uniform, steady-state atmospheric pressure dc plasma'
IEEE Trans. Plasma Sci. 30(1) 174
Alexeff I, Laroussi M, Kang Wand Alikafesh A 1999 'A steady-state one atmosphere
uniform dc glow discharge plasma' in Proc. IEEE Int. Conf Plasma Sci. p. 208
Andre P, Barinov Y, Faure G, Kaplan V, Lefort A, Shkol'nik S and Vacher D 2001
'Experimental study of discharge with liquid non-metallic (tap-water) electrodes
in air at atmospheric pressure' J. Phys. D: Appl. Phys. 34 3456
Bartnikas R 1968 'Note on discharges in helium under ac conditions' Brit. J. Appl. Phys.
( J. Phys. D.) Ser. 2 1 659
Davies R A and Hickling A 1952 J. Chem. Soc. Glow Discharge Electrolysis Part 13595
Donohoe K G 1976 'The development and characterization of an atmospheric pressure
non-equilibrium plasma chemical reactor' PhD Thesis, California Institute of
Technology, Pasadena
Gherardi N, Gouda G, Gat E, Ricard A and Massines A 2000 'Transition from glow
silent discharge to micro-discharges in nitrogen gas' Plasma Sources Sci. Technol.
9340
Kanazawa S, Kogoma M, Moriwaki T and Okazaki S 1988 'Stable glow at atmospheric
pressure' J. Phys. D: Appl. Phys. 21 838
Kogelschatz U 1990 'Silent discharges for the generation of ultraviolet and vacuum ultra-
violet excimer radiation' Pure Appl. Chem. 62 1667
Kogelschatz U 2002 'Filamentary, patterned and diffuse barrier discharges' IEEE Trans.
Plasma Sci. 30(4) 1400
Kogelschatz U, Eliasson Band Egli W 1997 'Dielectric-barrier discharges: principle and
applications' J. Physique IV 7(C4) 47
--- Page 321 ---
306
DC and Low Frequency Air Plasma Sources
Laroussi M 2002 'Non-thermal decontamination of biological media by atmospheric
pressure plasmas: review, analysis and prospects' IEEE Trans. Plasma Sci. 30(4)
1409
Laroussi M, Alexeff A, Richardson J P and Dyer F F 2002a 'The resistive barrier
discharge'IEEE Trans. Plasma Sci. 30(1) 158
Laroussi M, Malott C M and Lu X 2002b 'Generation of an atmospheric pressure non-
equilibrium diffuse discharge in air by means of a water electrode' in Proc. Int.
Power Modulator Conj, Hollywood, CA pp 556-558
Laroussi M, Lu X and Malott C M 2003 'A non-equilibrium diffuse discharge in atmos-
pheric pressure air' Plasma Sources Sci. Technol. 12(1) 53
Lu X and Laroussi M 2003 'Ignition phase and steady-state structures of a non-thermal air
plasma' J. Phys. D: Appl. Phys. 36 661
Massines F, Mayoux C, Messaoudi R, Rabehi A and Segur P 1992 'Experimental study of
an atmospheric pressure glow discharge application to polymers surface treatment'
in Proc. GD-92, Swansea, UK, vol. 2, pp 730-733
Massines F, Gadri R B, Decomps P, Rabehi A, Segur P and Mayoux C 1996 'Atmospheric
pressure dielectric controlled glow discharges: diagnostics and modelling' in Proc.
ICPIG XXII, Hoboken, NJ 1995, Invited Papers, AlP Conference Proc. vol. 363,
pp 306-315
Massines F, RabehiA, Decomps P, Gadri R B, Segur P and Mayoux C 1998 'Experimental
and theoretical study of a glow discharge at atmospheric pressure controlled by a
dielectric barrier' J. Appl. Phys. 8 2950
Okazaki S, Kogoma M, Uehara M and Kimura Y 1993 'Appearance of a stable glow
discharge in air, argon, oxygen and nitrogen at atmospheric pressure using a
50 Hz source' J. Phys. D: Appl. Phys. 26 889
Roth J R 1995 Industrial Plasma Engineering, vol. I (Bristol and Philadelphia, PA: lOP
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Roth J R, Laroussi M and Liu C 1992 'Experimental generation of a steady-state glow
discharge at atmospheric pressure' in Proc. 27th IEEE ICOPS, Tampa, FL,
paper P21
Siemens W, 1857 Poggendorfs Ann. Phys. Chern. 1266
Wang X, Li C, Lu M and Pu Y 2003 'Study on Atmospheric Pressure Glow Discharge'
Plasma Source Science and Technology 12(3) 358
Yokoyama T, Kogoma M, Moriwaki T and Okazaki S 1990 'The Mechanism of the
stabilized glow plasma at atmospheric pressure' J. Phys. D: Appl. Phys. 23 1125
6.5 Discharges Generated and Maintained in Spatially Confined
Geometries: Microhollow Cathode (MHC) and Capillary
Plasma Electrode (CPE) Discharges
Two discharge types that have been used successfully to generate and
maintain atmospheric-pressure plasmas in air are microhollow cathode
(MHC) and capillary plasma electrode (CPE) discharges. Common to both
discharges is the fact that they are created in spatially confined geometries,
--- Page 322 ---
Discharges Generated in Spatially Confined Geometries
307
whose critical dimensions are in the range 10--500 /lm. The MHC discharge is
based on the concept of the well-known low-pressure hollow cathode (HC)
and, in essence, represents an extension of the HC discharge to atmospheric
pressure. The CPE discharge, which uses electrodes with perforated dielectric
covers, may be thought of as a variant of the dielectric barrier discharge
(DBD). However, the perforated dielectric cover creates an array of
capillaries, which critically determine the properties of the discharge and
distinguish the CPE discharge properties from those of a DBD. A discharge
type which was derived from MHC discharges, but is not based on the hollow
cathode effect, has recently been added to the list of spatially confined micro-
discharges: the cathode boundary layer (CBL) discharge. Although this
discharge has so far only been operated in noble gases, a brief discussion
ofCBL discharges has been included, because of its potential for the genera-
tion of 'two-dimensional' plasmas in atmospheric pressure air.
6.5.1
The microhollow cathode discharge
It is illustrative to start with a brief review of the hollow cathode (HC)
discharge. HC discharges have been widely used since the early part of the
20th century, primarily as high-density, low-pressure discharge devices for
a variety of applications (Paschen 1916, Giintherschulze 1923, Walsh
1956). An HC discharge device consists of a cathode with hollow structure
(hole, aperture, etc.) in it and an arbitrarily shaped anode (figure 6.5.1).
Two scaling laws determine the properties of the discharge. The product
pd of the pressure p and the anode--cathode separation d obeys the well-
known Paschen breakdown law, which applies to all discharges and
determines the required breakdown voltage for given values of p, d, and
the operating gas (Paschen 1916, White 1959).
A scaling law that is unique to the HC discharge involves the product pD
of the pressure p and cathode opening D. If the product pD is in the range
from 0.1 to 10 torr cm, the discharge develops in stages, each with a distinc-
tive I-V characteristics. At low currents, a 'pre-discharge' is observed, which
is a glow discharge whose cathode fall region is generally outside the cathode
structure. Under these circumstances, there is a single region of positive space
charge and the electrons follow a path that is essentially determined by the
direction of the vacuum electric field between cathode and anode in the
absence of a discharge. As the current increases, the positive space charge
region moves closer to the cathode and eventually enters the hollow cathode
structure. Now a positive column, which serves as a virtual anode, is formed
along the axis of the cathode cavity between two separate cathode sheath
regions. This results in a change in the electric field distribution within the
hollow cathode. The electric field, which was initially axial, now becomes a
radial field and a potential 'trough' is created within the cavity. This
trough causes a strong radial acceleration of the electrons towards the
--- Page 323 ---
308
DC and Low Frequency Air Plasma Sources
r Anode
Cathode
d
Pre.alre p
Figure 6.5.1. General hollow cathode geometry.
axis, which may lead to an oscillatory motion of the electrons (,pendulum
electrons'; Giintherschulze 1923, Walsh 1956, Helm 1972, Stockhausen and
Kock 2001) when they are accelerated into the virtual anode and then
repelled at the opposing cathode fall. This may result in an oscillatory
motion with ever-decreasing amplitude between the two opposite cathode
fall regions. Thus, the path length of the electrons is increased and these
pendulum electrons can undergo many ionizing collisions with the back-
ground gas. Furthermore, energetic particles within the cathode hole such
as ultraviolet photons and metastables have a high probability of producing
secondary electrons at the cathode surface, which, in turn, can lead to further
ionization and excitation events.
In the transition from an axial pre-discharge to a radial discharge,
the sustaining voltage drops as the current increases (Fiala et at 1995).
The discharge has a 'negative differential' resistance, a mode which is
traditionally referred to as the 'hollow cathode' mode. As the current is
increased further, the cathode layer expands over the surface of the planar
cathode outside the hole. The current-voltage characteristic becomes that
of a normal glow discharge with constant voltage at increasing current.
Ultimately, when the cathode layer reaches the boundaries of the cathode,
any further current increase requires an increase in discharge voltage: the
discharge changes into an abnormal glow discharge.
HC discharges are known to have electron energy distributions that are
strongly non-Maxwellian and contain a significant amount of very energetic
electrons. Most of the earlier diagnostics studies (Gill and Webb 1977) of
the electron energy distribution function in HC devices were carried out
for low-pressure HC discharges. These studies found copious amounts of
electrons with energies well above 10 e V and a tail extending up to the
plasma operating voltage. Furthermore, a fraction of high-energy 'beam'
electrons was measured with energies near the plasma voltage. These are
electrons that were accelerated across the full potential of the cathode fall.
Efforts to increase the operating pressure ofHC discharges date back to
the late 1950s (White 1959, Sturges and Oskam (1964)). The so-called
--- Page 324 ---
Discharges Generated in Spatially Confined Geometries
309
'White-Allis' similarity law relates the discharge sustaining voltage V to the
product (PD) and the ratio (l / D), where I is the discharge current. As a
consequence of this law, operation of a HC discharge at higher pressures
can be accomplished by reducing the size D of the hole in the cathode. The
lowest value of pD for which the scaling law holds is determined by the con-
dition that the mean free path for ionization cannot exceed the hole diameter
(Helm 1972). For argon, the minimum pD value (Giintherschulze 1923) is
0.026 torr cm. Empirically, upper bounds for pD in the rare gases are
around 10 torrcm, but less for molecular gases (Gewartkowski and
Watson 1965). Physically, the upper limit is determined by the condition
that the distance between 'opposite' cathodes cannot exceed the combined
lengths of the two cathode fall regions plus the glow region. This would
lead to an upper limit (Schoenbach et al 1997), in pD for argon of about
1 torr cm, which is almost about a factor of 10 less than the empirically estab-
lished upper limit. As a result, high-pressure operation of a HC discharge at
or near atmospheric pressure in the rare gases is possible, but requires small
hole sizes in the cathode. Based on the upper limit of the product pD, atmos-
pheric-pressure operation in the rare gases would require hole sizes of about
10 ~m assuming that the gas is at room temperature. Empirically, stable HC
operation at atmospheric-pressure in the rare gases has been observed
(Schoenbach et al 2000) for holes sizes as large as 250 ~m. This indicates
that physical processes other than pendulum-electron coupling between
'opposite' cathodes must be present to account for the negative differential
resistance and the discharge stability at high pD values.
Discharges of this hollow cathode discharge type have been studied by a
number of groups and, dependent on particular electrode geometry or on
their arrangements in arrays, they have been named differently. In some case,
they are just named 'microdischarges' as by the group at the University of Illi-
nois (Frame et a11997) and that at Caltech (Sankaran and Giapis 2001). In
another case, where the electrode configuration was designed for parallel opera-
tion, the discharges are named by the group at the University of Frankfurt and
the University of Dortmund, Germany, 'microstructured electrode arrays'
(penache et al 2000). For cylindrical hollow cathode discharges, the term
'microhollow cathode discharge' (MHCD) was coined by the group at Old
Dominion University (Schoenbach et al 1996). This name is being used by
several other groups, who work with micro discharges based on the hollow
cathode principle, such as the group at the Steven Institute of Technology
(Kurunczi et al 1999), the University of Erlangen, Germany (Petzenhauser
et al 2003), the University of California, Berkeley (Hsu and Graves 2003),
the group at Yonsai University, Korea (Park et al2003), the National Cheng
Kung University, Taiwan (Guo and Hong 2003), and at the Institute for
Low Temperature Plasma Physics in Greifswald, Germany (Adler et al2003).
Most of the experimental studies in high-pressure hollow cathode
discharges have so far been performed in rare gases and rare gas halide
--- Page 325 ---
310
DC and Low Frequency Air Plasma Sources
mixtures. But there is an increasing emphasis on their use in atmospheric
pressure air, or at least mixtures of gases containing air. The following
sections will give an overview of the various electrode geometries and
modes of operation, their plasma parameter range, and some applications.
6.5.1.1
Electrode geometries, materials, and fabrication techniques
Any hollow cathode discharge electrode geometry needs to satisfy the
condition that surfaces of the cathode facing each other need to be separated
by a distance such that the high-energy electrons generated in one cathode
fall can reach the opposite cathode fall. Such cathode geometries can be
parallel plates, holes of any shape in a solid cathode, slits in the cathode,
and spirals (Schaefer and Schoenbach 1990). For microhollow cathode
discharges, initially, cylindrical holes were used to generate the hollow
cathode effect (White 1959, Schoenbach et al 1996, Frame et al 1997).
These geometries have been extended to micro tubes with the anode at the
orifice (Sankaran and Giapis 2002) or inserted through the walls (Adler
et aI2002), and microslots (Yu et al 2003). Paralleling the microholes has
resulted in micro arrays (Shi et al 1999, Park et al 2000, Schoenbach et al
2003, Allmen et a12003, Penache et a12000, Guo and Hong 2003). Adding
microdischarges in series has allowed increasing the light emission (El-
Habachi et a12000, Vojak et al200 1), and may possibly lead to laser emission
(Allmen et al 2003). Common to all these geometries are the dimensions
of the cathode hollow, which are on the order of 100 11m. Cross-sections of
electrode geometries used by the various groups are shown in figure 6.5.2.
Electrode materials range from refractive metals to semiconductors.
Whereas mainly molybdenum has been used for high current (> 1 rnA)
discharges (Schoenbach et al 2003, Kurunczi et a11999, Petzenhauser et al
2003), nickel, platinum, silver and copper were used as the electrode material
for microhollow cathode discharges and discharge arrays at lower currents
(generally in the sub-rnA range for individual holes in microdischarge
arrays) (Allmen et a12003, Park et a12003, Penache et al 2000). The group
at the University of Illinois has early-on concentrated on silicon as material
(Frame et a11997, Chen et at 2002) a material which allows use of micro-
machining techniques. Stainless steel was the choice for micro tube cathodes
(Sankaran and Giapis 2003). Generally, the choice of electrode materials
seems so far to be determined by available fabrication techniques, and the
ability to withstand high temperature operation, rather than being guided
by the physics of cathode and anode fall.
The dielectric material was mica in initial experiments, but was replaced
soon by alumina and other ceramics. In some cases polymers have been used
to generate flexible micro discharge arrays (Park et at 2000, Pen ache et al
2000). Such materials are well versed for discharges in rare gases or rare
gas-halide mixtures, where the gas temperature is relatively low. However,
--- Page 326 ---
Discharges Generated in Spatially Confined Geometries
311
A
a)
-
'" -=."-,,,~ .. ;;- - ... c -- d)
b)
A
C
c) _." ..• " ....... A
,., .... ,., ... ,
••
.••
C
---------
A
e)
A f)
Figure 6.5.2. Various hollow cathode electrode configurations either used for single
discharges or as an 'elementary cell' in arrays. (a) Old Dominion University, USA; Univer-
sity of Illinois, Urbana-Champaign, USA; Hyundai Research and Development Center,
Korea. (b) University of Illinois, Urbana-Champaign, USA. (c) Old Dominion University,
USA; Stevens Institute of Technology, USA; University of Illinois, Urbana-Champaign,
USA; University of Erlangen, Germany; University of Frankfurt, Germany; University
of Dortmund, Germany; Caltech, USA; University of California, Berkeley, USA; National
Cheng Kung University, Taiwan. (d) Institute for Low Temperature Plasma Physics,
Greifswald, Germany. (e) Caltech, USA. (f) Colorado State University, USA
for microdischarges in air the material choices are limited. The high gas
temperatures (",2000 K) in air micro hollow cathode discharges (Block et al
1999) require the use of dielectrics and electrode materials with high melting
points, such as alumina and molybdenum, respectively.
The microholes in such discharge geometries have initially been drilled
mechanically (White 1959, Schoenbach et a11996) or milled ultrasonically
(Frame et al 1997), with hole diameters of >200 !lm. For cylindrical holes
with smaller diameter in metals, laser drilling has been the method of
choice. For the fabrication of large arrays, silicon bulk micromachining
techniques have been successfully used (Chen et aI2002).
6.5.1.2
Array formation of micro discharges
The application of microdischarges generally requires the arrangement of
these discharges in arrays. Such arrays may consist of discharges placed in
parallel or in series, or both. Placing the discharges in parallel allows
plasma layers to form which could be used as flat plasma sources or as
flat light sources. If operated in discharge modes where the current-voltage
characteristic has a positive slope, the discharges can be arranged in parallel
without individual ballast. This includes operation in the predischarge mode
or in an abnormal glow mode.
Parallel operation in the predischarge mode, without individual ballast
has been demonstrated by the group at Old Dominion University (Schoen-
bach et al 1996), the University of Illinois (Frame and Eden 1998, Eden
--- Page 327 ---
312
DC and Low Frequency Air Plasma Sources
et at 2003), the University of Frankfurt and University of Dortmund,
Germany (Pen ache et al 2000), and the National Cheng Kung University,
Taiwan (Guo and Hong 2003). The reference list is by no means exhaustive
(only the first published refereed journal publications or papers in conference
proceedings for each group are listed), since most of the groups, particularly
the group at the University of Illinois, have published extensively on this
topic. Because of the relatively low current required for operation in this
phase, electrode materials and dielectrics do not need to withstand high
thermal loading, and can therefore be fabricated of semiconductor materials
(Chen et a12002, Penache et al2000).
Operation in the range of an abnormal glow discharge requires a
confined cathode surface. This has been achieved by using a second layer
of dielectric material which covers the face of the cathode, and allows the
discharge only to develop inside the cathode hole (Miyake et al 1999).
Another possibility of generating arrays in the abnormal glow mode is to
use a geometry as shown in figure 6.5.2a, where the cathode surface is
confined to the hole. An example of such an electrode structure with limited
cathode area is shown in figure 6.5.2c (Schoenbach et aI1997). A series of 30
microholes are placed along a line, with distances of 350 11m between hole
centers. The cathode area was limited by a dielectric (alumina) to a stripe
250 11m wide. The anode was placed on one side on top of the 250 11m thick
dielectric. The gas was a mixture of 1.5% Xe, 0.03% HCl, 0.06% H2, and
98.41 % Ne. When a voltage of 190 V was applied the microdischarges
turned on one after another until the entire set of discharges was ignited.
When all discharges were on, the current-voltage characteristic turned
positive since all discharges were now operating in an abnormal glow mode.
In the range of operation where the current-voltage characteristic has
a negative slope (hollow cathode mode) or is flat (normal glow mode) it
is also possible to generate arrays by using distributed resistive ballast.
This has been demonstrated by using semi-insulating silicon as the anode
material (Shi et al 1999). The use of multilayer ceramic structures where
each microdischarge has been individually ballasted, with the resistors
produced and integrated into the structure by a thick film process, has
allowed the generation of arrays 13 x 13 microdischarges (Allmen et al
2003).
Arranging the micro discharges in series, rather than in parallel (as was
discussed above) is motivated by the increased radiant excimer emittance.
Since the excimer gas does not reabsorb the excimer radiation, the excimer
irradiance generated by n discharge plasmas along a common axis should
be n times that of a single discharge. A second application for a string of
discharges would be its use as an excimer laser medium. A simple estimate
of the power density in a string of micro discharges indicates that small
signal gains of >O.l/cm are obtainable (El-Habachi et al 2000). First
experiments with two discharges in series have demonstrated doubling of
--- Page 328 ---
Discharges Generated in Spatially Confined Geometries
313
the studied XeCI excimer irradiance (EI-Habachi et al 2000). The stable
operation of three neon discharges in series in a ceramic discharge device
has been demonstrated by Vojak et al (2001). Allmen et al (2003), have
extended such a system to seven sections with an active length of approxi-
mately 1 cm, and have found indications of gains for 460.30 nm transition
of Xe +, making this the first example of a micro discharge optical amplifier.
6.5.1.3
Modes of operation
MHCDs are direct current devices, but are not necessarily restricted to dc
operation. They have been successfully operated in the pulsed mode as
well as in ac and rf modes. Sustaining voltages range from 150 to 500 V,
depending on the discharge current, the type of gas, and on the electrode
material. Lowest voltages are obtained with rare gases, highest voltages are
measured for attaching gases, or mixtures, which contain attaching gases,
such as air. The dc voltage-current characteristics of micro hollow cathode
discharges show distinct regions. An example for such a characteristic is
shown in figure 6.5.3 for a discharge in xenon at 760 torr, together with
•
a
b
c
205~--------------------------------. 50
G-
O)
0>
~ 200
>
0)
0>
....
~
() 6 195
Xe
"'
•
Discharge Voltage
/ ...
D= 250 llm
....
~.
p = 750 Torr
Radiant Power
.1('"
~/~:~~:1-.
................... ~ .. 1:··/ I /"
i
& ••••••••••••• ~
••••• + .......... ,i"",/
I
i a
i b
i C
2 i!
j
3
456
Current (rnA)
7
8
f- 40
r- 30
r- 20
r- 10
0
~
E
....
0)
~
0 n..
C
C\l
'6
C\l
0:::
Figure 6.5.3. (a--c) End-on photographs of microhollow cathode (250 fim) discharges in
xenon at a pressure of 750 torr for various currents. The photographs were taken through
an optical filter, which allowed only the excimer radiation to pass. (d) current-voltage
characteristic of the micro hollow cathode discharges, and VUV radiant power dependent
on current.
--- Page 329 ---
314
DC and Low Frequency Air Plasma Sources
images of the discharge obtained in the ultraviolet at 172 nm. In the
predischarge mode (lowest current, positive slope in the voltage--current
characteristics) and the plasma is confined to the hole. It expands beyond
the micro hole at the transition from the hollow cathode mode to the
normal glow mode. If the cathode surface is limited, the discharge enters
an abnormal glow mode, which in the I-V characteristics is indicated as
increasing voltage with current.
In order to reduce the thermal loading of micro hollow electrodes,
but still operate the discharge at high currents, micro hollow cathode
discharges have been operated in pulsed mode with various duty cycles
(such that the average power was kept below a level which causes thermal
damage). The pulses were monopolar pulses ranging from milliseconds to
nanoseconds. Whereas with millisecond pulses the discharge characteristics
was not different from the dc case (Schoen bach et al 2000), for microsecond
(Adler et at 2002, Kurunczi et at 2002, Petzenhauser et al 2003) and even
more for nanosecond pulses (Moselhy et al 2001b, 2003), the plasma
parameters change strongly. The increase in excimer emission from xenon
and argon discharges when pulses of nanosecond duration were applied
(and for xenon the increase in excimer efficiency) is assumed to be due to
pulsed electron heating (Stark and Schoenbach 2001). While the electron
temperature is increased during the pulse, the gas temperature change is
small as long as the pulse width is on the order of or less than the electron
relaxation time. The shift in the electron energy distribution function to
higher energy causes an increase in ionization and excitation rate coefficients.
This has been shown in pulsed air discharges where the electron density
increased strongly when a 10 ns pulse was applied to the discharge (see
chapter 8).
Besides dc and monopolar pulsed operation, radio frequency operation
has been explored as a method to generate microplasmas at atmospheric
pressure air (Guo and Hong 2003). At frequencies of 13.56 MHz, they
could in pure helium (flowed through a microhollow cathode array) generate
stable discharges at atmospheric pressure. Recently a group at the Colorado
State University has extended this concept to a slotted electrode geometry
(Yalin et al 2003, Yu et al 2003). Stable micro discharges in Ar, Ar-air
mixtures, and in open air have been generated when excited with
13.56 MHz with rf voltages of 50-230 V. The slot cathode dimensions are
200/lm by 400-600/lm deep, and 3-35 cm in length.
6.5.1.4
Plasma parameters
(a)
Electron temperature and electron energy distribution
Measurements of the electron temperature in microhollow cathode
discharges, in rare gases only, have been performed by means of emission
spectroscopy. Based on line intensity measurements in argon an electron
--- Page 330 ---
Discharges Generated in Spatially Confined Geometries
315
temperature of approximately 1 eV has been determined (Frank et aI200l).
The electron temperature in pulsed argon discharges was found to be more
than twice the dc value. The electron temperature in this case was obtained
using information on the temporal development of measured electron densi-
ties in plasmas pulsed with 20 ns high-voltage pulses (Moselhy et al 2003).
This increase in electron temperature, which is correlated to an increase in
electron density, is due to pulsed electron heating (Stark and Schoenbach
2001).
Measurements which provide information on average electron energies
only give us rather low values. However, from the fact that MHCDs are
efficient sources of excimer radiation, large concentrations of high-energy
electrons (in excess of the excitation energy of rare gas atoms) must be
present. That means that the electron energy distribution must be highly
non-thermal. Measurements in the low pressure range confirm this assump-
tion (Badareu and Popescu 1958, Borodin and Kagan 1966). Experiments on
plane parallel electrode hollow cathode discharges were performed by
Badareu and Popopescu (1958) using Langmuir probes. The electron
energy distribution in dry air showed the existence of two groups of electrons,
with mean energies of 0.6 and 5 eV. Borodin and Kagan (1966) determined
with a similar technique the electron energy distribution in a circular
hollow cathode and compared them to that in a positive column. Again,
the results indicated a two-electron group distribution with higher concen-
trations of electrons at high electron energies (> 16 eV) compared to that in
a positive column.
(b)
Electron density
Electron densities in microhollow cathode discharges in argon have been
measured using either Stark broadening and shift of argon lines at 801.699
and 800.838 nm (Penache et al 2003), and the hydrogen Balmer-,B line at
486.1 nm (Moselhy et aI2003). In both cases the measured electron densities
were for dc micro discharges on the order of 1015 cm-3, showing a slight
increase with current. When operated in the pulsed mode, with 10 ns
electrical pulses of 600 V applied, the electron densities increased to
5 x 1016 cm-3 (Moselhy 2003). Electron densities in microhollow cathode
discharges in atmospheric pressure air have been measured using heterodyne
infrared interferometry, a method which is described in chapter 8. In a
MHCD with a hole diameter of 200 11m, with a current of 12 rnA at a voltage
of 380 V, the electron density was found to be 1016 cm -3 (Block et al 1999).
( c)
Gas temperature
The MHCD plasma is a non-thermal plasma, that means that the gas
temperature is much lower than the electron temperature. Gas temperature
--- Page 331 ---
316
DC and Low Frequency Air Plasma Sources
measurements have been performed in rare gas MHCDs, as well as in
air MHCDs by using optical emission spectroscopy (Block et al 1999,
Kurunczi et al 2003) and by means of absorption spectroscopy (Penache
et al 2003). The gas temperature in atmospheric-pressure air MHC
discharges was measured to be between 1700 and 2000 K for discharge
currents between 4 and 12 rnA by evaluating the rotational (0,0) band of
the second positive N2 system (Block et al 1999). The temperature in a
neon MHC discharge (400 torr) was measured to be around 400 K (Kurunzci
et al 2003) at a current of 1 rnA. The temperature was obtained from the
analysis of the N2 band system (using a trace admixture of nitrogen added
to the neon). Absorption spectroscopy (Doppler broadening of argon
lines) has been used by Penache et al (2003) to determine the gas temperature
in argon microdischarges. It was found to increase with pressure from
380K at 50mbar to 1100K at 400mbar. The result indicate that the gas
temperature depends on the type of gas. It is highest for molecular gases,
such as air (2000 K), and lowest for low atomic weight rare gases (slightly
above room temperature). It increases with pressure, but only slightly with
current.
6.5.1.5
Applications of microdischarges
(a)
Microdischarges as ultraviolet radiation sources
The electrostatic non-equilibrium resulting from small size (the cathode
fall of MHCDs is commensurate with the radial dimensions of the
microhole) is the reason for an electron energy distribution with large
concentration of high-energy electrons. This, and the stable operation of
these discharges at high pressure favors three-body processes, such as
ozone generation, and excimer formation. The latter effect has been exten-
sively studied for rare gases such as helium (Kurunzci et al 2001), neon
(Frame et al 1997, Kurunzci et al 2002), argon (Schoenbach et al 2000,
Moselhy and Schoen bach 2003, Petzenhauser et al 2003), and xenon (EI-
Habachi and Schoenbach 1998a,b, Schoenbach et al 2003, Adler et al
2002, Petzenhauser et al 2003) and for some rare gas halide mixtures which
generated ArF (Schoenbach et a12000) and XeCI (EI-Habachi et al 2000)
excimer radiation. Internal efficiencies of up to 8% are reported for xenon
excimer MHCD sources (EI-Habachi 1998b). For rare gas halide mixtures,
efficiencies on the order of percent have been measured (Schoenbach et al
2000). Ultraviolet/vacuum ultraviolet radiant power densities of several
W jcm2 seem to be obtainable over large areas when MHCDs are operated
in parallel.
Applications of excimer light sources, based on microdischarge arrays
are flat panel deep ultraviolet sources for a variety of applications, similar
to those of barrier discharges (Kogelschatz 2004). One application, which
has been pursued at Hyundai Display Advanced Technology R&D Research
--- Page 332 ---
Discharges Generated in Spatially Confined Geometries
317
Center (Choi 1999, Choi and Tae 1999) and at the University of Illinois (Park
et al 2001), is their use in flat panel displays. However, applications of
microdischarges as light sources go beyond excimer lamps and flat panel
displays. First experiments to develop microlasers with a series of micro-
discharges have been reported (Allmen et aI2003).
Besides excimer radiation microhollow cathode discharges have also
been shown to emit line radiation at high efficiencies. Kurunczi et al (1999)
observed intense emission of the atomic hydrogen Lyman-a (121.6 nm)
and Lyman-,8 (102.5 nm) lines from high-pressure microhollow cathode
discharges in neon with a small hydrogen admixture. The atomic emission
is attributed to near-resonant energy transfer processes between the Neon
excimer and H2 • A similar resonant effect in argon microhollow cathode
discharges with small admixtures of oxygen has been reported by Moselhy
et al (2001). The emission of strong oxygen lines at 130.2 and 130.5 nm
indicates resonant energy transfer from argon dimers to oxygen atoms.
( c)
Microdischarges as plasma-reactors and detectors
The high-energy electrons in high-pressure microdischarges assist in the
production of a high-electron density plasma. This is for atmospheric
pressure operation desirable for materials processing and surface modifica-
tion where the micro discharges serve as sources of radicals and ions. Experi-
ments with electrode geometries as shown in figure 6.5.2(c), either in single
discharges or in discharge arrays, have been performed in rare gases and
mixtures of rare gases with molecular gases. Hsu and Graves (2003) have
explored the use of single discharges as flow reactors. Flow of molecular
gases was found to induce chemical modifications such as molecular
decomposition. Maskless etching of silicon and diamond deposition on a
heated Mo substrate has been demonstrated by Sankaran and Giapis
(2001,2003). Surface modifications of polymeric film substrates in a mixture
of argon and 10% air (Penache et al 2002), and fabrication of amorphous
carbon films by adding 1 % of hexamethyldisiloxane (HMDSO) to
atmospheric pressure helium in a microhollow cathode discharge array
with a third biased electrode (Guo and Hong 2003) has been pursued.
Microdischarges have also been used as detectors. Due to its high electron
density (1015 cm-3) and a gas temperature of approximately 2000 K in
molecular gases, the plasma has similar plasma parameters as plasmas
used in analytical spectroscopy. Based on this concept, high pressure
microplasma has e.g. been used as detector of halogenated hydrocarbons
(Miclea et al 2002). Another interesting application has been explored by
Park et al (2002). It was found that the photosensitivity of microdischarges
is such that microdischarges serve as photo detectors where the photocathode
determines the spectral response, and the microplasma serves as an
electro multiplier.
--- Page 333 ---
318
DC and Low Frequency Air Plasma Sources
(d)
Microdischarges as plasma cathodes
One of the major obstacles in obtaining glow discharge plasmas in gases at
atmospheric pressure are instabilities, particularly glow-to-arc transitions
(GAT), which lead to the filamentation of the glow discharge in times
short compared to the desired lifetime of a homogeneous glow. These
instabilities generally develop in the cathode fall, a region of high electric
field, which in self-sustained discharges are required for the emission of
electrons through ion impact. Eliminating the cathode fall, by supplying
the electrons by means of an external source, is therefore expected to prevent
the onset of GAT. Microhollow cathode discharges have been shown to serve
as electron emitters (plasma cathodes) for direct current glow discharges
between plane parallel electrodes. The stabilizing effect of MHCDs has
been demonstrated for rare gas discharges (Stark and Schoenbach 1999,
Park et al 2003, Guo and Hong 2003).
This concept has also been used to generate glow discharges in atmos-
pheric pressure air with dimensions up to cubic centimeters. In a three-
electrode system, as shown in figure 6.5.4, electrons are extracted through
the anode opening at moderate electric fields when the microdischarge was
operated in the hollow cathode discharge mode. These electrons support a
stable plasma between the micro hollow anode and a third electrode. The
sustaining voltage of the microhollow cathode discharge in air ranges from
200 to 400 V depending on current, gas pressure and gap distance. The
-- Electron Density
-
-
Gas Temperature
1.0
'1;- 1.0
/f\\
~: 0.8
II
\
0.8 ~
~
\
~
>-
/
\
~
'1il 0.6
0.6
~
/
,,~
c:
/
"t!
e 0.4 ;;....""'"
........ , 0.4
III
o
m
~
~
UJ
0.2
0.2
Distance from Center [mmJ
Figure 6.5.4. Left: cross-section of a micro hollow electrode geometry with third positively
biased electrode. Superimposed is the photography of a MHCD sustained atmospheric
pressure air plasma. Right: electron density and gas temperature profile of the air
plasma, measured by means of heterodyne infrared interferometry in the middle between
MHCD and the third electrode (anode) (Leipold et a/2000).
--- Page 334 ---
Discharges Generated in Spatially Confined Geometries
319
MHCD current was limited to values of less than 30 rnA dc to prevent
overheating of the sample. The glow discharges with the MHCVD as
plasma cathode were operated at currents of up to 30 rnA, corresponding
to current densities of 4A/cm2 and at average electric fields of 1.25kV/cm.
Electron densities and temperatures have been measured by means of
heterodyne laser interferometry and were found to be on the order of
1013 cm -3, and 2000 K, respectively (Leipold et al 2000). The air plasma
can be extended in size by placing MHCD discharges in parallel (Mohamed
et al2002).
One of the major obstacles in using such dc glow discharges in atmos-
pheric pressure air is the electrical power density required to sustain these
discharges. Operating the discharges in a pulsed mode, with pulses of 10 ns
superimposed on a dc MHCD glow discharge in air, has been shown to
reduce the required power density for the same average electron density
(Stark and Schoenbach 2001). This effect is based on the shift in the electron
energy distribution towards higher energies on a timescale shorter than the
critical time for the development of a glow-to-arc transition.
6.5.2 The cathode boundary layer discharge
The cathode boundary layer (CBL) discharge is a new type of high-pressure
glow discharge between a planar cathode, and a ring-shaped anode separated
by a dielectric, with a thickness on the order of 100 !lm, and with an opening
of the same diameter as the anode (figure 6.5.5) (Schoenbach et al2004). The
diameter of the opening is in the range of fractions of millimeters to several
millimeters. The discharge is restricted to the cathode fall and negative glow,
with the negative glow serving as a virtual anode: the plasma in the negative
glow region provides a radial current path to the ring-shaped metal anode.
This assumption is supported by the measured thickness of the plasma
layer (Moselhy et al2002), which corresponds to the thickness of the cathode
fall plus negative glow, but also by the measured sustaining voltage. For
high-pressure operation in xenon and argon, the pressure in the normal
glow mode was measured as approximately 200 V (Moselhy and Schoen bach
2004), which is on the order of measured cathode fall voltages in noble gases
(Cobine 1958).
Cathode Fall
Negative Glow
Anode
Dielectric
Cathode
Figure 6.5.5. CBL discharge electrode geometry and estimated current density pattern
(Schoen bach et at 2004).
--- Page 335 ---
320
DC and Low Frequency Air Plasma Sources
75
.-...
~ 200
C
7
1.1
0.85
0.67
0.49
u
1-0 =
fFl
fFl
U
400
1-0
A..
760
15.8
6.5
5.1
3.4
1.9
Current (rnA)
Figure 6.5.6 End-on images of CBL xenon discharges in the visible dependent on pressure
and current. The diameter of the cathode is 0.75 mm. The brightness of the images at 75,
200, and 400 torr is for all currents (except the largest one) increased relative to that at
760 torr, in order to better show the pattern structure (Schoenbach et at 2004).
The stability of CBL discharges, which allows us to operate them in a
dc mode, is assumed to be due to thermal losses through the cathode foil,
an effect that is also considered to be the reason for the observed self-
organization in xenon discharges (Schoen bach et al 2004). The plasma
pattern consists of filamentary structures arranged in concentric circles
(figure 6.5.6). The self-organization structures are most pronounced at
pressures below 200 torr, and become less regular when the pressure is
increased.
An important feature of CBL discharges is the positive slope in the
voltage-current characteristics over most of the current range, except for
low current values (figure 6.5.7). This shows that parallel operation of
these discharges is possible without using individual ballast resistors. A
consequence of this resistive discharge behavior is the possibility of
constructing large-area thin (100 ~m) plasma sources.
The experimental studies have so far focused on noble gas operation,
because of the importance of such discharges as flat excimer sources.
Medium- and high-pressure dc discharges in xenon and argon have been
found to emit excimer radiation with efficiencies reaching values of almost
5% in xenon and 2.5% in argon (Moselhy and Schoenbach 2004). However,
operation in atmospheric pressure air seems to be feasible, and would allow
the generation of ultra-thin (on the order of 100 ~m) non-thermal air plasma
layers over large surface areas.
--- Page 336 ---
Discharges Generated in Spatially Confined Geometries
321
450 r-------r-..,..------,
Xenon
400
.wOTan
-> 350
-
CI)
OJ
~ 300
0 >
250
•
200
0.1
• •
1
I I
~
I
II
/'
III 1 III .li
I I
:
! I •
! 1
1 ••
I
•
I .1
I
1
1 • I
~. I
I !
I
I
1
10
Current (mA)
Figure 6.5.7. Voltage-current characteristics of xenon discharges at 400 torr. The charac-
teristics can be divided into three regions. In region I, the discharge behaves as a normal
glow; in region II, the self-organized patterns are observed; region III corresponds to
abnormal glow (Schoenbach et at 2004).
6.5.3 The capillary plasma electrode discharge
The operating principles and basic properties of the capillary plasma elec-
trode (CPE) discharge are much less well understood and the discharge has
been much less researched than the MHC discharge. The basis for the atmos-
pheric-pressure operation of the capillary plasma electrode (CPE) discharge
is a novel electrode design (Kunhardt and Becker 1999). This design uses
dielectric capillaries that cover one or both electrodes of a discharge
device, which in many other aspects looks similar to a conventional dielectric
barrier discharge (DBD) as shown in figure 6.5.8. However, the CPE
discharge exhibits a mode of operation that is not observed in DBDs, the
so-called 'capillary jet mode'. Here, the capillaries, with diameters that
range from 0.01 to 1 mm and length-to-diameter ratios of the order of
~eee;e~
~eeeee
Dielectric
Electrode
~
Dielectric
-..
/' "-..,"',.-
Figure 6.5.S. Schematic diagram of a capillary plasma electrode (ePE) discharge
configuration.
--- Page 337 ---
322
DC and Low Frequency Air Plasma Sources
10: I, serve as plasma sources, which produce jets of high-intensity plasma at
atmospheric pressure under the right operating conditions. The plasma jets
emerge from the end of the capillary and form a 'plasma electrode' for the
main discharge plasma. Under the right combination of capillary geometry,
dielectric material, and exciting electric field, a stable uniform discharge can
be achieved. The placement of the tubular dielectric capillary(s) in front of
the electrode(s) is crucial for the occurrence of the 'capillary jet mode' of
the CPE discharge. In fact, the CPE discharge displays two distinct modes
of operation when excited by pulsed dc or ac. When the frequency of the
applied voltage pulse is increased above a few kHz, one observes first a
diffuse mode similar to the diffuse glow described of a DBD as described
by Okazaki et al (1993). When the frequency reaches a critical value
(which depends strongly on the length-to-diameter value and the feed gas),
the capillaries 'turn on' and a bright, intense plasma jet emerges from the
capillaries. When many capillaries are placed in close proximity to each
other, the emerging plasma jets overlap and the discharge appears uniform.
This 'capillary' mode is the preferred mode of operation and has been char-
acterized in a rudimentary way for several laboratory-scale research
discharge devices in terms of its characteristic electric and other properties
(Kunhardt et al 1997a,b, 1998, Panikov et al 2002, Moswinski et al 2003):
peak discharge currents of up to 2 A, current density of up to 80 mA/cm2,
E/p of about 0.25 V/(cm torr), electron density ne above 1012 cm-3 (which
is about two orders of magnitude higher than the electron density in the
diffuse mode of operation), power density of about 1.5W/cm3 in He and
up to 20W/cm3 in air. Using a Monte Carlo modeling code (Amorer
1999), the existence of the threshold frequency, which depends critically on
the length-to-diameter ratio of the capillaries and dielectric material, has
been verified (Kunhardt et al 1997a,b). The model also predicts relatively
high average electron energies of 5-6 e V in the 'capillary' mode.
CPE discharges have been operated at atmospheric-pressure in He, Ar,
He-N2' He-Air, He-H20, Nr H20, and air-H20 gases and gas mixtures
and discharge volumes of more than 100 cm3. The electron density was
calculated from the current density, the power input, and an estimate of
the electron drift velocity as well as measured using a mm-wave inter-
ferometer (Amorer 1999) operating at 110 GHz. Measurements were done
in a He discharge in the diffuse mode and in the capillary mode. As can be
seen in figure 6.5.9, the transition from the diffuse mode to the capillary
mode is accompanied by a drastic increase in the electron density from
about 1010 to 1012 cm-3.
Recently, a spectroscopic analysis of the emission of the unresolved N2
second positive band system from a CPE discharge in atmospheric-pressure
air was carried out. Measurements were done for various discharge powers in
two geometries. In one case, the emissions arising from inside the capillary,
presumably the hottest part of the plasma, were analyzed. In the other
--- Page 338 ---
Discharges Generated in Spatially Confined Geometries
323
175.---------__ ------------------~~~~~_.
Capillary Mode
Diffuse Mode
•
•
150
"I-
E
125
u
0
"'0
....
100
-
~
I/)
75
c
~
c
50
e i
25
iii
o+--~·'''·'· ~,·,·~·~··~·~·-·~··~·r·-·-·~·-·-·-·r·-·-·~··-·~I_.--~--._--~~
o
5
10
15
20
25
30
Input Power (arb. units)
Figure 6.5.9. Measurement of the electron density in a CPE discharge in He as a function
of power input. The transition of the discharge from the diffuse mode to the capillary mode
with a corresponding drastic increase in the electron density is clearly apparent.
arrangement, the emissions perpendicular to the axis of the capillary,
presumably a 'colder' plasma region as the plasma jet emerging from the
capillary is beginning to spread out spatially, were studied. The results
shown in figure 6.5.10 reveal higher rotational temperatures in the plasma
g
550
e
::l
500
i a
~
450
iii
400
~ ----
c
0
~
~ 350
.
./
a:: ..
~dlCUlar
to the capillary Axis
Z
300
•
0.2
0.3
0.4
0.5
Input Power per Capillary (W)
Figure 6.5.10. Rotational temperatures ofN2 in a CPE discharge in atmospheric-pressure
air obtained in two geometries from a spectroscopic analysis of the emission of the N2
second positive band system.
--- Page 339 ---
324
DC and Low Frequency Air Plasma Sources
inside the capillary rising from about 350 to 500 K at the highest power level
studied (slightly less than 0.5 W input power per capillary). In contrast, the
measurements made perpendicular to the capillary axis show a rotational
temperature of 300 K (essentially room temperature) at the lowest power
setting rising to only about 400 K at the highest power level.
While a full understanding of the fundamental processes in the CPE
discharge on a microscopic scale has not been achieved, it seems that the
capillaries act as individual high-density plasma sources. The initial step is
the formation of a streamer-like discharge inside each capillary, whose
properties are critically determined by their interaction with the dielectric
walls of the capillaries.
6.5.4 Summary
When the plasma size decreases, plasma-surface interactions gain in impor-
tance due to the increase of the surface-area to volume ratio. For microglow
discharges, this means that the processes in the cathode fall dominate the
discharge even more than in common glow discharges. This allows us to
generate plasmas with electron energy distributions which contain large
concentrations of high-energy electrons, at low gas temperatures. The
energy losses to the surfaces surrounding the plasma seem to be the reason
for enhanced plasma stability. Microdischarges have allowed us to generate
stable glow discharges in atmospheric-pressure gases. The high-pressure
operation, and a relatively large concentration of high-energy electrons
from the cathode fall of the discharge, favors three-body reactions, such as
excimer formation. Electron densities in dc microdischarges have been
found to be on the order of 1015 cm-3 (rather independent of gas type), gas
temperatures range from values close to room temperature to approximately
2000 K (lower for noble gases, higher for molecular gases). For the air plasma
community the most attractive feature of these microdischarges seems to be
the application as plasma cathodes, which support larger volume dc
atmospheric pressure air glows, and the application as plasma reactors for
chemical and bacterial decontamination of air. But other applications,
such as cold atmospheric air plasma jets, generated by flowing atmospheric
pressure air through these microdischarges, are emerging. This research
field is still young and promises rewards for researchers in non-equilibrium,
high pressure glow discharges.
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6.6 Corona and Steady State Glow Discharges
6.6.1
Introduction
The negative corona is one of the oldest electrical discharges in ambient air.
Usually, its operation is limited towards higher currents by transition to a
spark. Recent progress in a special discharge technique resulted in realizing
--- Page 344 ---
Corona and Steady State Glow Discharges
329
a glow discharge in ambient air (Akishev et all99l), which has a cathode in
the form of a pin array and exists at much higher electric current per pin. It is
well known that with increase of gas pressure a glow discharge becomes
unstable against spark formation. Until now it has been the common opinion
that the classical glow discharge may exist only at low gas pressures. Actu-
ally, detailed studies on the mechanisms of glow discharge instabilities
resulted in a substantial extension of the gas pressure range (up to about
1 atm), where a stable glow discharge can be maintained. Evidently, an alter-
native way to realize the glow discharge could be stabilization of the tradi-
tional corona. Now both these approaches (increase of pressure in the
classical glow discharge and increase of current in the traditional negative
corona discharge) were pursued, and transitions between negative corona,
glow and spark forms of discharge were studied. One of the purposes of
this section is to present a modern understanding of relationships between
the mentioned forms of discharges at atmospheric pressure.
The material in this section is organized as follows: first, the methods to
control negative corona parameters are described, then properties of sub-
and atmospheric pressure glow discharge (APGD) in air flow and results
of studies on transitions between corona, glow and spark forms are reported,
and, finally, pulsed diffused discharge techniques are discussed briefly.
Particular attention will be paid to basic physical processes lying behind
the observed phenomena.
6.6.2
Methods to control negative corona parameters
Upon applying a step of high voltage (that is, over an inception one), the
ignition of a negative corona is accompanied by a sharp peak of discharge
current with duration of a pulse of about 10-7 s. For electronegative gases
(air, O2, etc.), in which electrons are quickly converted to negative ions,
the pulsed regime of the corona with regular spikes of discharge current is
established. The current pulses are named Trichel pulses. It is well known
(Cross et al 1986) that the amplitude of established Trichel pulses is much
lower than of the first pulse. The total voltage concentrated around the pin
controls the dynamics of the first pulse. The extremely strong electron
avalanches create a wave of growing positive charge that moves rapidly to
the cathode (Morrow 1985, Cernilk and Hosokawa 1991, Napartovich et al
1997). As a result, the cathode layer and a plasma region are formed in the
generation zone. At this moment, the corona current has a maximum
value. On the anode this current is closed by the displacement current. In
the following pulses, the voltage, which can drop within the pin vicinity,
diminishes due to appearance of negative charge in the drift zone. Therefore,
these pulses are lower as it is seen in figure 6.6.1 (Akishev et al 1999). As
expected, the experiments revealed that the amplitude of the first Trichel
pulse grows with increasing the step of applied voltage (see figure 6.6.2). In
--- Page 345 ---
330
DC and Low Frequency Air Plasma Sources
20000
<'
:I.
'-'
.....
10000
0
20000
,......
-<
:I.
'-'
.....
10000
0
1
Experiment
2
3
4
Theory
3
Time (l1s)
5
5
Figure 6.6.1. The establishment in time of Trichel pulses in negative corona in ambient air.
Pin to plane distance 7 mm, tip curvature radius 0.057 mm, voltage applied Uo = 6 kV.
contrast, the amplitude of the regular Triche1 pulse diminishes with an
increase in the applied voltage (figure 6.6.2). The amplitude of the first
pulse is greater for shorter spacing, and can reach 0.25 A (figure 6.6.2).
Using squared voltage pulses of length shorter than the duration between
the first and second pulses T12 and a repetition period long enough to clear
300
225
<-
E!
150
'-'
<'
75
~
hac = 15 nun
Ambient air
'0.... hac =22nun
, hac = 30 nun
Cathode
rc =O.I'mm
7
9
11
13
15
-17
,19
:21
23
U(kV)
Figure 6.6.2. Amplitude of the first Trichel pulse versus height of applied voltage step for
different inter-electrode spacings.
--- Page 346 ---
Corona and Steady State Glow Discharges
331
4,-----------------------------,
Ambient air
3
1
h
Cathode (re = 0.1 MM)
OL---------------------------~
012
3
h/r
Figure 6.6.3. Influence of dielectric screens on amplitude of regular Trichel pulses at the
near-inception applied voltage.
the space from negative charges, one can realize a periodical pulse regime
with the height of each pulse of about 1 A.
This auto-pulsing mode of the negative corona in air is observed at low
currents of this discharge. This regime can be useful for different practical
applications because the current amplitude of a single pulse is far in excess
of the average corona current. Experimental studies were carried out on
the influence of geometric and gas-dynamic factors and on amplitude and
repetition frequency of Trichel pulses, to find out the main experimental
parameters controlling them (Akishev et al 1996). Generally, it is known
that the amplitude of the regular Trichel pulse rises as the radius of pin
increases (see, for example, Scott and Haddad 1986). Akishev et at (1996)
have shown that in dependence on parameter variation a strong increase
of the Trichel pulse amplitude, as well as full suppression of them, can be
realized for a fixed pin radius.
It was found for ambient and dry air that the amplitude of the regular
Trichel pulse depends strongly on the divergence of current lines in the
vicinity of the corona pin and on the aperture of the drift region of the
corona. To change the geometry of current spreading near the pin, dielectric
shields around the pin with variable parameters were employed. Using
different shapes of the anode and restriction of the corona cross section
modified the geometry of current lines in the drift region. Some results
illustrating effects produced by these means on the amplitude of the regular
Trichel pulse are shown in figures 6.6.3 and 6.6.4. Restriction of the corona
cross-section also influences the repetition frequency of Trichel pulses. Some
experimental data are shown in figure 6.6.5. One can see in figures 6.6.4 and
6.6.5 that restriction of the corona space with a dielectric tube results in
diminishing the peak corona current and in the rise of the repetition
--- Page 347 ---
332
DC and Low Frequency Air Plasma Sources
3
2.S
<'
2
e
'-'
-< I.S
1
O.S 0
Anode
Anode
V~
2r~6mm IOmm
40
2
80
J (10-6 A)
Anode
Anode
c=:=:::J C==::J
DID
3.5mm
4
120
Figure 6.6.4. Amplitude of regular Trichel pulses versus corona current for various corona
geometries.
frequency. Figure 6.6.6 demonstrates how the shape of the anode influences
the repetition frequency of Trichel pulses. The current profile on the anode
can also be broadened by use of a resistive anode. An effect of this resis-
tance-induced current expansion in the drift zone on the amplitude of the
regular Trichel pulses is illustrated in figure 6.6.7.
An alternative method to influence the near-pin region of the corona is a
powerful jet stream of air directed through a plane mesh anode towards the
tip of the pin. The amplitude of the Trichel pulses and repetition period grew
with increasing gas stream speed (see figures 6.6.8 and 6.6.9). This effect can
be explained by an extension of the generation zone in the vicinity of the
corona pin produced by the gas jet stream, which is equivalent, in some
degree, to the increase of the pin radius known to enhance pulse amplitudes.
1000
Anode
Ambient air
700
~ 11
2r~10mm
Cathode
Anode
=
400
Cathode
100~~------~~------~----~
S
2S
4S
J (10-6 A)
Figure 6.6.5. Frequency of regular Trichel pulses versus corona current for restricted and
free-space coronas.
--- Page 348 ---
Corona and Steady State Glow Discharges
333
600
400
200
10
20
30
40
J (10~ A)
Figure 6.6.6. Repetition frequency of Trichel pulses for different shapes of anode.
hac = 35mm, rc = O.08mm, ambient air. 1, pin-plane geometry; 2, pin inside of semi-sphere.
The presented experimental results demonstrate an opportunity of
active control of parameters of regular Trichel pulses by gas-dynamic and
geometric factors without changing the pin radius.
Akishev et al (1996) reported on a hysteresis in the voltage--current
characteristics of the negative corona in the auto-pulsing regime. The
6 "0....
AnQd!:l
Metallic anode
'0.... Resistive anode
4.5
p = 500 kOhm*cm
Cathode
rc=O.lmm
<'
3
hac h7mm
a
'-'
Ambient air
<
1.5
0 0
20
40
60
80
100
120
J (10~A)
Figure 6.6.7. Amplitude of regular Trichel pulses versus corona current for metal and
resistive anodes.
--- Page 349 ---
334
DC and Low Frequency Air Plasma Sources
4
3
Ambient air
Cathode-
rc = 0.057 rom
Anode (mesh)
Il O-
Il Gas flow
lL-~ ________ :h~~e=~l~O~rom=:-.------~--~
OL---------~----------~--------~
o
~
~
m
V (mfs)
Figure 6.6.8. Amplitude of regular Trichel pulses versus longitudinal gas flow velocity.
experiment showed that the average corona current in this regime depends on
the direction of change of the applied voltage (figure 6.6.10). Figure 6.6.11
demonstrates the increase of the upper current of the hysteresis region with
gas pressure. While the form and repetition frequency of Trichel pulses can
be satisfactorily explained by numerical modeling (Napartovich et al 1997,
Akishev et al 2002b), the phenomenon of hysteresis of this regime reflects
complicated physics in the generation zone, which still cannot be described
adequately.
6.6.3 DC glow discharge in air flow
The first report on observation of steady glow discharge in transverse air flow
at atmospheric pressure (Akishev et al 1991) was the result of long-term
600
~ 400
"" 200
Cathode
Il O~
o Gas flow
Anode (mesh)
rc = 0.057 mm
hac = lOmm
Ambient air
'0.... V= 5 M/c
'n.. V = 100 M/c
O~----~------~---L~~--~~~
o
10
20
30
40
J (10-6 A)
Figure 6.6.9. Frequency of regular Trichel pulses versus!longitudinal gas flow velocity.
--- Page 350 ---
Corona and Steady State Glow Discharges
335
150
Anode
100
Cathode
--
-<
"I
~
...
'-'
..,
50
o ~~~~=-----~--------------~--------~
2
5
8
U(kV)
Figure 6.6.10. Hysteresis in voltage--current characteristic (VCC) of negative corona. 'upper is
the current at pulses disappearance on the growing branch ofthe VCC, "ower is the current for
appearance of Trichel pulses at diminishing voltage, hac = 7 mm, rc = 0.08 mm, ambient air.
studies on glow discharge properties at moderate pressures summarized in a
paper of Napartovich and Akishev (). The following features were
recognized as the most important for approaching the atmospheric pressure
range: cathode sectioning with individual ballast resistors for each cathode
--
-<
~
...
'-' ..
l ..
..:
140
0
100
60
20~----~--~------~~--~--~--~--~~--~
o
200
400
P(fOIT)
600
800
Figure 6.6.11. Current of disappearance of Trichel pulses in pin-plane corona versus gas
pressure. hac = IOmm,"c = 0.06mm, ambient air.
--- Page 351 ---
336
DC and Low Frequency Air Plasma Sources
segment and fast gas flow. Cathode sectioning serves to elucidate transition
from a high current density at the cathode surface to a required lower current
density in the discharge volume. Ballast resistors limiting the current on each
segment stabilize the glow discharge against arcing. The gas flow serves to
remove heated gas from the discharge gap and additionally stabilizes the
discharge by restriction of the residence time of gas in a region with a high
electric field.
Sectioning of a cathode makes the spatial structure of a glow discharge
near the cathode rather complicated. A transient region appears where the
separate current channels originated from different cathode elements are
expanding and combining with each other. The cathode is a periodic array
of sharp pins, and the anode is a flat plate. In the discharge structure
inside one cell of the nearly-periodical array, five regions can be distinguished
known from the classical glow discharge at low gas pressures: a cathode
layer, a negative glow, a Faraday dark space, a plasma column, and an
anode layer.
The well-known dependence of the cathode current density of a normal
glow discharge on the gas density Uc >=:;j N 2) retains its validity up to the
pressure of the order of 1 atm. At a fixed cathode area, the current per pin
grows with pressure. It was shown by Akishev et al (1984) that at higher
pressures the amplitude of the current per pin is limited by some instability
of the cathode layer resulting in the formation of a cathode spot differing
from known low pressures arc spots (Mesyats and Proskurovsky 1989).
Non-uniform dielectric films, which are usually present on a metal surface,
can trigger this instability. If the current per pin exceeded this critical
value, an intermediate cathode spot forms with a current density of the
order of 300 A/cm2 • With further current increase, this intermediate spot
transforms to the arc spot (Akishev et al 1985a) destroying the cathode
surface. Existence of the limiting current per pin determines the allowable
size of the pin at a given pressure.
The negative glow appears as a result of the relaxation of suprathermal
electrons with energies nearly corresponding to the cathode voltage drop, Vc.
The thickness of the negative glow region is nearly inversely proportional to
pressure, and is on the order of fractions of 1 mm for ambient air. In the
Faraday dark space the plasma density decreases from the high value
caused by the non-equilibrium ionization by the cathode electron beam to
the value corresponding to the balance of ionization, attachment, detach-
ment and recombination processes. The size of this zone is determined by
the rate of the plasma decay and by plasma transport processes. For an air
plasma, the size of this zone turned out to be on the order of a few centimeters
at pressure p = 100 torr (Akishev et all981). With rising pressure the length
of this transition region is rapidly decreasing, because a three-body attach-
ment process with the rate proportional to /
governs the plasma decay.
At atmospheric pressure this length is about of 1-2mm. Respectively, at
--- Page 352 ---
Corona and Steady State Glow Discharges
337
"" •
Figure 6.6.12. Photograph (negative) of the discharge in room air; the discharge current
per pin is 39 1lA.
atmospheric pressure the discharge in the gap of length about 1 cm consists
mostly of a plasma column with an electric field strength determined by
the local plasma density balance.
Neighboring plasma columns in the multi-pin cathode construction
overlap at the distance approximately equal to the pin array period. Provided
this period is less than the discharge gap, the major part of the discharge
space is occupied by combined plasma columns with weak modulation of
its properties. Figure 6.6.12 shows the photograph of this discharge taken
in the direction of the air flow. In this device only a single row of pins trans-
verse to gas flow was installed. In general, the multi-pin cathode was
arranged in a form of rectangular blocks with some tens of the pins ballasted
individually. Parameters of this plasma column in dry and humid air were
measured and numerically simulated for fast-flow multi-pin glow discharges
(Akishev et aI1994a).
Although the anode layer occupies a relatively small fraction of discharge
volume, it is of great importance for discharge stability. The voltage-current
characteristic of an anode layer at higher gas pressure has a negative slope
(Pashkin 1976). As a result, it is unstable to anode spot formation with a
high current density and elevated electric field (Dykhne and Napartovich
1979). The plasma layer adjoined to the negatively charged anode sheath
plays the role of a distributed ballast resistor that stabilizes the spot-forming
instability. Two-dimensional numerical simulations by simultaneous solution
of plasma transport equations and the Poisson equation (Dykhne et a11982,
1984) for the glow discharge in nitrogen and air demonstrated that anode
spot formation is followed by the contraction of the current channel uniformly
through the discharge gap. This model did not include any mechanism of the
bulk plasma instability. The formation of anode spots in glow discharges in
mixtures ofN2 and O2 at a very low discharge current was observed experimen-
tally (Akishev et al 1982). Because of a low discharge current density it is
improbable that any bulk plasma instability may play some role. The time
for the appearance of anode spots in the experiment was of the order of that
calculated later by Dykhne et al (1984). Since the plasma in the plasma
--- Page 353 ---
338
DC and Low Frequency Air Plasma Sources
column is stable, the formation of the anode spot results in a situation where the
high plasma density and the high electric field strength are localized in the same
space. Conditions for triggering plasma instability are realized in this region
earlier than anywhere else. Then the plasma density will grow further because
of the instability and this object will propagate into the bulk of plasmas,
forming a bright filament.
Special experiments with plasma perturbations produced by an auxiliary
pulsed discharge demonstrated high stability of the bulk plasma (Akishev
et aI1985b). It turned out that any perturbation created, decayed quickly.
However, this perturbation can initiate the formation of the anode spot.
Thus this spot serves as an embryo for filament growth.
Akishev et al (1987) made special arrangements to study the evolution of
a filament under controlled conditions. Filaments propagating from the
anode and from the cathode were studied. The influence of a distributed
resistance of the anode on the filament evolution was also explored. A simpli-
fied theory was formulated which satisfactorily describes the propagation of
the filament as a function of its length. The filament growth time was found
to be of the order of 100 IlS. This indicates that a fast gas flow can prevent its
formation.
The knowledge gained in these studies on the glow discharge in air at
moderate pressures served as a basis for the development of non-thermal
plasma sources in atmospheric pressure air, which were successfully applied
for pollutant removal and surface treatments (Akishev et al 1993a, 1 994a,
2001, 2002a, Napartovich et aI1993a,b, Vertriest et al 2003). A photograph
(negative) of the discharge in the steady-state glow regime is shown in figure
6.6.12. Depending on the gas-flow velocity, the spacing length and the electrode
construction (form of the individual pin, shape and resistance of the anode)
electric power densities in glow discharge may vary in the interval 30-500 W /
cm3, which are values that are much higher than those obtained in corona
discharges.
6.6.4 Transitions between negative corona, glow and spark discharge forms
To get a clear understanding of how the dc glow discharge in flowing gas
relates to known electric discharges at atmospheric pressure, it is important
to explore how this form transforms to the known corona and spark
discharges under proper variation of parameters. Such studies were
performed for single-pin as well as for multi-pin cathode configurations.
6.6.4.1
Single-pin to plane discharge
As a first step, the peculiarities of the voltage--current characteristics (VCC)
of the low current discharge between a single cathode pin and an anode
plate in air at atmospheric pressure were explored. Contrary to the known
--- Page 354 ---
Corona and Steady State Glow Discharges
339
experimental studies of other authors (see review article by Chang et aI1991),
a very large ballast resistor for the cathode pin was taken in the experiments
(R ~ 20 Mn) in order to observe the corona-to-glow discharge transition
and to avoid the spark discharge. Fast circulation of gas through the
inter-electrode gap prevents the local overheating of gas in the vicinity of
electrodes and intensifies the turbulent diffusion in the bulk of corona. There-
fore, it is a very effective method for stabilization of the diffusive mode of a
negative corona. The large ballast resistor is also an effective stabilizer at
small gas flow velocities. Use of special procedures for perfecting the shape
of electrodes and gas-dynamic stabilization of the near-electrode regions of
the corona led to a dramatic increase of the threshold current for sparking,
and resulted in a new current mode of discharge, interposed between
corona mode *nd spark mode. The typical reduced VCC of the discharge
in transverse fl0fv 'of air at atmospheric pressure is presented in figure
6.6.13 for metitllic Jnd /resistive anodes. The reduced electric field in the
near-anode region/risel with current and reaches a critical value at some
critical current I). 1he~~fter the ionization and detachment processes in
the drift zone become' more intense. This results in the formation of a
quasi-neutral plasma. As a consequence, the electrons make a contribution
(that will grow more and more with increasing total current) to the charge
transfer through the drift zone. In this way, the corona discharge has
turned into a glow discharge (Akishev et aI1993b).
160
Figure 6.6.13. Experimental reduced vee for pin-plane construction in transverse air
flow, h = 10.5 mm, pin curvature radius 0.06 mm, p = 750 torr, gas flow velocity 65 m/s.
--- Page 355 ---
340
DC and Low Frequency Air Plasma Sources
Let us designate II as the threshold current for the corona-to-glow
discharge transition and /z as the threshold current for the glow discharge-
to-spark transition. The discharge mode is the classical negative corona, if
the current is lower than II' The gap between the electrodes is dark in this
case. There is a negative space charge in the bulk between electrodes owing
to the negative ions. The negative point-to-plane corona at the discharge
current lower than nearly 120llA generates regular Trichel pulses. The
typical repetition frequencies for the Trichel pulses were in the range 10-
50 kHz. The pulseless corona was observed for currents in excess of 120 IlA
and lower than II' Parametric dependences of II are illustrated in figure
6.6.14 for a metallic plate anode. The critical current grows with gas flow
velocity and spacing length.
Once the amplitude of the current has reached the value II, the transition
from the negative corona to the glow discharge occurs. In this regime, a diffu-
sive glow column is formed near the axis of a pin-plane discharge. The
current of the glow discharge is steady and has no pronounced modulation
in time. The principal difference between the glow discharge and the negative
corona is the existence of quasi-neutral plasma in the bulk of the APGD. The
dominant current carriers in the glow mode are free electrons instead of nega-
tive ions in the case of the negative corona. If the amplitude of the current
surpasses the critical value /Z, the discharge turns into the non-stationary
regime. In this regime a lot of irregular bright and fine sparks are observed
750
500
250
Corona - to - glow discharge transition
(metallic anode)
),.,.,.,
'------~-..
/
.
, //./
...................... : ...................... ;
,,,""
.
•
x
• •
......... ;
V=OmJs
V=12mJs
V=36mJs
V=65mJs
O+-~~~~~~~~~-r;-~~~~~~~~~~-r~~
o
5
10
15
h,mm
20
25
30
Figure 6.6.14. Critical current of corona discharge, II, corresponding to appearance of
glow discharge within pin-plane gap versus inter-electrode gap length, h. Ambient air at
atmospheric pressure. Anode is metallic plate.
--- Page 356 ---
1000
750
"i
_N 500
250
0
Corona and Steady State Glow Discharges
341
Glow discharge - to - spark transition
(metallic anode)
..
H"'H"H"~'.""","-_________
"
....
.------'-----,
0
•
..
..... ~ .... ,-, ...... ,.' ....... : ..
:
~
'YIHHHHH
5
10
··········1····················
......... !
.
x"
•
15
h,mm
Ii
X
•
20
••••••••• H •••••••••
25
•
V=Om's
x V=12m's
•
V=36m's
•
V=65m's
.• HHHHH
30
Figure 6.6.15. Critical current of glow discharge, lz, corresponding to appearance of spark
within pin-plane gap versus inter-electrode gap length, h. Ambient air at atmospheric
pressure. Anode is metallic plate.
in the gap, and the discharge current exhibits drastic irregular changes in
time. Traditionally, spark formation was observed in the corona discharge
prior to its transition to the recently revealed glow discharge mode (Akishev
et aI1993). Special research on the scenarios of corona-to-spark transition
is described in this book in section 2.5.2. Parametric dependences of h
corresponding to glow discharge-to-spark transition are illustrated in
figure 6.6.15 for the metallic anode plate. It is seen that the gas flow velocity
is the most important factor efficiently stabilizing the glow discharge. By
replacing the metallic anode by a resistive plate the critical current for
glow discharge-to-spark transition can be further increased about two to
five times. Further studies inspired by an idea to diminish the current density
at the anode axis, in order to improve glow discharge stability against
sparking, resulted in the development of practical recommendations
demonstrating their fruitfulness (Akishev et al 2001). Experimental data
showed that the local current density on the anode could be decreased by
shaping the anode surface, by using a resistive anode material, by using
specific-shape cathode pins and by applying a gas flow.
6.6.4.2 Multi-pin to plane discharge
Historically, corona and glow forms of the discharge were studied separately:
classical glow discharges were observed in low-pressure gases, whereas
--- Page 357 ---
342
DC and Low Frequency Air Plasma Sources
corona discharges were observed in high-pressure gases, specifically in
atmospheric pressure air. The glow discharge is characterized by a high
value of the reduced electric field E / N in the inter-electrode gap. This field
is sufficiently high for producing intense ionization of a gas resulting in the
gap filling with quasi-neutral plasma. In the case of a negative corona, the
reduced field in the gap is much lower, and there is a negative space charge
in the major part of the gap (ion drift region).
A special electrode system with a multi-pin cathode and a flat metal
anode was made to investigate the transition from a negative corona to a
glow discharge in air at atmospheric pressure (Akishev et al 2000). The
pins were stainless-steel needles, 0.5 mm in diameter, tapered to a cone
with a tip curvature radius of Rc = 0.06 mm. 52 needles were uniformly
distributed over an area of 1 cm x 4 cm in four rows of 13 needles in each.
The distance d between needles (i.e. the spatial period of the cathode struc-
ture) was equal to 3.5 mm and was small compared to the distance between
their tips and the anode, h = 5-20 mm. In this case, the current density in the
negative-corona gap increases substantially (by nearly a factor of 3(h/ d)2) in
comparison with the pin-plane configuration, and the transition from the
corona to glow discharge occurs at a relatively low current through each pin.
In order to ensure a stable diffusive regime of the negative corona, the
high voltage to each needle was supplied through a high-resistance load:
R = ",2 MD. In addition, the anode plate was connected to a high-voltage
supply through a 0.2 MD resistor. The stability of the corona against its tran-
sition to a spark was also ensured by an air flow through the discharge; the
cathode unit was oriented with the longer side perpendicular to the air flow.
A typical flow velocity was on the order of several tens of meters per second.
Along with recording I-V characteristics, the discharge was photo-
graphed in the direction transverse to the air flow. If the discharge is in the
corona regime, only the needle ends are luminous, whereas the inter-
electrode gap is hardly visible and the anode is dark. The glow discharge,
on the other hand, is diffuse and rather uniform, although the discrete
structure of the plasma column caused by the discrete structure of the
multi-pin cathode is also clearly seen (figure 6.6.12). Figure 6.6.16 shows a
typical reduced I-V characteristic of the discharge under study. Here, the
ratio 1/ U (instead of the total discharge current) is plotted versus the
discharge voltage U, I being the discharge current per pin.
In the reduced I-V characteristics, we can distinguish two segments (the
first in the region of initial corona currents and the second in the region of
high currents corresponding to the regime of a developed glow discharge),
in which the reduced current is a nearly-linear function of the voltage. It is
seen that in the glow discharge the current increases with voltage much
more steeply than in the corona regime. This is explained by the increasing
role of ionization (which depends strongly on the field) in creating the
conductivity in the inter-electrode gap of the glow discharge.
--- Page 358 ---
6
4
:::l
:::::
2
4
6
Corona and Steady State Glow Discharges
343
I .
8
10
12
14
16
18
U (kV)
,
, . , . . ,
20
I ,
22
24
Figure 6.6.16. Reduced /-V characteristic of the mUlti-pin to plane discharge in room air
(/ is the current per pin). The points correspond to the experiment; the solid and dashed-
and-dotted lines correspond to the calculations for relative humidity of 30 and 65%,
respectively.
The kink point of the reduced 1-V characteristics can be considered as a
critical voltage corresponding to the transition of the corona to a glow
discharge. Near this point of the I-V characteristic, a luminous thin sheath
appears on the anode. This evidences formation of the anode sheath,
which is characteristic of a glow discharge. At voltages higher than the
critical one, the gap luminosity increases sharply with the current and the
discharge exhibits more and more features typical of glow discharges.
Let us define a threshold 1\ for the transition from the corona to a glow
discharge as a moment when the luminous anode sheath becomes visible.
Figure 6.6.17 shows the dependence of the threshold current on the inter-
electrode distance h. A similar dependence of the threshold current h for
the transition from the glow discharge to a spark is also shown. Hence, the
current range in which a uniform glow discharge at atmospheric pressure
can exist is bounded by two curves 1\ (h) and h(h). Note that this range
may be extended substantially by using gas-dynamic effects and anodes of
special design.
A 1.5-dimensional numerical model of the discharge described in
section 2.5.2 was employed for modeling corona-to-glow discharge transition
in multi-pin-to-plane geometry for humid air. The model includes the
--- Page 359 ---
344
DC and Low Frequency Air Plasma Sources
80'---~~---r----r----r----~--~----~--~---'
60
,~ 40
-
20
O;---~-----r----r----r----~--~----~--~--~
o
5
10
15
20
h (mm)
Figure 6.6.17. Threshold currents II (curve I) and h (curve 2) per pin for the transition
from the corona to a glow discharge and from the glow discharge to a spark, respectively,
as functions of the inter-electrode distance h.
ionization, three-body attachment of electrons to an oxygen molecule,
detachment, and ion-ion recombination. The presence of water vapor in
air was taken into account by introducing an additional attachment rate
caused by three-body attachment to oxygen with the participation of water
molecules acting as a third body. In these calculations, the equivalent
radius of the discharge at the anode was determined from the discharge
area per pin.
The total area was
calculated by the
formula
S = So + 2a(a + b)h, where So is the area enveloped by the contour drawn
through the edge pins, 2(a + b) is the circumference of this contour, and a
is a phenomenological parameter (a = 0.5). The shape of the current channel
was chosen according to visual observations: in a distance of one third of the
full distance between the electrodes, the channel rapidly broadens until its
radius becomes equal to the anode radius; further, the cross section area
remains constant. Possible variations in the shape of the current channel
due to variations in the current value were neglected in calculations.
In the calculations, all the parameters were reduced to the conditions
referred to one pin. The equivalent ballast resistance in the discharge circuit
for one pin was R = 12.2 MD (the resistance in the anode circuit was taken
into account). Note that a series of calculations of I-V characteristics was
performed with various values of the ballast resistance (from 100 kD to
--- Page 360 ---
Corona and Steady State Glow Discharges
345
18 MO). These calculations showed that the value of the ballast resistance has
little effect on the shape of the I-V characteristics.
Upon calculating the distribution of the reduced electric field across the
discharge gap, we calculated the distribution of radiation intensity in the
discharge. It was assumed that the first and second positive systems of
nitrogen make the main contribution to the radiation and that the total
radiation intensity is proportional to the total excitation rate for these
levels. The excitation rate constants for these levels were determined
numerically by solving the Boltzmann equation for the electron energy
distribution function. Densities in the inter-electrode gap were computed
based on the numerical 1.5-dimensional code, the 1-V characteristics of
the discharge, the light emission distribution along the current channel
of an individual pin, the longitudinal profile of the electric field, the
components of the total current, and the charged-particle (electron, ion,
and negative ion).
An example of comparison between the computed reduced I-V
characteristics and the experimental ones is shown in figure 6.6.16. It is
seen that, for the parameters given, the calculation results are in good quali-
tative and quantitative agreement with the experimentally observed I(V)
dependence. The influence of water vapor on the reduced 1-V characteristic
is illustrated by calculations for two values of air humidity. The calculated
distribution of the radiation intensity across the gap is also in good
agreement with the experiment. Figures 6.6.18-6.6.20 show self-consistent
variations in the profiles of electric field, relative electron current and
charge density in the inter-electrode gap as the discharge current varies.
The computation was performed for ambient air (relative humidity 30%)
and an inter-electrode distance of 10.5 mm. It is seen in figure 6.6.18 that
the electric field within the gap (outside of the cathode sheath) has a
maximum near the anode. Hence the ionization rate also has a maximum
near the anode. Growth of the field to the anode is explained by the
attachment of electrons and the decrease in their contribution to the total
current (figure 6.6.19). A specific feature of this discharge is a noticeable
space charge even at highest discharge current seen in figure 6.6.20.
For higher discharge voltages the profile of the electron component of
the current along the discharge gap becomes non-monotonic: after decrease
in the region of low fields near the cathode, the electron flux increases
again in the region of high fields far from the cathode. As the voltage
increases, the electron current minimum shifts inside the gap, and the
contribution of the electron current to the total current increases. It is
noteworthy that the electron flux in the gap starts to increase at field
values when the ionization rate is still low compared to the attachment
rate. This finding indicates that the processes of destruction of negative
ions play an important role in the growth of the electron flux and the
formation of the anode sheath.
--- Page 361 ---
346
DC and Low Frequency Air Plasma Sources
o
2
4
6
8
10
12
X (mm)
Figure 6.6.18. Axial profile of the reduced electric field for different values of the discharge
current listed in table 1 according to numbers 1-11.
Thus, the calculations show that in a multi-pin construction the plasma
column in the glow discharge does not form simultaneously along the entire
inter-electrode gap. After the anode sheath has formed, the quasi-neutrality
conditions are first created near the anode. As the discharge current
increases, the region of quasi-neutral plasma extends toward the cathode
progressively covering the inter-electrode gap (figure 6.6.20).
It should be noted that the parameters of the plasma column calculated
with use of the 1.5-dimensional code are close to that of a glow discharge,
which have been computed previously with the zero-dimensional kinetic
model (Akishev et al 1994a). The results of experimental studies and
numerical calculations allow tracing the evolution of the parameters of a
Table 1. Calculated values of current and discharge voltage (V) as a function of power
supply voltage (Vo) for ambient air with 30% relative humidity).
2
3
4
5
6
7
8
9
10
11
Vo (kV) 6
8
10
12
14
16
18
20
22
24
26
V (kV)
5.93 7.90
9.86 11.81 13.75 15.66 17.43 18.92
19.97
20.62
21.08
I (IlA)
1.4
2.79
4.76
7.34 10.8
17.5
34.3
75.2
152
261
386
--- Page 362 ---
Corona and Steady State Glow Discharges
347
1,0
0,8
0,6
S.
0,4
0,2
0,0
0
2
4
6
8
10
12
x (mm)
Figure 6.6.19. Axial profile of the electron current contribution to the total current for
different values of the discharge current listed in table I according to numbers I-II.
2
0
I:\,
E:
-1 -c
Z , •
Z
-2
'I:\,
Z - -3
\
\
1
7
-4
-5
0
2
4
6
8
10
12
X (mm)
Figure 6.6.20. Axial profile of the normalized space charge for different values of the
discharge current listed in table I according to numbers 1-11.
--- Page 363 ---
348
DC and Low Frequency Air Plasma Sources
multi-pin negative corona during the transition to the glow discharge regime
at atmospheric pressure.
6.6.5 Pulsed diffuse glow discharges
At low over-voltages applied to a discharge gap, electron avalanches started
near the cathode are weak ones, and the formation of the plasma requires
multiple avalanches to proceed with a feedback produced by the
secondary-emission processes at the cathode surface (see e.g. Llewellyn-
Jones 1966). This is the so-called Townsend mechanism of discharge
formation. At high over-voltages in high-pressure gases the discharge gap
breakdown usually proceeds in a form of streamers, the number of which
depends on many parameters, in particular, on an amount of seed electrons
(Korolev and Mesyats 1998). In earlier studies of pulse discharge develop-
ment in hydrogen at pressures about 1 bar in narrow gaps, Doran and
Meyer (1967), Cavenor and Meyer (1969), and Meyer (1969) observed at
low over-voltages the formation of a diffuse glow form of the discharge
followed by sparking (see also section 2.4).
Applications of high-pressure plasmas for the excitation of gas mixtures
for achieving laser action gave a strong impetus to pulse discharge studies.
Lasers oscillating on optical transitions of CO2, excimers, Ar/Xe, N2 and CO
can effectively operate at atmospheric pressures and above, and they have
found a wide range of applications (see, for example, Baranov et al 1988).
For laser applications, it is important to produce uniform non-thermal
plasma in a large volume. To solve this problem, a number of methods were
proposed for discharge initiation allowing one to avoid streamer and arc forma-
tion. In particular, an initial electron number density necessary for overlap of
streamers initiated by these electrons was evaluated in works by Koval'chuk
et al (1970), Baranov et al (1972), and Palmer (1974). The criteria derived
agreed qualitatively with further more detailed studies. A number of discharge
techniques varied by methods of pre-ionization and electrode constructions
were developed allowing for pulse glow discharge maintenance in highly
electronegative gases like HCI, F2, and SF6. An overview of these techniques
can be found in Baranov et al (1988) and in Korolev and Mesyats (1998).
The pulse-periodical glow discharge is characterized typically by high
energy deposition into single pulses, dictated by the necessity to provide
sufficiently strong excitation of the laser medium (the almost exclusive
application for this discharge type). The pulse periodical mode introduces
additional problems of discharge stability (Baranov et aI1988): gas-dynamic
perturbations from the preceding pulse distort the uniformity of gas flow,
resulting in an earlier development of instability in the form of arcs or
micro-arcs (also-called filaments). This, in turn, limits repetition frequency,
and results in incomplete usage of the gas mixture flow, a serious handicap
for some applications of this kind of discharge in industry. However, this
--- Page 364 ---
References
349
problem is important only for high-energy loading in every pulse. Applica-
tions not requiring high-energy density can benefit from existing pulse
discharge techniques allowing one to achieve homogenous gas excitation
with many types of electro-negative additives.
References
Akishev Yu S, Dvurechenskii S V, Zakharchenko A I, Napartovich A P, Pashkin S V and
Ponomarenko V V 1981 Sov. J. Plasma Phys. 7 700
Akishev Yu S, Napartovich A P, Pashkin S V and Ponomarenko V V 1982 Sov. J. Tech.
Phys. Lett. 8 512
Akishev Yu S, Napartovich A P, Pashkin S V, Ponomarenko V V, Sokolov N A and
Trushkin N I 1984 High Temp. 22 157
Akishev Yu S, Napartovich A P, Ponomarenko V V and Trushkin N I 1985a Sov. Phys.
Tech. Phys. 30 388
Akishev Yu S, Napartovich A P, Pashkin S V, Ponomarenko V V and Sokolov N A 1985b
High Temp. 23 522
Akishev Yu S, Volchek A M, Napartovich A P, Sokolov N A and Trushkin N 11987 High
Temp. 25 465
Akishev Yu S, Levkin V V, Napartovich A P and Trushkin N I 1991 Proc. XX ICPIG, Pisa,
Italy, vol 4, p 901
Akishev Yu S, Deryugin A A, Kochetov I V, Napartovich A P and Trushkin N I 1993a
J. Phys. D: Appl. Phys. 26 1630
Akishev Yu S, Deryugin A A, Karal'nik V B, Kochetov I V, Napartovich A P and
Trushkin N I 1993b Proc. ICPIG XXI, Bochum, vol. 2, p 293
Akishev Yu S, Deryugin A A, Karal'nik V B, Kochetov I V, Napartovich A P and
Trushkin N I 1994a Plasma Phys. Rep. 20437
Akishev Yu S, Deryugin A A, Elkin N N, Kochetov I V, Napartovich A P and Trushkin
N I 1994b Plasma Phys. Rep. 20 511
Akishev Yu S, Deryugin A A, Kochetov I V, Napartovich A P, Pan'kin M V and Trushkin
N I 1996 Hakone V Contr Papers (Czech Rep.: Milovy) p 122
Akishev Yu S, Grushin M E, Kochetov I V, Napartovich A P and Trushkin N I 1999
Plasma Phys. Rep. 25 922
Akishev Yu S, Grushin ME, Kochetov I V, Napartovich A P, Pan'kin M and Trushkin N I
2000 Plasma Phys. Rep. 26 157
Akishev Yu S, Goossens 0, Callebaut T, Leys C, Napartovich A P and Trushkin N I 2001
J. Phys. D: Appl. Phys. 34 2875
Akishev Yu S, Grushin M E, Napartovich A P and Trushkin N I 2002a Plasmas and Poly-
mers 7 261
Akishev Yu S, Kochetov I V, Loboiko A I and Napartovich A P 2002b Plasma Phys. Rep.
281049
Baranov V Yu, Borisov V M, Vedenov A A, Drobyazko S V, Knizhnikov V N, Naparto-
vich A P, Niziev V G and Strel'tsov A P 1972 Preprint of Kurchatov Atomic Energy
Inst. #2248 Moscow (in Russian)
Baranov V Yu, Borisov V M and Stepanov Yu Yu 1988 Electric Discharge Excimer Noble-
Gas Halides Lasers (Moscow: Energoatomizdat)
--- Page 365 ---
350
DC and Low Frequency Air Plasma Sources
Cavenor M C and Meyer J 1969 Aust. J. Phys. 22 155
Cermik M and Hosokawa T 1991 Phys. Rev. A 43 1107
Chang J-S, Lawless P A and Yamamoto T 1991 IEEE Trans. Plasma Science 19(8) 1152
Cross J A, Morrow R and Haddad G N 1986 J. Phys. D: Appl. Phys. 19 1007
Doran A A and Meyer J 1967 Brit. J. Appl. Phys. 18793
Dykhne A M and Napartovich A P 1979 Sov. Phys. Dokl. 24632
Dykhne A M, Napartovich A P, Taran M D and Taran T V 1982 Sov. J. Plasma Phys. 8422
DykhneAM, ElkinNN, NapartovichAP, TaranM Dand Taran TV 1984Sov. J. Plasma
Phys. 10366
Korolev Yu D and Mesyats G A 1998 Physics of Pulsed Breakdown in Gases (Yekaterina-
burg: URO-PRESS)
Koval'chuk B M, Kremnev V V and Mesyats G A 1970 Sov.Phys. Dokl. 191 76
Llewellyn-Jones F 1966 Ionization and Breakdown in Gases (London: John Wiley)
Mesyats G A and Proskurovsky D I 1989 Pulsed Electrical Discharge in Vacuum (New
York: Springer)
Meyer J 1969 Brit. J. Appl. Phys. 20221
Morrow R 1985 Phys. Rev. A 321799
Napartovich A P and Akishev Yu S 1993a Proc. XXI ICPIG, Bochum, Germany, vol 3,
pp 207-216
Napartovich A P, Akishev Yu S, Deryugin A A, Kochetov I V and Trushkin N I 1993b
in Penetrante B M and Schultheis S E (eds) Non-Thermal Plasma Techniques for
Pollution Control Part B, NATO ASI Series G, vol 34, pp 355-370
Napartovich A P, Akishev Yu S, Deryugin A A, Kochetov I V and Trushkin N I 1997
J. Phys. D: Appl. Phys. 30 2726
Palmer A J 1974 Appl. Phys. Lett. 25 138
Pashkin S V 1976 High Temp. 14581
Scott D A and Haddad G N 1986 J. Phys. D: Appl. Phys. 19 1507
Vertriest R, Morent R, Dewulf J, Leys C and van Langenhove H 2003 Plasma Sources
Sci. Technol. 12412
6.7 Operational Characteristics of a Low Temperature AC
Plasma Torch
6.7.1
Introduction
Dense atmospheric-pressure plasma can be produced through dc or low
frequency discharge operating in the high-current diffused arc mode, such
as a plasma torch (Gage 1961, Koretzky and Kuo 1998), which introduces
a gas flow to carry the plasma out of the discharge region. Non-transferred
dc plasma torches (Boulos et al 1994, Zhukov 1994) are usually designed
for power levels over 10 kW. In this work, an ac torch for lower power
(less than 1 kW) use is described. The volume of a single torch is generally
restricted by the gap between the electrodes, which in turn is limited by the
available voltage of the power supply. A simple way to enlarge the plasma
--- Page 366 ---
Characteristics of a Low Temperature AC Plasma Torch
351
volume is to light an array of torches simultaneously (Koretzky and Kuo
1998). The torches in an array can be arranged to couple to each other, for
example, through capacitors. In doing so, the number of power sources
needed to operate the array can be reduced considerably, so that the size
of the power supply can be compact-an advantage for practical reasons.
The installation of an array of plasma torches is made easy by introdu-
cing a cylindrical-shape plasma torch module (Kuo et a11999, 2001), which
has been designed and constructed by remodeling components from two
commercially available spark plugs and adding a tungsten wire as the central
electrode. A ring-shaped permanent magnet is introduced in the set-up to add
a dc magnetic field between the electrodes (Kuo et al 2002). Thus each torch
module has the size slightly larger than a spark plug and is in the form of a
module unit, which screws easily into the base surface of an array. The
module as a building block simplifies the design of a large-volume plasma
source. It makes the maintenance of the source easy.
The operation and performance of the torch module are described in the
following. Power consumption of low frequency discharge for plasma
generation is evaluated numerically. The results of numerical simulations
for a broad parameter space of plasma species establish a dependence of
power consumption on plasma parameters (Koretzky and Kuo 2001),
which is useful for minimizing the power budget for each application.
6.7.2 Torch plasma
6.7.2.1
A magnetized plasma torch module
A torch module is fabricated by using a surface-gap spark plug (Nippon
Denso ND S-29A), which has a concentric electrode pair, as the frame.
For torch operation, a gas flow between the electrodes is necessary. Thus,
the original electrode insulator, which fills the space between the central
and outer electrodes, is replaced with a new one taken from a different
spark plug (Champion RN 12YC). This new ceramic insulator has a smaller
outer diameter than the original one; hence, an annular gap of 1.81 mm is
created for the gas flow. Moreover, the central electrode set in the new
ceramic insulator is replaced by a solid 2.4 mm diameter tungsten rod,
which is held in place concentrically with the outer electrode, having inner
and outer diameters of 6 and 12 mm, by the new insulator and axially by a
setscrew in the anode terminal post. The relatively high melting point of
tungsten is desirable in the high-temperature environment of the arc. Eight
holes of 2 mm diameter each are drilled through the frame (in the section
having a screw thread as seen in figure 6.7.la) of the module to pass gas
into the region between the electrodes. The torch is screwed into a plenum
chamber (which is not shown) that supplies the feedstock gas and hosts the
ring-shaped permanent magnets, one for each torch. The geometry of the
--- Page 367 ---
352
DC and Low Frequency Air Plasma Sources
(a)
(b)
Figure 6.7.1. (a) A photo of the plasma torch module, (b) circuit of 60 Hz power supply to
run the torch. (Copyright 2002 by AlP.)
electrodes and the dimensions of the parts in the frame of the module are
presented in figure 6.7.1a. This torch module has relatively large gap
(2 mm) between two electrodes compared to the gaps (usually less than
1 mm) used in the non-transferred dc plasma torches (Boulos et al 1994,
Zhukov 1994). The discharge is restricted to occur only outside the module
by the ceramic insulator inserted between the electrodes. Thus this torch
can be operated even with very low gas flow rates. On the other hand, the
non-transferred dc plasma torch requires sufficient gas flow to push the arc
into the anode nozzle. This electrode feature reduces the power loss to the
electrodes considerably.
The ring magnet has outer and inner diameters of 5l.8 and 19.6mm,
respectively, and a thickness of 12.2 mm. It produces an axial magnetic
field of 0.14 Tesla at the central location of the ring. Each magnet is posi-
tioned concentrically around the outer electrode of each module and held
inside the plenum chamber. The torch is run by a 60 Hz power supply
shown in figure 6.7.1 b, which will be described later. Operation of the
torch in 60 Hz periodic mode, rather than in dc mode, gives the feedstock
--- Page 368 ---
Characteristics of a Low Temperature AC Plasma Torch
353
(c)
• dimetlsioM iR miltilllcWB
.aotll.t seale
Mt4xUS
Figure 6.7.1. (c) Schematics of the top and side views of a magnetized torch module.
(Copyright 2002 by AlP.)
gas sufficient time between two consecutive discharges to cool the electrodes.
Shown in figure 6. 7.lc are schematics of the top and side views of a module.
The annular chamber designed for hosting one torch module only is inside
the aluminum body indicated in the side view of figure 6.7.lc.
6.7.2.2 Power supply
The power supply and the electrical circuit used to light a single torch module
is shown in figure 6.7.1 b. As shown, the discharge voltage is provided by a
power supply, which includes a power transformer with a turns ratio of
--- Page 369 ---
354
DC and Low Frequency Air Plasma Sources
1: 25 to step up the line voltage of 120 V from a wall outlet to 3 kV, and a 11lF
capacitor in series with the electrodes (i.e. the torch). A branch consists of a
diode (15 kV and 750 rnA rating) and a resistor (1 kO), which is connected in
parallel to the torch, is added to the circuit to further step up the peak voltage
in half a cycle. During one of the two half cycles when the diode is forward
biased, the capacitor is charged to reduce the voltage across the electrodes.
During the other half cycle, the diode is reverse biased. The charged
capacitor increases the voltage across the electrodes and uses its stored
energy to assist the breakdown process and to enhance the discharge.
Using the same circuit for each torch, in general, all of the torches can be
connected in parallel to a common power source (i.e. the power transformer)
if it has the required power handling capability. The capacitors in the circuit
play a crucial role in the discharge. Without them, the torches in the set
cannot be lit up simultaneously by a single common source. This is because
once one is lit up, it tends to short out the voltage across all of the other
electrode pairs connected in parallel. The capacitors work as active ballasting
circuit elements. Charging and discharging of each capacitor provides
feedback control to the voltage across the corresponding electrode pair.
6.7.2.3
Plasma torches
The magnetic field introduced by the ring-shaped permanent magnet is in the
(axial) direction perpendicular to the discharge electric field (in the radial
direction). It rotates the discharge by the J x B force around the electrodes
(in the azimuth direction) and thus enhances the strength and stability of
plasma produced by the module, and the lifetime of the electrodes by
avoiding discharge at a fixed hot spot. Shown in figure 6.7.2a is a photo of
torch plasma produced by this module. Backpressure of air is 17 psia
('" 1.156 atm). This torch module can also be run without the ring magnet.
A photo of unmagnetized torch plasma is presented in figure 6.7.2b for
comparison. The first noticeable difference between these two is their sizes.
The volume of magnetized torch plasma is evidently larger. The evenly
distributed bright anode spots around the base of magnetized torch
demonstrate the rotation of the discharge by the magnetic field, which
helps to optimize the torch volume by ballasting the arc constriction and
to reduce erosion at hot spots. The disadvantage of adding the magnet to
the module is to increase the space between two modules in the array. Use
of four magnetized torch modules to enlarge the volume of plasma is
demonstrated in figure 6.7.2c.
6.7.2.4
Voltage and current measurements
Shown in figure 6.7.3a are the voltage and current waveforms of the
discharge in one cycle. During the first half cycle when the diode in the
--- Page 370 ---
Characteristics of a Low Temperature AC Plasma Torch
355
Figure 6.7.2. Torch plasmas produced by (a) a magnetized and (b) an unmagnetized, torch
module; the backpressure is 17 psig; (c) a photo of four plasma torches produced by a
portable array. (Copyright 2002 by AlP.)
circuit is reversed biased, the discharge is in the low-voltage-high-current
arc mode; it evolves to a high-voltage-Iow-current glow discharge in the
other half cycle when the diode becomes forward biased. The product of
the voltage and current measurements gives the power function of a single
torch, which is shown in figure 6.7.3b. As shown, the peak and average
power are about 1.5kW and 320W, respectively. The power factor is
about 0.62. This may be because the inductance of the transformer is too
large. When two torch modules discharge simultaneously by a single
power supply, the capacitance of the circuit increases; moreover, the
coupling capacitors work as additional dependent sources providing feed-
back control of the phases of the discharge voltage and current of each
torch so that the discharge can stay longer and the system operates with
improved power efficiency, as evidenced by the increase of the power
factor to 0.96 and the reduction of the total harmonic distortion of the
power line to a very low percentage. The results indicate that the electrical
performance of the circuit with coupled torches is significantly improved,
suggesting that the capacitively coupled plasma torch array be an excellent
self-adjusting resistive load to the power line.
--- Page 371 ---
356
DC and Low Frequency Air Plasma Sources
(a)
3
-1
-2
(b)
Figure 6.7.3. (a) Voltage and current, and (b) power functions of the torch module.
(Copyright 2002 by AlP.)
It is noted that the power of this plasma torch depends strongly on the
power supply. In an application requiring high power and high temperature
torch plasma, the 1 IlF capacitor in the power supply is replaced by a 3 IlF
one and the resistor in series with the diode is increased from 1 to 4 kD.
--- Page 372 ---
Characteristics of a Low Temperature AC Plasma Torch
357
The results (Kuo et al 2003) show that the torch plasma has a peak and
average power of 3.8 and 1.5 kW, respectively.
6.7.2.5
Temperature and density measurements
A method (Kuo et al 1999) based on thermal equilibrium and a detailed
analysis of heat loss from a copper wire placed in a torch is applied to
measure the temperature of the torch plasma. Consider the model of a
long wire with only a portion immersed in the torch. The wire in the torch
heats up due to forced convection from the torch and loses energy in the
torch via radiation. Outside the torch, the wire acts as a cylindrical pin fin
and loses energy via conduction along the wire and natural convection
with ambient air. A wire with a small diameter reduces heat loss from the
pin fin, which increases the wire temperature in the torch, compared to a
larger diameter wire. So systematically reducing the wire diameter placed
in the torch eventually results in a critical wire diameter that just melts or
shows signs of softening. The wire so determined has a temperature nearly
equal to its melting temperature.
Copper wires of different diameters were used in the experiment, because
it is easy to assemble a set of different diameter wires with known purity and
emissivity E: = 0.8. The diameters of the wires varied from 10 to 33 mil
(1 mil = 1/1000 inch, 0.0254 mm) and the burning time of the torch was up
to 1 min. It was found that 10 mil wire melted right away and 33 mil wire
remained unscathed. By increasing the diameter of the wire from 10 mil
graduately, it was found that 16mil was a critical diameter. For the 16mil
wire, its status (melted or not melted) depended on its surface condition
and location in the torch. The hottest burning spot in the torch was identi-
fied. With the temperature of the 16 mil wire determined to be about the
melting temperature of copper (1083 0c), a power balance equation could
be set up, to determine the torch temperature.
In the experiment, the wire was held by a holder placed at
x = 10 = 27.5mm from the center at x = -1Omm of the torch. To reach
thermal equilibrium, the power qinO, convected from the gas flow in the
torch to the wire, must be balanced by the power losses PradO and PeondO of
the wire, via thermal radiation and thermal conduction, respectively. The
power balance condition is written as
qinO = Ahe(T - Two) = PradO + PeondO = qoutO
where A = 7rDDt = 2.55 x 10-5 m2 is the area of the portion of WIre
immersed in the torch, D = 406 Jlm (16 mil) and Dt = 20 mm are the
diameters of wire and torch plasma; he =0.75(k/D)Re°.4prO.37Wm-2K-l
is the forced heat convection coefficient; the Prandtl number Pr ~ 0.7 and
k is the thermal conductivity; T and Two are the temperatures of the
torch and wire. Based on data for air in table A.4 of the reference book by
--- Page 373 ---
358
DC and Low Frequency Air Plasma Sources
Incropera and DeWitt (1996), the Reynolds number is calculated for the flow
speed u = 20m/s with the air temperature T as a parameter varying from
1350 to 2200 K. Hence, the power input from torch to wire can be evaluated
as a function of T.
The temperature gradient of the wire at x = 0 (boundary of torch) is
determined by the local power balance condition (Siegel and Howell 1992)
for the segment of wire outside the plasma flow (0 < x < 10)
Awkw d2Tw/dx2 = (d/dx)(Prad + Pfin ) = a(T! - r:) + b(Tw - Tair) (6.7.1)
where Aw, kw, and Tw are the cross section area, thermal conductivity, and
temperature of the copper wire; Prad and Pfin are the thermal radiation
and natural convection power of wire; a = nDea and b = nDhen;
a = 56.7 n W m -2 K -4 is the Stefan-Boltzmann constant; hen and Tair are
the natural heat convection coefficient, and temperature of air next to the
wire.
Collisions keep the plasma flowing with the gas flow. The temperature
Tair of air outside the plasma is expected to drop quickly to the ambient
temperature Ta ~ 300 K. Thus, an average value of86Wm-2 K- 1 is assumed
for the natural heat convection coefficient hen' which is much smaller than he.
Equation (6.7.1) can be integrated to be
dTw/dx = -{(2aJ5)[Tw(T! - Ti) - 4Ti(Tw - Ta)]
(6.7.2)
subjected to the boundary conditions Tw(O) = Two and Tw(lo) = Ta, where
a = a/Awkw = 1.324 x 1O-6 m-2 K-3, (3 = b/Awkw = 2.51 x 103 m-2, and
Pholder is the conduction power from wire to the holder.
To
match
the
boundary
condition
Tw(lo) = Ta
at
x = 10 ,
Pholder = 1.12 W is determined self-consistently. The conduction loss of the
segment of wire inside of torch can now be evaluated to be
PeondO ~ 3.33 W. Therefore, the total power loss for the 16mil wire is
qoutO = PeondO + PradO = 7.16W. Set qino(T) = qoutO, the time averaged
torch temperature T is found (Kuo et al 1999) to be about 1760 K.
The electron density of the torch plasma can be deduced, with the aid of
temperature information, from the microwave absorption measurements.
The experiment (Koretzky and Kuo 1998) was conducted by streaming
torch plasma through aligned holes on the bottom and top walls of a rectan-
gular X-band waveguide. This plasma post has a complex dielectric constant
,
."
h
'
1
2/( 2
2)
d"
2/ (2
2)
e = e - Je , were e = - Wp
W + 1/
an e = I/Wp W W + 1/
; W, wp'
and 1/ are the wave, plasma, and electron-neutral collision, frequencies,
respectively, and e" is determined from the absorption measurement.
Since w~ ex ne and 1/ ex TN e:! T, the time-dependent electron density was
found to have a spatially averaged maximum value nemax of about 1013
electrons/cm3.
--- Page 374 ---
Characteristics of a Low Temperature AC Plasma Torch
359
6.7.3 Power consumption calculation
Plasma growth and decay are governed by the rate equations of plasma
species (Zhang and Kuo 1991) in each torch
dne
dt = -Vane + Vdn_ - omen+ + Vjne
dn+
dt = -anen+ - (3n+n_ + Vjne
(6.7.3)
dn_
dt = Vane - Vdn_ - (3n+n_
where ne, n+, and n_ are the densities of electrons, positive ions, and negative
ions, respectively, in cm-3; Va is the attachment rate and Vd is the detachment
rate; and a and (3 are the electron-ion recombination coefficient and ion-ion
recombination coefficient, respectively, in cm3 S-I. The ionization frequency
Vi representing the external driver of the discharge is given by (Lupan 1976,
Kuo and Zhang 1990)
(6.7.4)
where € = E / Ecr is the discharge field E normalized to the breakdown
threshold field Ecr.
By solving (6.7.3), the net electron loss during a number of discharge
periods can be evaluated. It turns out that the rate terms on the left hand
side of (6.7.3) can be neglected in calculating the electron density decay. It
is understandable because the temporal variation of the discharge voltage
is, in general, much slower than the transient variations of (6.7.3). The
steady state solution of (6.7.3) is given by
Vd((3va + aVd - (3Vj -",)
ne = - ----:--:--'----,-----:--':,,--------,----'-'-----:-
a((3va - (a - 2(3)Vd - (3Vj +",)
(3va - aVd - (3Vj - ",
n+ = -
2a(3
(6.7.5)
Vd((3va + aVd - (3Vj -",)
n = ~~~~-~,,___~~~----:-
-
(3((3va - (a - 2(3)Vd - (3Vj +",)
where", = J
4a(3vdVj + ((3va + aVd - (3Vj)2 is used to simplify the presenta-
tion of (6.7.5). The average power consumption is given by the average
electron loss per second times the average ionization energy (~1O e V) of air
(Brown 1967). Shown in figure 6.7.4 is a parametric dependence of the
power consumption (W/cm3) on the average electron density (cm-3)
maintained in the plasma, where the electron-ion recombination coefficient
a (cm3 s-l) is used as a variable parameter. It provides a very useful reference
for choosing the density regime for the most efficient operation of the plasma
torch. The results for two situations are shown. The first is for a completely
--- Page 375 ---
360
DC and Low Frequency Air Plasma Sources
J;'" 1 0 .,
E
~ 10'
3:
-
10'
~
'0 10"
c:
~ 10:t
... .,
• 10'
&. 10
10
11
10"
lOu
10'·
10's
Averoge Electron Density (em-')
Figure 6.7.4. Dependence of the average power consumption per cubic meter on the
average electron density per cubic centimeter with the electron-ion recombination
coefficient Q (cm3 S-I) as a variable parameter. Solid lines are for transient plasma
generation case and the dashed lines are for steady state plasma maintenance case. Q is
given as (0) 10-6, (D) 10-7, and (1I) 10-8. (Va = 4.56 X 107 S-I, vd = 1.52 X 107 s-I, and
(3 = 1.2 X 10-9 cm3 s -I). (Copyright 2001 by IEEE.)
transient plasma generation system using equation (6.7.3), where an initial
electron density is created and then allowed to recombine. The electron
density is averaged over ~T = 1 ms, which is shorter than the discharge
duration of presently reported experiments, but yet very long to demonstrate
a significantly different result from that of the second case. The second is for a
steady state plasma generation system using equation (6.7.5). The large
difference in the average power consumption between the two situations
for each 0: shows the importance of plasma maintenance, which can reduce
the power budget considerably. In other words, an increase of the repetition
rate of the discharge (i.e. reducing ~T) works to reduce the power consump-
tion in the transient case. However, the engineering problem of the power
supply becomes an issue. The simulation results also show that the power
budget is reduced by decreasing the value of 0:, which can be achieved by
increasing the temperature of the plasma (Christophorou 1984, Rowe 1993).
Since the power consumption for plasma maintenance is much less than
that for pulse generation, it suggests that a proper trigger mechanism for the
start of plasma production may work to reduce the power requirement.
--- Page 376 ---
References
361
U sing the fitting curves of the simulation results, a function giving a parametric
dependence of the consumed average power density (P) on the normalized
average electron density (1Je) maintained in the plasma is derived (Koretzky
and Kuo 2001) to be (P) ~ 48(1Je)1.9g 0.4 (W/cm3), where (1Je) is normalized
to 1013 cm -3 and where g, the electron-ion recombination coefficient, nor-
malized to 10-7 cm3 s-l, is used as a variable parameter in the simulation.
This relationship provides a useful guide for the choice of the plasma density
and temperature to achieve an efficient operation of the plasma torch.
References
Boulos M, Fauhais P and Pfender E 1994 Thermal Plasmas Fundamentals and Applications
voll (New York: Plenum Press) pp 33-47 and 403-418
Brown S C 1967 Basic Data of Plasma Physics (Cambridge, MA: MIT Press)
Christophorou L G 1984 Electron-Molecule Interactions and Their Applications vol 2
(Orlando: Academic Press)
Gage R M 1961 Arc Torch and Process (United States Patent No. US 2858411)
Incropera F P and DeWitt D P 1996 Fundamentals of Heat and Mass Transfer 4th edition
(John Wiley)
Koretzky E and Kuo S P 1998 'Characterization of an atmospheric pressure plasma gener-
ated by a plasma torch array' Phys. Plasmas 5(10) 3774
Koretzky E and Kuo S P 2001 'Simulation study of a capacitively coupled plasma torch
array' IEEE Trans. Plasma Sci. 29(1) 51
Kuo S P and Zhang Y S 1990 'Bragg scattering of electromagnetic waves by microwave
produced plasma layers' Phys. Fluids B 2(3) 667
Kuo S P, Bivolaru D and Orlick L 2002 'A magnetized torch module for plasma genera-
tion' Rev. Sci. Instruments 73(8) 3119
Kuo, S P, Bivolaru D, Carter C D, Jacobsen L and Williams S 2003 'Operational charac-
teristics of a plasma torch in a supersonic cross flow' AIAA Paper 2003-1190
(Washington, DC: American Institute of Aeronautics and Astronautics)
Kuo S P, Koretzky E and Orlick L 1999 'Design and electrical characteristics ofa modular
plasma torch' IEEE Trans. Plasma Sci. 27(3) 752
Kuo S P, Koretzky E and Vidmar R J 1999 'Temperature measurement of an atmospheric-
pressure plasma torch' Rev. Sci. Instruments 70(7) 3032
Kuo S P, Koretzky E and Orlick L 2001 Methods and Apparatus for Generating a Plasma
Torch (United States Patent No. US 6329628 Bl)
Lupan Y A 1976 'Refined theory for an RF discharge in air' Sov. Phys. Tech. Phys. 21(11)
1367
Rowe B R 1993 Recent Flowing Afterglow Measurements, in Dissociative Recombination:
Theory, Experiment and Applications (New York: Plenum Press)
Siegel R and Howell J R 1992 Thermal Radiation Heat Transfer (Hemisphere Publishing)
Zhang Y Sand Kuo S P 1991 'Bragg scattering measurement of atmospheric plasma decay'
Int. J. IR & Millimeter Waves 12(4) 335
Zhukov M 1994 'Linear direct current plasma torches' in Solonenko 0 and Zhukov M
(eds) Thermal Plasma and New Material Technology vol I: Investigations of Thermal
Plasma Generators (Cambridge Interscience Publishing) pp 9-43
--- Page 377 ---
Chapter 7
High Frequency Air Plasmas
J Scharer, W Rich, I Adamovich, W Lempert, K Akhtar, C Laux,
S Kuo, C Kruger, R Vidmar and R J Barker
7.1
Introduction
The use of high-frequency power to produce plasmas in air and high-pressure
gases is a relatively new development. These methods span the regimes of
seed gas ionization via carbon monoxide (CO) and ultraviolet flash tubes
and lasers, seed gas ionization and optical pumping via carbon monoxide
lasers and ionization sustainment by rf plasma torches and microwave
plasma sources. Their advantage is that power can be spatially focused
away from electrodes or wall materials by means of antennas or optical
lenses. In addition, since the focus is adjustable, large, three-dimensional
volumes of plasma can be created in space without the need for electrodes
that can degrade. Historically, rf air plasma torches in air were the first to
be investigated. Then microwave and later flash-tube and laser sources
became of interest. Recently, electron beams propagated through a
vacuum window to protect the cathode and short-pulse high-voltage
plasma sources in air have been investigated. Much of the recent research
presented in this chapter was supported by a Defense Department Research
and Engineering multi-university research initiative (MURI) entitled 'Air
Plasma Ramparts' and AFOSR grants administered by Dr Robert Barker.
This chapter is organized as follows. First, laser and flash-tube ioniza-
tion and the excitation of gas seeds in air are discussed by Professors William
Rich, Igor V Adamovich and Walter Lempert of Ohio State University in
section 7.2.2. Then laser-formed, seeded, high-pressure gas and air plasma
research is presented by Professor John Scharer and Dr Kamran Akhtar of
the University of Wisconsin in section 7.2.3. This is followed by a presenta-
tion on the rf torch in Section 7.3 by Professors Christophe Laux of Ecole
Centrale Paris and Stanford University and Dr Kamran Akhtar and
Professor John Scharer from the University of Wisconsin. Then microwave
362
--- Page 378 ---
Introduction
363
air plasma sources are presented in section 7.3.4 by Professor Spencer Kuo of
Polytechnic. Thereafter, more complex short-pulse, high-voltage experi-
ments involving rf gas preheating and electrode discharges and laser
excitation of electron beam heated air plasmas is presented. This research
is described in sections 7.4 and 7.5 by Professors Christophe Laux of the
University of Paris and Stanford University, and by Professors William
Rich, Igor Adamovich and Walter Lempert of Ohio State University.
Finally, section 7.6 presents challenges and new opportunities for research
and applications in this field.
Section 7.2 presents an investigation of optically pumped excitation of
carbon monoxide (CO) and laser excitation and ionization of organic gas
tetrakis-dimethyl-amino-ethelyene (TMAE) seed gases under high pressure
and atmospheric air conditions. This is done to create non-equilibrium
high-density plasma conditions and maintain low gas kinetic temperatures
with a lower power budget. The low power optically pumped CO experiment
is augmented with an rf capacitive source and produces air component and
air plasma densities in the 1010-10 11 /cm3 density range. In addition, detailed
optical spectra illustrating the vibrationally excited states are presented. This
optically pumped plasma is used together with an electron-beam-produced
plasma that is discussed in section 7.5. The ionization of a low ionization
energy (6.1 e V) organic seed gas in high-pressure gases and atmospheric air
by a short-wavelength (193 nm) high-power excimer laser is then discussed
in section 7.2.3. High density (1013/cm\
large volume (SOOcm\ low
temperature plasmas are obtained and millimeter wave interferometry and
optical spectra measurements are presented to determine the two- and
three-body recombination rates for different cases. Both direct and delayed
ionization processes are found to influence the plasma decay process. The
high-density and large volume plasma formed in this case provides an excel-
lent load for reduced power rf inductive sustainment that is discussed in
section 7.3.3.
Section 7.3.2 presents a review of rf plasma torch experiments that are
the most developed of the high-frequency high-pressure plasma sources.
They have applications in materials processing and biological decontamina-
tion. High density (> 1013 /cm\ large volume (1000 cm3) air plasmas in near
thermal equilibrium are obtained and electron temperatures and densities in
air plasmas as well as the wall plug power density required to sustain the
plasma are discussed. This technique is used to increase the neutral air
temperature in order to reduce electron attachment to oxygen for the
short-pulse high-density experiments discussed in section 7.4. Next, the use
of the laser initiated seed gas discussed in section 7.2.3 as a seed plasma
load for high-power inductive rf sustainment is presented. It is found that
much lower rf power densities for sustainment compared to initiation can
be obtained and enhanced rf penetration well away from antenna is
observed. Section 7.3.4 discusses the use of higher frequency microwave
--- Page 379 ---
364
High Frequency Air Plasmas
discharges in air to obtain spatially localized high-density plasmas and can be
compared with rf methods.
Section 7.4 discusses a short repetitive pulse, low-duty cycle, high-
voltage discharge in air that is used to produce non-equilibrium plasmas
with time-averaged densities in the (1012 jcm3) range and greatly reduced
power consumption and lower neutral temperatures relative to thermal
equilibrium. Section 7.S discusses the reduction in electron attachment to
oxygen, one of the major loss processes for air plasmas, for a 60-80 kV
electron beam-formed, 1011 jcm3 density plasma resulting from CO laser
pumping of the seed gas that can couple to and detach the electron from
the oxygen. Recombination rates and power density estimates are also
presented. Section 7.6 concludes with challenges and opportunities for
future research.
7.2
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
7.2.1
Introduction
Laser pumping of seed gas and laser ionization of low ionization potential
seed organic gas in high-pressure gases and atmospheric air to obtain
non-equilibrium, high-density plasmas is presented in this section. These
techniques are relatively new and have an objective of high-density, remote
plasma creation with substantial reduction in power compared to plasma
production in high-pressure gas alone. These experiments are grouped
together since they both utilize lower concentration seed gas for which
laser power can be efficiently coupled or used for ionization than is the
case for the high-pressure gas into which they are injected. They also
create non-equilibrium, large volume plasmas that can be sustained remotely
from the source region. A key scientific property that is examined is the seed
gas and plasma interaction with the background high-pressure gas. The
carbon monoxide (CO) laser (A ~ Sllm) pumping technique is used to
efficiently pump vibrational states of the seed CO gas in the high-pressure
background gas. Efficient coupling and transfer to metastable states of
high-pressure seed gas and capacitive rf coupling of power to associative
ionization of the CO-laser-pumped plasma is discussed. Optical spectra
and the associated plasma density are presented.
The use of a low ionization potential seed gas that is ionized and excited
by a 193 nm wavelength excimer laser is discussed in section 7.2.3. Both direct
ionization and delayed ionization of the seed gas produces a high-density
large-volume plasma in high-pressure gases and atmospheric air. This
plasma can be produced in space well away from the laser source and can
--- Page 380 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
365
be used as a large volume seed plasma that can be sustained by lower
power inductive rf coupling that can be pulsed or continuous. This topic is
discussed in section 7.3 on rf and microwave plasmas. Fast Langmuir
probe measurements, optical spectroscopy and millimeter wave inter-
ferometry are used to determine the plasma density, super-excited neutral
states and recombination rates for seed plasma and the properties in
high-pressure background gas.
7.2.2 Laser-sustained plasmas with CO seedant
Creating considerable levels of ionization, uniformly distributed in a large-
volume high-pressure molecular gas mandates a non-thermal, or non-
equilibrium, plasma approach, if relatively low gas kinetic temperatures
must be maintained. The first point to be clarified is what is meant by a
non-equilibrium, as opposed to an equilibrium, plasma. Figure 7.2.2.1
shows a simple schematic indicating the various modes of motion of diatomic
molecules, the dominant species making up the air plasmas which are a prin-
cipal focus of this book. The plasma can store energy in each of the indicated
modes, and each therefore can contribute to the specific heat of the plasma.
Note that in addition to the modes shown, the translational motion of the
plasma atoms and free electrons are also participating modes. Polyatomic
species, if present, would also contribute additional modes. The total
energy of each atom, molecule, ion, or free electron in the gas may be written
in the form
E = Etrans + E rot + EVib + Eelectron + Einteraction
TRANSLATIONAL MOTION:
~ ~
%~
fho~
ROTATIONAL MOTION:
VIBRATIONAL MOTION:
-
O'V\I\IO -
-~-
ELECTRONIC: ~.~ GAS RADIATES IN
VISIBLE, UV
(
0 fe·\
(7.2.2.1)
Figure 7.2.2.1. Schematic of the various modes of motion for diatomic molecular species in
a plasma.
--- Page 381 ---
366
High Frequency Air Plasmas
where each of the energies shown corresponds to one of the modes of motion
shown in figure 7.2.2.1. Various other possible energy storage modes
(chemical, nuclear) are omitted, both for simplicity and because they are
not primarily participating in the processes being described here. Einteraction
represents energies associated with the coupling of various modes within a
single molecule (vibration with rotation, or vibration with electronic
motion, etc.). The 'internal' energy modes (rotation, vibration, electronic)
are quantized into discrete energy levels. For engineering systems of macro-
scopic dimensions, the translational modes of the plasma species are not
quantized, and translational motion is described by classical mechanics.
It is convenient to designate the total energy of an atom or molecule
corresponding to a particular array of specific quantum energy states as
E;, where the subscript i refers to the collection of quantum numbers for
each mode designating the specific energy level. When the plasma is in
thermal equilibrium, the distribution of populations of plasma species (elec-
trons, ions, atoms, molecules) among the various energy states E; is typically
governed by Maxwell-Boltzmann statistics. In this equilibrium case, the
fractional number of plasma species in the ith energy state, E;, is
n;
g; exp( - Ed kT)
N
Q
(7.2.2.2)
where the partition function, Q, is given by:
Q = L g;exp(-EdkT)
(7.2.2.3)
where N = ~; n; is the total number of species, g; is the statistical weight of
the ith internal energy state, k is Boltzmann's constant and T is the tempera-
ture of the plasma. For this equilibrium case, specification (or measurement)
of the single plasma temperature, T, allows the distribution of energy and
populations of states to be determined.
In the molecular plasmas of primary interest in this book, one or more
modes of motion are not in thermal equilibrium, and some states are not
populated according to the simple expressions above. It must be recognized
that producing large degrees of such non-equilibrium requires input of
considerable work to the plasma, to maintain the non-equilibrium. Thermo-
dynamic laws dictate that this work input must exceed the heat input neces-
sary to maintain a thermal, equilibrium plasma having the same ionization
fraction. Non-equilibrium, cool molecular plasmas are easily created in
lower pressure gases, usually in small volumes. These are the familiar glow
discharge plasmas, that can have near-room gas kinetic (translational
mode) temperatures, and which can be readily struck in a gas with electrodes
biased with dc or rf electrical potentials. The specific non-equilibrium modes
in such glow-type discharges in molecular gases are (1) the free electron
gas, whose mean energy or effective temperature is much higher than the
--- Page 382 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
367
translational mode temperature of the molecular and atomic species, (2) at
least some of the vibrational modes, whose mean energy is, again, much
higher than the mean translational mode energy of atoms and molecules,
and, often, (3) some of the electronic modes of the atomic and molecular
species, which again may have much higher mean energies than their mean
translational mode temperatures. It is this third non-equilibrium that creates
the defining 'glow' of the ordinary glow discharge. This often-visible glow
arises from radiative decay of the highly energetic electronic states. While
such intense radiation is only achieved by heating thermal equilibrium
plasmas to thousands of degrees, in radiating glow plasmas, the gas tempera-
ture may be only slightly above room temperature. We cite the common
examples of 'neon' sign plasmas, or normal fluorescent lighting tubes,
which are cool to the touch. In all these glow discharges, it is electrical
power that supplies the requisite work for maintaining non-equilibrium.
Creating such a cool, non-thermal plasma in any atmospheric pressure gas,
and especially in air, is, however, beset with many difficulties, and is
exacerbated when a uniform, diffuse ionization is required in a large
volume. Chief among these difficulties is the instability that causes the
plasma to condense into a thermal arc.
Stability control of large-volume high-pressure non-equilibrium
molecular plasmas has long been one of the most challenging problems of
gas discharge physics and engineering. At high pressures, the most critical
instability, which produces the transition of a diffuse, non-equilibrium,
self-sustained discharge into a higher temperature, higher ionization fraction,
near-thermal equilibrium arc, is the ionization heating instability. Basically,
the transition to an arc develops due to a positive feedback between gas
heating and the electron impact ionization rate (Raizer 1991, Velikhov et al
1987). In the transition, small electron density perturbations, producing
excess Joule heating, result in a more rapid electron generation and even-
tually lead to runaway ionization. Since the advent of very high-power gas
lasers, which require production of extreme disequilibrium in internal
molecular energy modes, coupled with low gas kinetic temperature, various
approaches to this stabilization problem have been developed. Among a
few well known high-pressure plasma stabilization methods are the use
of separately ballasted multiple cathodes (Raizer 1991), aerodynamic
stabilization (Rich et aI1979), rf frequency high-voltage pulse stabilization
(Generalov et al 1975), and external ionization by a high-energy electron
beam (Basov et aI1979).
The use of these techniques is tantamount to introducing an additional
damping factor into a conditionally stable system, which raises the instability
growth threshold and allows the sustainment of a diffuse discharge at higher
pressures and/or electron densities. However, they do not affect the original
source of the ionization heating instability. For this reason, raising the gas
pressure or discharge current eventually results in a glow-to-arc transition.
--- Page 383 ---
368
High Frequency Air Plasmas
Even the non-self-sustained dc discharge with external ionization produced
by an e-beam is in fact self-sustained in the unstable cathode layer, where
ionization is primarily produced by secondary electron emission from the
cathode (Velikhov et al 1987). Therefore instability growth in the cathode
layer of high-power discharges sustained by an e-beam results in the develop-
ment of high-current density cathode spots extending into the positive
column and eventually causing its breakdown.
The cathode layer instability of the e-beam-sustained discharge can be
avoided by using an rf instead of a dc electrical field to draw the discharge
current between dielectric-covered electrodes. In this case, secondary emis-
sion from the electrodes is precluded, the cathode regions do not form,
and the current loop is closed by the displacement current in the near-
electrode sheaths. This type of discharge remains non-self-sustained in the
entire region between the electrodes and is therefore not susceptible to the
cathode layer instability (Velikhov et al 1987). Indeed, experiments show
that an rf beam-driven discharge remains stable at higher E / N and current
densities than a dc discharge (Kovalev et al 1985). However, at high
e-beam currents this type of discharge also becomes unstable since the rate
of ionization by the beam is inversely proportional to the gas density, so
that gas heating by the beam would eventually produce an ionization
instability.
The above discussion shows that even the use of external ionization does
not always allow unconditionally stable discharge operation at high currents
and pressures. On the other hand, it suggests that a discharge system
sustained by an external source with a negative feedback between gas heating
and ionization rate, and, if necessary to provide work input to internal
modes, using sub-breakdown electric fields to draw the discharge current,
might be unconditionally stable (Plonjes et al 2000). An ionization process
that satisfies this condition is the associative ionization in collisions of two
highly vibrationally excited molecules (Plonjes et al 2000, Polak et aI1977,
Adamovich et a11993, 1997,2000, and Palm et aI2000),
AB(v) + AB(w) -
(AB)i + e-,
Ev + EM' > Eion .
(7.2.2.4)
In equation (7.2.2.4), AB represents a diatomic molecule, and v and ware
vibrational quantum numbers. Basically, ionization is produced in collisions
of two highly vibrationally-excited molecules when the sum of their vibra-
tional energies exceeds the ionization energy. This volume ionization
method was first detected in nitrogen plasmas, and is the key ion-producing
process in many of the well-known CO2/N2 high-power gas lasers (Polak et al
1977). Of direct relevance for application to air plasmas, ionization by this
mechanism has been previously observed in CO-Ar and CO-N2 gas mixtures
optically pumped by resonance absorption of CO laser radiation at pressures
of P = 0.1-1.0atm and temperatures of T = 30o-700K (Plonjes et a12000,
Adamovich et a11993, 1997, 2000, and Palm et aI2000). In these optically
--- Page 384 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
369
pumped non-equilibrium plasmas, where high vibrational levels of CO are
populated by near-resonance vibration-vibration (V-V) exchange (Treanor
et a11968, Rich 1982), a gas temperature rise results in rapid relaxation of
the upper vibrational level populations because of the exponential rise of
the vibration-translation (V-T) relaxation rates with temperature (Billing
1986). In other words, ionization by mechanism (1) can be limited and
even terminated by the heating of the gas.
The present section reviews the work in exciting high-pressure molecular
plasmas by such 'optical pumping' of CO. While such plasmas can be created
in high-pressure mixtures of pure CO, or CO in an inert (Ar, He) diluent, CO
can also be used as a seed ant to create other diatomic gas plasmas (N2' O2,
air). This unconditionally stable high-pressure molecular plasma concept will
be reviewed here. To accomplish this, carbon-monoxide-containing gas
mixtures are vibrationally excited at high pressures using a combination of
a CO laser and a sub-breakdown rf field. More extensive presentations of
work with plasmas of this type are given in (Lee et al 2000, Plonjes et al
2001), from which most of the data given below are obtained.
A schematic ofa typical experimental set-up is shown in figure 7.2.2.2. A
continuous wave (c.w.) carbon monoxide laser is used to irradiate a high-
pressure gas mixture, which is slowly flowing through an optical absorption
cell. For purposes of the present discussion consider that gas mixture to be
nitrogen containing 1 % of carbon monoxide and trace amounts ("-'10-
100 ppm) of nitric oxide or oxygen, at pressures of P = 0.4--1.2 atm. The
residence time of the gases in the cell is about 1 s. The CO pump laser is
electrically excited, producing continuous wave output on approximately
20 vibrational-rotational lines of the CO fundamental infrared bands,
vibrational quantum transitions ~v = 1. It produces a substantial fraction
of its power output on the v = 1 -
0 fundamental band component
in the infrared. (Note that 50% efficiencies have been demonstrated for
these lasers at very high powers.) A typical small-scale laser operates at
10-15 W continuous wave broadband power on the lowest ten fundamental
bands. The output on the lowest bands (l -
0 and 2 -
1) is necessary to
start the absorption process in cold CO (initially at 300 K) in the cell. The
laser is mildly focused to increase the power loading per CO molecule,
providing an excitation region of, typically, ,,",1-2 mm diameter and up to
10 cmlong. The absorbed laser power is of the order of 1 W/cm over
the absorption length of about 10cm, which gives an absorbed power
density of ""' 100 W /cm3. It is important to note that this technique is not
the laser-induced 'breakdown', familiar from the many focused pulsed
laser experiments, which create an intense arc-like plasma. In the present
technique, up to at least 70% of the laser power is absorbed, but by
resonance transitions, initially, into the vibrational mode of the CO seedant
only. This use of the CO laser to excite high-pressure gas mixtures is an
extension of a technique described numerous times in the literature
--- Page 385 ---
370
High Frequency Air Plasmas
ToFTIR
ToOMA
Emission Spectroscopy:
Linc-of·Sight Inrograti<.lfl
impact
applied
lOmzatJ7 n.t ~eld
k;.,n-exp(-N/E)t
jt
f
J Joule
\
heat
ElNt~ Tt
Self-sustained discharge
Ruman ~'pcctrOSCQPY:
Point M~'t\lrum"''11t
stabilizing link
n
associative
n..l. n.t
applied
ionization I'
kjonn(v)n(w),j,
'\ field
jt
J
Joule
heat
n(v),n(w),l,
~
V-T
Tt
relaxation
CO laser I RF pumped plasma
Figure 7.2.2.2. Schematic of the CO Jaser/rf field pumping experiment.
(Rich et a11979, DeLeon and Rich 1986, Flament et a11992, Wallaart et al
1995, Diinnwald et al 1985, Saupe et al 1993, Plonjes et al 2000, Lee et al
2000).
The low vibrational states of CO, v ~ 10, are populated by direct
resonance absorption of CO pump laser radiation in combination with
rapid redistribution of the population by vibration-vibration (V-V)
exchange processes [14],
CO(v) + CO(w) -
CO(v - 1) + CO(w + 1).
(7.2.2.5)
The V-V processes then continue to populate higher vibrational levels of
CO as well as vibrational levels of N2, which are not coupled to the laser
radiation (Diinnwald et a11985, Saupe et a11993, Plonjes et aI2000),
CO(v) + N2(w) -
CO(v - 1) + N2(w + 1).
(7.2.2.6)
The large heat capacity of the gases, as well as conductive and convective
cooling of the gas flow, allow the translational/rotational mode temperature
--- Page 386 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
371
in the cell to be controlled. Under steady-state conditions, when the average
vibrational mode energy of the CO would correspond to several thousand
Kelvin, the temperature never rises above a few hundred degrees (Dunnwald
et al 1985, Saupe et al 1993, Plonjes et al 2000). Thus a strong non-
equilibrium distribution of mode energies can be maintained in the cell,
characterized by a very high energy of the vibrational modes and a low
translational-rotational mode temperature. The populations of the
vibrational states of N2 and CO in the cell are monitored by infrared
emission and Raman spectroscopy (Plonjes et al 2000, Lee et al 2000).
Under these highly non-equilibrium conditions, the optically pumped
gas mixture becomes ionized by the associative ionization mechanism of
equation (7.2.2.4). The ionization of carbon monoxide by this mechanism
has been previously observed in CO-Ar and CO-N2 gas mixtures optically
pumped by resonance absorption of CO laser radiation (Plonjes et al 2000,
Adamovich et al 1993, 1997, 2000, and Palm et al 2000). The calculated
(Adamovich et al 1993, 1997, 2000) and measured (Plonjes et al 2000,
Palm et al 2000) steady-state electron density sustained by a lOW CO laser
in these optically pumped plasmas is in the range ne ~ 1010_1011 cm -3.
Such ionization levels are maintained in CO-Ar and CO-N2 mixtures by
the mechanism of equation (7.2.2.4) with the laser pump only. It is not
necessary to do additional work on the plasma. However, an rf field can
be imposed, and further energy inputed to the vibrational modes without
gas breakdown. For this purpose, two 3 cm diameter brass plate electrodes
were placed in the cell as shown in figure 7.2.2.2, so that the laser beam
creates a roughly cylindrical excited region between the electrodes, 1-2mm
in diameter. The probe electrodes, 13.S mm apart, are connected to a
13.S6 MHz rfpower supply via a tuner used for plasma impedance matching.
Typically, the reflected rf power does not exceed S-lO% of the forward
power. The applied rf voltage amplitude, measured by a high-voltage
probe, is varied in the range of 2-3 kV at P = 0.8-1.2 atm, so that the peak
reduced electric field does not exceed E / N ~ 1 X 10-16 V cm2. It should be
emphasized that this low value of E / N precludes electron impact ionization
by the applied field, so that the associative ionization of equation (7.2.2.6)
remains the only mechanism for electron production in the plasma. The
applied rffield is used to heat free electrons created by the associative ioniza-
tion mechanism and to couple additional power to the vibrational modes of
the gas mixture molecules by electron impact processes,
CO(v) + e-(hot) -
CO(v + ~v) + e-(cold)
N2(v) + e-(hot) -
N2(v + ~v) + e-(cold).
(7.2.2.7)
(7.2.2.8)
It is well known that over a wide range of reduced electric field values
(E/ N = (O.S-S.O) X 10-16 V cm2) more than 90% of the input electrical
power in nitrogen plasmas goes to vibrational excitation of N2 by electron
--- Page 387 ---
372
High Frequency Air Plasmas
CO laser Vibrational Mode
....
of CO
'-
(CO)t
RFfirld
+
....
Vibrational Mode
N/
ofN2
Electron Impact
(up to 90% of the total power)
Figure 7.2.2.3. Schematic of the dominant kinetic processes in a CO---N2 plasma pumped
by a CO laser and a sub-breakdown rf field.
impact (Raizer 1991). Combined with the high efficiency of the CO laser, this
provides a very efficient method of sustaining extreme vibrational
disequilibrium in high-pressure molecular gases. In this approach, the laser
need only be powerful enough to load one of the molecular vibrational
modes to vibrational levels producing significant ionization, in accordance
with equation (7.2.2.4). It is not necessary to use a high-power pump laser.
However, as shall be seen subsequently, considerably greater laser powers
are needed to achieve the same states in air mixtures.
The strong vibrational disequilibrium enhanced by the electron impact
processes of equations (7.2.2.7) and (7.2.2.8) results in a faster electron
production by the associative ionization mechanism of equation (7.2.2.6).
The resultant electron density increase in turn further accelerates the rate
of energy addition to the vibrational modes of the molecules. However,
this self-accelerating process does not produce an ionization instability
such as occurs in other types of high-pressure non-equilibrium plasmas.
The reason for this is a built-in self-stabilization mechanism existing in
plasmas sustained by associative ionization. In high-pressure self-sustained
discharge plasmas, excess Joule heating produced by a local electron density
rise accelerates the rate of impact ionization and therefore results in a further
increase of electron density (see figure 7.2.2.3). This is the well-known
mechanism of ionization-heating instability development (Raizer 1991,
Velikhov et al 1987). In a plasma sustained by associative ionization,
excess Joule heating due to a local electron density rise sharply increases
the vibration-translation (V-T) relaxation rates, which results in a rapid
depopulation of high vibrational energy levels, slows down the ionization
rate, and reduces the electron density (see figure 7.2.2.2). This provides
negative feedback between gas heating and the ionization rate and enables
the unconditional stability of the plasma at arbitrarily high pressures, for
--- Page 388 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
373
as long as the applied rf field does not produce any impact ionization.
Obviously, optically pumped plasmas sustained by the CO laser alone (without
the externally applied field) are always unconditionally stable. Indeed, stable
and diffuse plasmas of this type have been sustained in CO-Ar mixtures at
pressures up to 10 atm (Rich et aI1982). Figure 7.2.2.3 shows a schematic of
the dominant kinetic processes in the CO laser/rf field sustained CO-N2
plasma.
Triggering the rf power coupling to the vibrational modes of the cell
gases requires the initial electron density, ne, to exceed a certain threshold
value. Recent studies of associative ionization in CO laser pumped plasmas
(Plonjes et al 2000, Adamovich et al 2000, Palm et al 2000) showed that the
electron density in these plasmas can be significantly increased (from
ne < 1010 cm-3 to ne = (1.5-3.0) x 1011 cm-3) by adding trace amounts of
species such as O2 and NO to the baseline CO-Ar or CO-N2 gas mixtures;
as discussed in (Lee et aI2000), this has the net effect of significantly altering
the dissociative recombination rate in the plasma.
Figures 7.2.2.4-7.2.2.7 show the levels of non-equilibrium mode
excitation and plasma production with this method. Figure 7.2.2.4 shows
the spectrally-resolved emission from the first overtone infrared bands of
CO in the CO-N2 plasma, displayed against the frequency (in wavenumbers)
for two plasma pressures, 600 and 720 torr. In this spectrum, each of the
peaks displayed is roughly indicative of the population of a CO vibrational
quantum level. The large peaks on the left correspond to the lower quantum
levels (v = 2, 3, and so on) with the highest populated levels (near v ~ 38) at
the right of the spectrum. The greatly increased populations when the
subcritical rf field is turned on are also displayed. Figure 7.2.2.5 shows the
corresponding N2 vibrational populations for one of the same CO-N2
plasmas, namely for the 600 torr case, from a Raman spectrum. In this
figure, each peak is indicative of the vibrational population, starting with
v = 0 on the right, and increasing to v = 4 on the left. Again, the much
greater population of the upper states with the rf field on is evident. The
Raman measurements are also used to infer the gas kinetic temperature
(i.e. the rotational/translational mode temperature) of these plasmas. This
temperature is 360 K for excitation with the CO laser alone, not greatly
above room temperature, and rises to 540 K when the rf is on for the
conditions of the figures. The photograph of figure 7.2.2.6 shows the visual
appearance of the plasma, again, with and without the rffield on. The visible
emission is from the small amounts of C2 and CN radicals formed from the
reaction of the vibrationally excited CO and N2. Chemical reaction is not a
significant energy absorption channel in the plasmas under these conditions,
but the visible electronic emission provides an easy qualitative diagnostic of
the plasma size. The substantial increase in volume with the rf is apparent.
Again, the electron densities, measured both by probes and microwave
attenuation techniques, are in the range 1.5-3.0 x 1011 cm -3.
--- Page 389 ---
374
High Frequency Air Plasmas
Intensity (arbitrary units)
P=600 torr, 1 % CO in N2
RFfieldoff
RFfieldon
4500
4000
3500
3000
2500
Wavenumbers
P=720 torr, 1% CO in N2
RF field off
RFfieldon
~I
#l
I I
I
4500
4000
3500
3000
2500
Wavenumbers
Figure 7.2.2.4. CO first overtone infrared emission spectra in the CO laserjrffield pumped
I %CO-99%N2-ISO ppm NO gas mixture at P = 600 torr (laser power 10 W) and
P = 720 torr (laser power 15 W).
Figure 7.2.2.7 shows the levels of excitation achieved when pumping
atmospheric air, inferred from the Raman spectra of a dry air mixture at
one atmosphere, with CO seedant, pumped by the CO laser. Figure 7.2.2.7
is a semilog plot of these experimentally determined relative populations of
--- Page 390 ---
Laser Initiated or Sustained, Seeded High-Pressure Plasmas
375
6E+4
4E+4
Intensity (arbitrary units)
602
RF field off (T=380 K, Tv = 1900 K)
RF field on (T=530 K, Tv =2500 K)
604
606
Wavelength, run
v=o
608
Figure 7.2.2.5. Raman spectra of nitrogen in the CO laser/rf field pumped I %CO-
99%N2-150ppm NO gas mixture at P = 600 torr. The spectra are normalized on the
v = 0 peak intensity.
each vibrational level for the three species, N2, CO, and °2, plotted against
the vibrational quantum level number. The vibrational quantum level
number is roughly proportional to the energy of the level. Accordingly, a
Boltzmann distribution of populations in such a plot would approximate
Figure 7.2.2.6. Photographs of the CO laser/rf field pumped 1 %CO-99%N2-10 ppm NO
gas mixture at P = I atm. Top, rf field turned off; bottom, rf field turned on.
--- Page 391 ---
376
High Frequency Air Plasmas
Relative population
1.0E+000
•
N2 , experiment (Tv ~2480 K)
•
CO,experiment(Tv~3410K)
'"
O2 , experiment (Tv ~3660 K)
l.OE-OOI
--- N2 , calculation (Tv~2470 K)
l.OE-002
l.OE-003
l.OE-004 -+--r----T-~-r__...,..-_r_--r-""T'"-~__,
o
4
8
12
16
20
Vibrational quantum number
Figure 7.2.2.7. Experimental (symbols) and calculated (lines) vibrational population
distribution functions on centerline of optically pumped atmospheric pressure air, for a
580/120/40 torr mixture of N2/02/CO.
a straight line; the obvious departure from Boltzmann equilibrium,
even within a single species vibrational mode, is evident. The higher level
populations are overpopulated in comparison to a Boltzmann plot. Since
an equilibrium (Boltzmann) distribution cannot be fitted to these data, a
unique 'vibrational mode temperature' cannot be assigned to each species.
We can, however, use the populations of only the lowest two vibrational
levels in each species to define an approximate vibrational mode temperature.
These approximate vibrational temperatures are given on the figure. It can be
seen that even these temperatures, which ignore the higher level overpopula-
tions, still are far above the translational mode, or gas kinetic temperature, of
the plasma, T = 540 K. It can be seen that approximately five vibrational
levels of the N2, eight vibrational levels of the CO, and 12 vibrational
levels of the O2 have significant non-equilibrium populations. The kinetics
of such vibrationally excited systems are now well understood, and dictate
that in mixtures of species such as in figure 7.2.2.7, the greatest energy
loading accumulates in the vibrational mode of the lowest frequency
oscillator, in this case, 02' The figure shows this, and also displays a kinetic
modeling calculation confirming this basic result.
The advantages of producing high-pressure low-temperature molecular
gas plasmas by the above method are apparent. There are two principal
--- Page 392 ---
References
377
limitations to using the CO seed ant optical pumping method as the sole
source of volume ionization. One is that associative ionization of the type
given by equation (7.2.2.4) is not a particularly efficient volume ionization
process, although it is a common ionizing process in conventional glow
discharges. It requires that a great deal of the work applied to the plasma
must go into vibrational mode excitation; the actual ionization energy
supplied to the plasma is only perhaps 0.1 % of the total power input. A
second limitation is that the laser power requirements rise substantially
with more fast-relaxing vibrationally-excited species present. To maintain
very high vibrational mode power loadings, the input laser power must
be increased. In the dry air case of figure 7.2.2.7, the oxygen is a faster
relaxing species than either the N2 or the CO seed ant. With the power
density of "-' 1-10 W /cm2 available from the laser used for these
experiments, no molecular species of the 1 atm air case were pumped to
levels high enough to give substantial associative ionization. With higher
powers, it is possible to achieve this in air mixtures. However, given the rela-
tively inefficient volume ionization obtainable by these means alone, the
optical pumping method should be supplemented by more efficient
ionization methods if large volume, high electron density plasmas are
wanted with minimum work input. When combined with an efficient ioniza-
tion technique, the vibrationally excited air produced by the optical pumping
exhibits striking increases in plasma lifetimes. The means of accomplishing
very high levels of ionization in relatively cold air by a combination of optical
pumping and an efficient ionizer are presented in a subsequent section
(section 7.5).
References
Adamovich I V, 2001 J. Phys. D: Appl. Phys. 34 319
Adamovich I V and Rich J W 1997 J. Phys. D: Appl. Phys. 30 1741
Adamovich I, Saupe S, Grassi M J, Schulz 0, Macheret S and Rich J W 1993 Chern. Phys.
173491
Basov, N G, Babaev, I K and Danilychev, V A et al1979 Sov. J. Quanturn Electronics 6
772
Billing, G D 1986 'Vibration-vibration and vibration-translation energy transfer, induding
multiquantum transitions in atom-diatom and diatom-diatom collisions' in None-
quilibriurn Vibrational Kinetics (Berlin: Springer) ch 4, pp 85-111
DeLeon R L and Rich J W 1986 Chern. Phys. 107283
Diinnwald H, Siegel E, Urban W, Rich J W, Homicz G F and Williams M J 1985 Chern.
Phys. 94 195
Flament C, George T, Meister K A, Tufts J C, Rich J W, Subramaniam V V, Martin J P,
Piar B and Perrin M Y 1992 Chern. Phys. 163241
Generalov, N A, Zimakov V P, Kosynkin V D, Raizer Yu P and Roitenburg D I 1975
Tech. Phys. Lett. 1431
--- Page 393 ---
378
High Frequency Air Plasmas
Kovalev AS, Muratov E A, Ozerenko A A, Rakhimov A T and Suetin N V 1985 Sov.
J. Plasma Phys. 11 515
Lee W, Adamovich I V and Lempert W R 2000 J. Chern. Phys. 114 117
Palm P, Plonjes E, Buoni M, Subramaniam V V and Adamovich I V 2000 'Electron density
and recombination measurements in co-seeded optically pumped plasmas',
submitted to J. Appl. Phys., December
Plonjes E, Palm P, Chernukho A P, Adamovich I V and Rich J W 2000a Chern. Phys. 256
315
Plonjes E, Palm P, Lee W, Chidley M D, Adamovich I V, Lempert W R and Rich J W
2000b Chern. Phys. 260 353
Plonjes E, Palm P, Adamovich I V and Rich J W 2000c J. Phys. D: Appl. Phys. 33(16) 2049
Plonjes E, Palm P, Lee W, Lempert W Rand Adamovich I V 2001 J. Appl. Phys. 89 5911
Polak L S, Sergeev P A and Slovetskii D I 1977 Sov. High Temp. Phys. 15 15
Raizer, Y P 1991 Gas Discharge Physics (Berlin: Springer)
Rich, J W 1982 'Relaxation of molecules exchanging vibrational energy,' in Massy H S W,
McDaniel E, Bederson Band Nighan W (eds) Applied Atomic Collision Physics, vol
3, Gas Lasers, ch 4, pp 99-140 (New York: Academic Press)
Rich J W, Bergman R C and Williams M J 1979 'Measurement of kinetic rates for carbon
monoxide laser systems', Final Contract Report AFOSR F49620-77-C-0020
(November)
Rich W, Bergman R C and Lordi J A 1975 AIAA J. 13 95
Saupe S, Adamovich I, Grassi M J and Rich J W 1993 Chern. Phys. 174219
Treanor, C E, Rich, J Wand Rehm, R G 1968 J. Chern. Phys. 48 1798
Velikhov E P, Kovalev A Sand Rakhimov A T 1987 Physical Phenomena in Gas Discharge
Plasmas (Nauka: Moscow)
Wallaart H L, Piar B, Perrin M Y and Martin J P 1995 Chern. Phys. 196 149
--- Page 394 ---
Ultraviolet Laser Produced TMAE Seed Plasma
379
7.2.3 Ultraviolet Laser Produced TMAE Seed Plasma
Experiments were performed to explore the possibility of creating an initial
seed plasma that can be sustained efficiently by the inductive coupling of
radiofrequency (rf) power. A large volume (500 cm\ axially long (100 cm)
tetrakis (dimethyl-amino) ethylene (TMAE) seeded plasma in a high-
pressure background gas is created by a uniform intensity ultraviolet beam
of 193 nm wavelength produced by a Lumonics Pulsemaster (PM-842)
excimer laser. The laser runs in the ArF mode (6.4eV). The long axial
extent of the electrodeless laser seed plasma is attractive since it can allow
enhanced rf penetration and ionization well away from the 20 cm axial
extent of the antenna. A schematic illustrating the initial University of
Wisconsin-Madison laser-initiated plasma experiment is shown in figure
7.2.3.1 (Ding et aI2001).
The efficiency of the subsequent rf sustainment of the plasma was
determined by the plasma density and lifetime that depends on the two-
and three-body recombination loss processes in the presence of background
gases and electron attachment to oxygen. In this section the laser-produced
TMAE plasma is characterized. The first measurement of temporal density
and temperature decay of the laser-produced TMAE plasma was carried
out using a special fast (7 ~ 10 ns) Langmuir probe whose structure is
Beam Splitter
Laser Light
Photodiode
Lens5ystem
Boxcar
Trigger
TMAE
Chamber
Voltage
1------1 Scanning
Figure 7.2.3.1. Laser seed plasma experiment. (Ding et aI200!.)
--- Page 395 ---
380
High Frequency Air Plasmas
Figure 7.2.3.2. Fast Langmuir probe structure. (Ding et aI200l.)
illustrated in figure 7.2.3.2 (Ding et al 2001). The instantaneous Langmuir
probe (LP) current-voltage characteristic curve is measured by a sampling
technique using a boxcar averager triggered by the laser pulse. A heated tung-
sten wire was used to keep the probe surface very clean and a dummy probe
was used differentially to reduce the noise from the laser, the electromagnetic
pulse and transient plasma oscillations. The LP current-voltage traces for
this plasma were extremely sharp. Very accurate temporal density and
temperature data was obtained for the plasma.
The LP temporal plots of electron density and temperature at 20 cm
from the Suprasil laser window are shown in figures 7.2.3.3 and 7.2.3.4
(Ding et al 2001). The high-density, cold plasma (1012_1013 cm-3, ,,-,0.2-
O.4eV) decay was accurately measured lOOns after the initial 20ns laser
pulse of 4-8 mJ/cm2 that created the plasma. The electron densities were
higher for higher TMAE pressure whereas the electron temperature was
higher for lower TMAE pressures. It was also observed that the electron
temperature decays sharply for earlier times as compared to the electron
density.
Consider the temporal decay of the plasma density. In the absence of an
ionizing source, the plasma decay can be described as (Akhtar et al 2004,
Ding et a12001, Kelly et a12002, Stalder et aI1992),
(7.2.3.1)
Here, Da is the ambipolar diffusion term, Ctr (cm3/s) is the two-body
(electron-ion) recombination coefficient and (3j=e,g (cm6/s) is the three-
body (electron-ion) recombination coefficient involving either a neutral
--- Page 396 ---
10"
0.0
Ultraviolet Laser Produced TMAE Seed Plasma
381
500.0
'9--1i3 2ntTarr TMAE
G-E><lmTorrTMAE
o--£JemTol1'TIotAE
~lemTarr1MAE
1000.0
Time (ns)
1510.0
2000.0
Figure 7.2.3.3. Temporal plots of electron density under conditions of 4mJjcm2 laser
fluence. (Ding et a12001.)
atom ({3g; ng) or an electron ({3e; ne) as the third species. Here, ng is the
neutral particle density of the neutral background gas. ria (cm6/s) is the
three-body
electron
attachment
rate
coefficient
for
the
process
e + O2 + M -
O2 + M (M = O2, N2). The diffusive loss in the TMAE
plasma after the application of the 20 ns laser pulse is small on the micro-
second time scale and can be neglected. Since the TMAE molecule is a
strong electron donor (Nakato et a11971, Holroyd et aI1987), the electron
attachment in a pure TMAE plasma is also very small and is neglected.
The rate coefficient for the three-body recombination process where the
third body is an electron (i.e. A + + e + e -
A* + e) is given by
{3e ~ 1.64 X 10-9 {T (Kelvin)} -9/2 cm6/s (Capitelli et al 2000). For electron
densities, ne ~ 1013 cm-3, at room temperature, the loss factor, {3ene, is
1.2 X 10-7 cm3/s. The neutral-stabilized, electron-ion collisional recombina-
tion rate for the process, A + + e + B -
A * + B, where B is a neutral atom,
is given as (Capitelli et a12000, Bates 1987).
(
300
)1.5
(3g ~ 6 X 10-27
T (Kelvin)
(cm6/s).
(7.2.3.2)
--- Page 397 ---
382
High Frequency Air Plasmas
~~------~--------~--------~-------,
0.10
soo.o
..-..1' mTorr TUAE
~8
mTOII' 1'UAE
ts---6'" mTOII'lIME
G---C2 mlblrTIIAE
lsoo.o
2000.0
Figure 7.2.3.4. Temporal decay of electron temperature corresponding to the plasma
density plots in figure 7.2.3.3. (Ding et aI200!.)
For a pure TMAE plasma at a maximum pressure of 50mtorr at 300K
(ng;:::; 1.6 x 1015 cm-3 using Loschmidt's number (NRL Plasma Formulary
2002)), the loss factor, {3gng = 9.6 x 10-12 cm3/s, can be neglected. However,
at 760 torr where the neutral particle density, ng = 2.45 x 1019 cm -3, the loss
factor, {3gng = 1.5 x 10-7 cm3/s, becomes important.
As a result, for a TMAE partial pressures of 4-16mtorr, the three-body
loss processes involving A + + e + e --- A' + e and A + + e + B --- A' + B
can be neglected along with the loss due to electron attachment to oxygen.
Therefore, for a temporally decaying TMAE plasma, the continuity equation
(7.2.3.1) takes the form
(7.2.3.3)
The effective recombination coefficient (£1) for a TMAE plasma can be
measured from the temporal plot of the plasma density. The numerical solu-
tion of equation (7.2.3.3) is obtained by determining the electron densities,
nel and ne2' at two closely-spaced measurement times, tl and t2, respectively.
It is given as
(7.2.3.4)
--- Page 398 ---
3.0 I
I
I
"'.!!! E
j
u
2.0 r
.,
Q ... --
....
r::
!
G)
:y
t
i 0 0
1
§
i
111 1.0 ~
r::
:S'
i
J I
I
t I I
I I
0.0 I
0.0
4to'
Ultraviolet Laser Produced TMAE Seed Plasma
383
500.0
1000.0
Time (ns)
1500.0
I
i J
I
2000.0
Figure 7.2.3.5. Temporal plot of effective electron-ion recombination coefficient under
conditions of 4mJ/cm2 laser fluence with TMAE pressures of (*) 16mtorr, (D) 8 mtorr,
(0) 4mtorr, and (V) 2mtorr and under 8mJ/cm2 laser fluence with a TMAE pressure
of (+) 8 mtorr. (Ding et aI200!.)
Using the data from the temporal density plot in figure 7.2.3.3, a temporal plot
of 0: starting 100 ns after the initial application of the 20 ns laser pulse is shown
in figure 7.2.3.5 (Ding et at 2001). As shown in the plot, the recombination
coefficient increases with time. The experimental result cannot be interpreted
by either three-body recombination or multi-ion species effects (Ding et al
2001). Since the neutral TMAE density was constant, the three-body process,
A + + e + TMAE -
A * + TMAE, remained constant in time. The recombi-
nation process, A + + e + e -
A* + e, will cause O:r to decrease as the
electron density decays. Multi-ion species will also cause O:r to decrease with
time. If two components are assumed, the component with a larger O:r
decays more rapidly and as a result the global value of O:r must decrease
with time. None of these processes can explain the increase of O:r with time.
This increase in O:r with time can be explained in terms of a delayed
ionization process in TMAE (Ding et al2001). This has also been observed
in large molecules such as metal clusters and C60 molecules (Schlag and Levin
1992, Levin 1997). Single photon ionization of large molecules does not
necessarily result in prompt ionization, even though the photon energy is
--- Page 399 ---
384
High Frequency Air Pfasmas
above the vertical ionization potential of the molecule (Schlag and Levin
1992). The photons absorbed by molecules AB produce super-excited
neutrals AB**. The super-excited AB** molecules store energy in the vibra-
tional states and it is the slow, diffusive-like transfer of this energy to the
departing electrons that determines the ionization rate (Levin 1997). This
process is known as delayed ionization and plays an important role in the
TMAE plasma formation and subsequent decay process. These super-excited
TMAE** neutrals decay by electron emission
TMAE + hv -
TMAE** -
TMAE+ + e (delayed ionization).
(7.2.3.5)
The process of delayed ionization can be incorporated in the temporal
TMAE plasma density decay as (Ding et af200l)
dne
,2
()
-= -an +D t
dt
e
(7.2.3.6)
where D(t) is the delayed ionization coefficient. Substituting dne/dte = -arn;
from equation (7.2.3.3), we obtain D(t) = (a' - ar)n;. This implies that
a' - a r is the change in recombination due to the delayed ionization.
The presence of air components such as oxygen at room temperature has
a substantial impact on the TMAE plasma formation and plasma decay
process essentially through the electron attachment process. In order to
achieve efficient rf sustainment of a laser-preionized TMAE seed plasma,
the following scientific issues have to be resolved: (i) The effect of the back-
ground gas on the formation and decay characteristics of the TMAE plasma,
(ii) the role of delayed ionization, (iii) whether the lifetime of the laser-
produced TMAE plasma is long enough such that rf power can be coupled
efficiently through inductive wave coupling at lower power levels to sustain
the plasma, and (iv) the time scale for modification of TMAE vapor due
to its chemical interaction with oxygen, which could reduce its viability as
a readily ultraviolet-ionized seed gas in air. In addition, the presence of a
background gas makes the plasma very collisional and, therefore, a plasma
diagnostic that measures plasma collisionality and recombination losses is
also required. Since the previous fast (10 ns) Langmuir pro be (LP) measure-
ments (Ding et af200l) could only be carried out 100 ns after the application
of the laser pulse when the plasma was in a quiescent decay state, many
physical processes, such as delayed ionization, present during the formation
and early stages of the decay of the TMAE plasma could not be examined.
Recent work (Akhtar et af2003, 2004) with millimeter wave interferometry
and fast emission spectroscopy diagnostics have been used to obtain the
full temporal decay characteristics of the TMAE plasma.
A 105 GHz (QBY-lAlOUW, Quinstar Technology) quadrature-phase,
millimeter wave interferometer was used to characterize the temporal
development of the plasma during and following the application of the
--- Page 400 ---
Ultraviolet Laser Produced TMAE Seed Plasma
385
In-Phase
Figure 7.2.3.6. Interferometer trace showing the phase and amplitude variation for
35 mtorr TMAE plasma after the application of a 20 ns laser pulse reaching a maximum
line-average plasma density of 4 x 1013 cm-3 (A-tB), followed by the plasma decay
(B -t C -t A) at a distance of 20 cm from the laser window. The outside circle represents
the vacuum phase variation. (Akhtar et al2004 (© 2004 IEEE).)
20 ns laser pulse. The millimeter wave interferometery technique is described
in detail in chapter 8 of this book (Akhtar et al 2003). The interferometer
worked in the Mach-Zehnder configuration, in which the plasma was in
one arm of the two-beam interferometer. The interferometer utilized an I-Q
(In-phase and Quadrature phase) mixer to obtain the phase and amplitude
change of the 105 GHz mm wave signal that passed through the plasma.
The interferometer trace shown in figure 7.2.3.6 is a function of time as
the 35 mtorr TMAE plasma formed by the application of 20 ns laser pulse
decayed.
Since
the
laser
intensity
(I = 6 mJ /cm2)
was
uniform
(tlI/ I ~ 10%) over its 2.8 em diameter, a uniform radial plasma profile
could be assumed. The outside circle represents the phase variation for
vacuum conditions without plasma. The onset of plasma followed the path
A ----> B. The line-average plasma density reached its maximum value of
4 x 1013 cm-3 at z = 20 em from the Suprasil window. The temporal decay
of TMAE plasma was along the path B ----> C ----> A. A plane wave model
and software were utilized to obtain the plasma density in this collisional
regime.
In figure 7.2.3.7, the temporal plot of the TMAE plasma density for 4,
16, and 50mtorr TMAE vapor pressures is shown. It should be noted that
the peak plasma density occurred fairly late in time (t = 140 ± IOns) after
the application of the laser pulse. Optical emission data also showed the
presence of a small (two orders of magnitude lower) direct ionization process
during the laser pulse. However, the initial (T::; 20ns) low density plasma
(rv 1011 em -3) produced by direct ionization could not be accurately
--- Page 401 ---
386
High Frequency Air Plasmas
1.0E+14
'?;
~ 1.0E+13
1
a 1.0£+12
<U s::
1.0E+11
o
~
50mTorr
500
1000
Time (ns)
1500
2000
Figure 7.2.3.7. Plots of TMAE plasma density versus time for different TMAE vapor
pressures for a laser fluence of 6 mJ /cm2, TL = 20 ns. (Akhtar et al2004 (© 2004 IEEE).)
measured by the 105 GHz interferometer. It was also observed that the
plasma density increased with vapor pressure, while the plasma density
decay was more rapid at higher vapor pressures. The axial plasma density
plot in figure 7.2.3.8 reveals a rapid axial plasma density decay for higher
vapor pressure plasmas. The fractional peak plasma density at an 80 cm
axial location with respect to its value at 20 cm was 40, 30, 14, and 8 % for
the 4, 10, 30, and 50 mtorr cases, respectively. This was due to the enhanced
laser absorption nearer the Suprasil window at higher pressures.
5.0
~i
4.0
=6 3.0
e
£
....
..
lOmToIT
=
"
a 2.0
~ ..
..
,
!
8mToIT
..
..
..
it 1.0
4mTorr
~--
0.0
20
30
40
50
60
70
80
Axial Distance (cm)
Figure 7.2.3.8. Axial density plot for various TMAE vapor pressures. (Akhtar et al2004
(© 2004 IEEE).)
--- Page 402 ---
Ultraviolet Laser Produced TMAE Seed Plasma
387
3.5E+13
3.0E+13
.... -; 2.5E+13
y
;5' 2.0E+13
l!!
,:!! 1.5E+13
01 a
~ 1.0E+13
5.0E+12
TMAE (16 mTorr)
+ Helium
+ Argon
+ Air
o
100
200
300
400
500
Time (DlI)
Figure 7.2.3.9. TMAE plasma density versus time plot for different background gases at
760 torr. (Akhtar et al2004 (© 2004 IEEE).)
In order to study the effect of background gases on the TMAE plasma
formation and decay characteristics in an evacuated chamber, the TMAE
pressure was raised to 16 mtorr and then the background gas pressure was
increased slowly to 760 torr. A temporal plot of the TMAE plasma density
in the presence of different background gases is shown in figure 7.2.3.9. A
laser fiuence of 6mJjcm2 was maintained. The temporal variation of
l6mtorr of pure TMAE plasma density is also shown in the plot for
reference.
The peak plasma density of pure TMAE was 3.2 x 1013 cm-3 . In the
presence of 760 torr of noble gases such as helium and argon, the TMAE
peak plasma density was reduced to 2.9 x 1013 and 2.3 x 1013 cm -3, respec-
tively. This corresponds to a density reduction of 10% for helium and
30% for argon background gas. It was also observed that a high-density
(> 1012 cm -3) plasma is maintained in the presence of noble background
gases for over 2 JlS. Since the background gas was at atmospheric pressure
with neutral particle densities ,.,.,2.5 x 1019 cm-3, the effect of three-body
recombination involving a neutral as the third particle became an important
factor. In the experiment with room temperature air constituents as the back-
ground gas, the effect of electron attachment was evident. The peak TMAE
plasma densities obtained in the presence of 760 torr of nitrogen, oxygen and
air were 1.8 x 1013,5.8 X 1012 and 9.8 x 1012 cm-3, respectively. In addition,
a TMAE plasma density :::::5 x lOll cm-3 was maintained in atmospheric air
for t ::::: 0.3 JlS. This was long enough so that rfpower could be coupled to the
seed plasma efficiently (Kelly et al 2002). It was also observed that the seed
TMAE vapor remained viable for large-volume (,.,.,500 cm3) and high-density
(1013 cm-3) laser ionization in air for t :-:; 10 minutes.
--- Page 403 ---
388
High Frequency Air Plasmas
7.2.3.1
TMAE density decay in the presence of Noble Gases
In the presence of noble gases at 760 torr, three-body recombination
involving neutrals as the third particle becomes significant. Neglecting
electron attachment, equation (7.2.3.1) can be expressed as
(7.2.3.7)
Here 0: represents the recombination losses for the pure TMAE plasma
described in equation (7.2.3.3) and f3g is the loss due to three-body recombi-
nation where the third body is a neutral atom. In order to determine f3g for
TMAE in the presence of helium and argon, a numerical derivative of the
TMAE plasma density temporal plot in figure 7.2.3.9 is obtained. Using
the recombination coefficients, 0:, already obtained for pure TMAE (figure
7.2.3.5) along with the neutral particle gas density, ng , equation (7.2.3.7)
was numerically solved in time to determine f3g• A plot of the resultant
three-body recombination coefficient, f3g, is presented in figure 7.2.3.10.
Since the three-body recombination process depends on the neutral gas
density (maintained at 760 torr during this experiment) only a very small
temporal variation in f3g was observed. The small variation (,,-,5%) is
within statistical error. In this experiment, the three-body recombination
rate coefficients for TMAE in the presence of helium and argon were
determined to be f3 (He) = (4.35±0.7) x 10-26 cm6 S-I and f3g(Ar) =
(9.5 ± 0.8) x 10-26 cme
S-I, respectively. The values obtained were compar-
able to the published collisional three-body recombination rates for singly
ionized plasmas (Zel'dovich and Raizer 1966).
l.5E-25
~~ 1.0E-25
..,
"'s
~
e.o
c:c.. 5.0E-26
O.OE+OO
o
~
200
+ Helium
400
Time (ns)
600
800
Figure 7.2.3.10. Three-body recombination rate coefficients for a TMAE plasma in the
presence of helium and argon at 760 torr. (Akhtar et at 2004 (© 2004 IEEE).)
--- Page 404 ---
Ultraviolet Laser Produced TMAE Seed Plasma
389
7.2.3.2
TMAE density decay in the presence of air constituent gases
In atmospheric pressure air at room temperature, the dominant density loss
mechanism in a TMAE plasma in air is electron attachment with oxygen
through the process e + O2 + M -
O2 + M (M = O2, N2). Negative
oxygen ions are rapidly removed by ionic recombination and this results in
a significant reduction in the plasma density and life-time. The density
decay equation (equation (7.2.3.1)) for this case is written as
(7.2.3.8)
Here {3g is the three-body recombination rate coefficient with either oxygen or
nitrogen as the third species and /'l,a is the electron attachment rate coefficient
for oxygen and nitrogen. Based on the classical diffusion model that includes
the elastic scattering of electrons by diatomic molecules, the {3g values at room
temperature are assumed to be ~1O-26 cm6 s-l (Bates 1980, Biberman et al
1987) for the present calculation. The differences in {3g values for diatomic
molecules with mirror symmetry like oxygen, nitrogen and hydrogen are
small due to the absence of permanent dipole moments (Bates 1980).
A numerical solution of equation (7.2.3.8) is obtained for the electron
attachment coefficient, /'l,a' by using numerical differentiation of the temporal
decay of the TMAE plasma density in the presence of air constituents (figure
7.2.3.9) along with the known effective two-body recombination coefficient,
0:, for TMAE (figure 7.2.3.5). A temporal plot of the electron attachment rate
coefficient, /'l,a, for nitrogen, oxygen and air when they are individually added
to TMAE is shown in figure 7.2.3.11 (Akhtar et al 2004). As shown in that
1.0E-30
,:,_1.0£-31
.. .. 8
'-' •
~ 1.0£-32
1.0£-33
o
200
400
600
Time (os)
Figure 7.2.3.11. Electron attachment rate coefficients for a TMAE plasma in the presence
of nitrogen, oxygen and air at 760tOff. (Akhtar et al2004 «(0 2004 IEEE).)
--- Page 405 ---
390
High Frequency Air Plasmas
figure, the electron attachment rate decreases temporally with the TMAE
plasma density. This illustrates that the probability of electron capture for
attachment decreases with a decrease in the plasma density. In the presence
of nitrogen, the peak value at the peak plasma density (t = 140 ns) for K;a(N2)
is S.6 X 10-32 cm6 s-l. As a result, the subsequent nitrogen contribution to
the TMAE plasma loss for air is small. This is to be expected since nitrogen
does not readily form a negative ion and the dominant plasma loss can be
attributed to the presence of the oxygen (Capitelli et al 2000). However,
for oxygen, the peak electron attachment rate coefficient K;a(02) at
t= 140ns, when the TMAE density is maximum, is 3.2x 1O-31 cm6 s-1.
This is almost an order of magnitude higher than that for nitrogen. In the
presence of atmospheric air, the TMAE plasma electron attachment rate
to oxygen is 1.1 x 10-31 cm6 S-I. These electron attachment rate coefficients
for TMAE plasmas in nitrogen, oxygen and air are lower by almost an
order of magnitude than the values obtained for the process,
e + O2 + M -
O2 + M (M = O2, N2, H20) in room temperature air
(Raizer 1991). This indicates that the process of delayed ionization of
TMAE that has a much longer lifetime (T = 140 ns) than the direct ionization
gradually populates the emissive state and plays an important role in
increasing the lifetime of the TMAE plasma for rf sustainment at lower
power.
7.2.3.3
Plasma emission spectroscopy
The optical emission spectra of a 193 nm laser-produced TMAE plasma was
obtained using a high-resolution spectrometer (Akhtar et al 2004). Plasma
emission passed through a high-quality ultraviolet (200-800 nm) fiber-optic
bundle into a spectrometer, and was then detected by a photomultiplier
tube (PMT). An ultraviolet cutoff filter «300 nm) is used in front of the
fiber-optic bundle to eliminate the scattered 193 nm high-power source
laser pulse that can saturate the PMT. It utilizes a SOO mm focal length
monochromator (Acton Research SpectraPro-SOOi, Model SP-SS8) with a
1200 g/mm grating and a high-resolution of O.OS nm at 43S.8 nm. The
entrance and exit slit widths were set at 2000 11m to obtain a statistically
large number of photon counts per acquisition. A schematic is shown in
figure 7.2.3.12.
A wavelength scan of the emission spectrum from 300 to 6S0 nm, with a
step size of 4 nm and averaged over 200 laser pulses was obtained. A user-
defined program written in Lab View provided the flexibility of arbitrary
integration window size, accurate referencing of the integration window
with respect to the laser pulse, and better statistics by averaging over a
large number of laser pulses. The emission spectrum of 16mtorr TMAE
plasma alone and in the presence of air constituents, measured for the time
window 100 ns < t < 11 00 ns referenced to the laser pulse turn on with the
--- Page 406 ---
Ultraviolet Laser Produced TMAE Seed Plasma
391
Figure 7.2.3.12. Schematic of the experimental arrangement of the laser-initiated and rf
sustained plasma. The lens system is used to modify the laser footprint cross-section to
2.8 cm x 2.8 cm. In this experiment the rf coil has not been energized. (Akhtar et al 2004
(© 2004 IEEE).)
laser flux held constant at 6mJ/cm2 is shown in figure 7.2.3.13. The spectrum
has maxima at 448 and 480 nm. The 480 nm maximum was reported as a
peak emission and corresponds to the first Rydberg state TMAE* (Rl)
with a 20ns lifetime (Hori et a11968, Nakato et aI1972).
The emission spectrum increased in the presence of nitrogen as
compared to the pure TMAE spectrum, whereas the peak emission dropped
significantly in the presence of pure oxygen and it was only slightly higher
than the noise level. The decrease in plasma emission in the presence of
oxygen could be explained in terms of the rapid quenching of TMAE
plasma through the process of electron attachment to oxygen. This result
is in agreement with the interferometric measurements of lower density
and a shorter lifetime of the TMAE plasma in the presence of room tempera-
ture oxygen. A decrease was observed in the plasma emission with atmos-
pheric pressure air compared to TMAE alone. However, the plasma
emission as well as the peak plasma density measurement (ne i'::j 1013 cm-3)
indicates that a high-density (>5 x lOll cm-3) TMAE plasma in air can be
maintained for t :S 0.3 IlS such that efficient coupling at lower rf power for
sustainment can occur (Kelly et al 2002).
In order to obtain the temporal evolution of the 480 nm line corre-
sponding to the TMAE*(Rl) state over t :S 800 ns, a narrow integration
window of IOns was used. Figure 7.2.3.14 clearly shows that the peak of
--- Page 407 ---
392
High Frequency Air Plasmas
6.0 ~------------....,
5.0
·i 4.0
5
.E
Q.) > 3.0
]
~ 2.0
1.0
0.0
(\N2
, \
\
\
\
I
\
250.0
350.0
450.0
550.0
650.0
750.0
Wavelength (run)
Figure 7.2.3.13. Effect of 760 torr background gases nitrogen, oxygen and air on the
emission spectra of a 16mtorr TMAE plasma measured during the time window
lOOns < t < 1l00ns. (Akhtar et al2004 (© 2004 IEEE).)
480nm emISSIOn for 16mtorr TMAE occurred fairly late in time
(T= 140± IOns) after the application of the 20ns laser pulse. Small (two
orders of magnitude lower) 480 nm emission was also observed due to
the direct ionization process during the laser pulse. In order to reference
1.40
1.20
1.00
0.40
~
O:z
0.20
0.0
"
.
:"' '\
1 Air'
, ,
200.0
400.0
TIme (ns)
600.0
Figure 7.2.3.14. The temporal evolution of the 480nm line corresponding to TMAE
Rydberg states (Rl) for 16mtorr TMAE plasma in the presence of air constituent gases
nitrogen, oxygen and air at 760 torr. (Akhtar et al 2004 (© 2004 IEEE).)
--- Page 408 ---
Ultraviolet Laser Produced TMAE Seed Plasma
393
the plasma temporal emission to the turn-on of the laser pulse, the
laser temporal profile was accurately measured by a fast ultraviolet
photodiode (Hamamatsu S 1226-18BQ with less than 10 ns rise-time) using
a 2 GSa/s Lecroy sampling oscilloscope. This late emission of the 480 nm
peak was interpreted in terms of the phenomenon of delayed ionization of
TMAE.
The absence of direct ionization in TMAE is contrary to the traditional
interpretation of the ionization process associated with small molecules. The
process of ionization of small molecules is very direct and once the ionization
energy is exceeded, free electrons depart on a femtosecond time scale
(Platzman 1967). However, for larger molecules such as C60 and metal
oxide clusters, the ionization is no longer prompt and there is a measurable
time delay in the appearance of the electrons (Platzman 1967, Campbell
et at 1991, Wurz et al 1991, Remacle and Levin 1993). Research on
photo-ionization of C60 (Schlag et at 1992, Levin 1997) proposed that
even though the photons provide the energy necessary to initiate electron
removal, the actual departure of electrons and, hence, ionization is
delayed.
Most of the photons absorbed by the TMAE molecules do not
contribute to the direct ionization process. Even though the laser photon
energy of 6.4eV was above the TMAE vertical ionization potential
(6.1 eV) (Nakato et al 1971, 1972), the experiment indicated that the
additional energy of 0.3 eV above the ionization potential was not sufficient
to produce substantial direct ionization of the large TMAE molecule
(molecular weight = 200.3). Instead, these photons excited the neutrals to a
super-excited state. These super-excited TMAE neutrals (TMAE**) stored
energy in the many degrees of freedom of the molecule and then transfered
energy to the departing free electrons on a slower time scale (7 = 140ns).
The delay in the peak 480 nm emission after the application of the laser
pulse corresponded to the relaxation time of the super-excited state. From
the temporal plot of the 480nm emission, the relaxation time (the lifetime)
of the super-excited state was found to be 7 ~ 140 ± 10 ns. The lifetime of
the first Rydberg state of TMAE given by the observed emission spectrum
full width at half maximum (FWHM) was 30 ns.
The increase in plasma emission, as shown in figure 7.2.3.13, due to the
presence of nitrogen is on the higher wavelength side close to the 480 nm
Rydberg line. In addition, figure 7.2.3.13 shows that the peak of the
480 nm line occurs 200 ns after the laser pulse and that the full-width at
half-maximum of the Rydberg emission process increased to 170 ns. Since
nitrogen does not react with TMAE and also does not absorb 193 nm
photons, the enhancement of the emission intensity implies that the nitrogen
molecules enhanced the excitation of the TMAE** state, where energy was
stored, during the application of the laser pulse (Ding et al 2001). These
highly excited TMAE** states gradually decayed by electron emission and
--- Page 409 ---
394
High Frequency Air Plasmas
populated the first Rydberg state through the process, TMAE** +
N2 ---+ TMAE*(Rl) + N2. This gradual population of the TMAE*(RI)
state and subsequent emission resulted in a broad temporal profile of
480 nm emission.
The experiment showed that it is possible to create a large-volume
(",SOOcm\ high-density (",1013 cm-3) TMAE plasma in 760 torr air. The
density decay was such that ne ::::: S x 1011 cm-3 for t::::: 0.3 J.ls. In addition,
the long axial extent (l00 cm) of the laser seed plasma allowed enhanced rf
penetration and ionization well away from the 20 cm antenna axial extent.
This suggests an optimum electrodeless scenario where TMAE is pulse-
injected into heated air at 2000 K, thus reducing the electron attachment
and enhancing plasma lifetime in air. The plasma could be fonned by
ultraviolet flash tube optical means that facilitates the efficient coupling of
high-power pulsed rf power to the plasma and substantially reduces rf
power requirements for high-density (1013 cm-3), large volume air plasma
for a variety of applications.
References
Akhtar K, Scharer J, Tysk S and Denning C M 2004 IEEE Trans. Plasma Sci. 32(2) 813
Akhtar K, Scharer J, Tysk Sand Kho E 2003 Rev. Sci. Instrum. 74996
Bates D R 1980 J. Phys. B 13 2587
Biberman L M, Vorob'ev V Sand Yakubov I T 1987 Kinetics of Nonequilibrium Low-
Temperature Plasmas (New York: Consultants Bureau) p 412
Campbell GEE B, Ulmer G and Hertel I V 1991 Phys. Rev. Lett. 67 1986
Capitelli M, Ferreira C M, Gordiets B F and Osipove A I 2000 Plasma Kinetics in Atmos-
pheric Gases (Berlin: Springer) p 140
Ding G, Scharer J E and Kelly K 2001 Phys. Plasmas 8 334
Holroyd R A, Preses J M, Woody C L and Johnson R A 1987 Nuc!. Instr. and Meth. Phys.
Res. A 261 440
Hori M, Kimura K and Tsubomura H 1968 Spectrochimica Acta A 24 1397
Kelly K L, Scharer J E, Paller E S and Ding G 2002 J. Appl. Phys. 92 698
Levin R D 1997 Adv. Chern. Phys. 101 625
Nakato Y, Ozaki M, Egawa A and Tsubomura H 1971 Chern. Phys. Lett. 9(6), 615
Nakato Y, Ozaki M and Tsubomura H 1972 J. Phys. Chern. 76 2105
NRL Plasma Formulary, revised edition 2002
Platzman R L 1967 in Silini G (ed) Radiation Research (Amsterdam: North-Holland)
Raizer Y P 1991 Gas Discharge Physics (Berlin Heidelberg: Springer) p 62
Remade F and Levin R D 1993 Phys. Lett. A 173284
Schlag E Wand Levin R D 1992 J. Phys. Chern. 96 10608
Stalder K R and Eckstrom D J 1992 J. Appl. Phys. 72 3917
Stalder K R, Vidmar R J and Eckstrom D J 1992 J. Appl. Phys. 72 5098
Wurz P, Lykke K R, Pellin M J and Gruen D M 1991 J. App. Phys. 706647
Zel'dovich Y Band Raizer Y P 1966 Physics of Shock Waves and High-Temperature
Hydrodynamic Phenomena (New York: Academic Press) vol 1, p 407
--- Page 410 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
395
7.3 Radiofrequency and Microwave Sustained High-Pressure
Plasmas
7.3.1
Introduction
Radiofrequency and microwave sources for plasma production at low
pressures in the milli-torr range are highly developed and used in applications
for materials processing and surface modification. In this section, we describe
their characteristics for high density plasma production at high pressure and
in atmospheric air. The properties of near thermal equilibrium air plasmas
produced by a rf inductive source or plasma torch are discussed in section
7.3.2. Optical spectroscopy is used to measure the plasma density and elec-
tron temperature. Radiofrequency plate power is used to determine power
balance and efficiency characteristics for the air plasma in steady-state.
These results serve as a benchmark for air plasmas and illustrate the power
densities required to sustain air plasmas near thermal equilibrium at high
density.
Section 7.3.3 discusses rf sustainment of a flashtube or laser initiated
plasma. This can be accomplished at much lower power levels than is
required for breakdown and ionization in high-pressure air or other gas. It
should be noted that power levels for initial ionization of atmospheric air
are substantially higher that those discussed for steady-state in section
7.3.2. The laser-formed, large volume, high density plasma provides an
ideal plasma load that can be efficiently sustained at lower power levels by
short pulse or steady-state rf power. Detailed characteristics of the temporal
density characteristics of these plasmas are discussed using millimeter
wave interferometry, optical spectroscopy and detailed rf coupled power
measurements.
Section 7.3.4 discusses the use of microwaves to produce breakdown and
high density in air. Intersecting microwave beams can produce spatial
localization and microwaves can be used in a microwave cavity for highly
localized plasmas. They can also be beamed to space for plasma ionization
for use as a microwave mirror reflector in the atmosphere.
7.3.2 Review of rf plasma torch experiments
7.3.2.1
Introduction
Thermal plasma devices, such as rf or microwave torches, represent a con-
venient way to produce relatively large volumes of atmospheric pressure
air plasma with electron number densities up to 1015 cm -3. However, the
plasmas generated with such devices are generally near local thermodynamic
equilibrium (LTE), which implies that the gas temperature increases with the
electron number density as shown in figure 7.3.2.1. From that plot, one can
--- Page 411 ---
396
High Frequency Air Plasmas
1015
'?~
~ 1013
~
.~ 1011
CD
0
Gi 109
.0
E
:::l 107
Z
c
0 ts 105
CD
iIi
1rOOO
2000
LTE Air
P = 1 atm
3000
4000
5000
6000
Temperature (K)
Figure 7.3.2.1. Electron number density in atmospheric pressure air under LTE
conditions.
see that the equilibrium electron density in atmospheric pressure aIr IS
approximately 3.3 x 106 cm-3 at 2000 K, 6.5 X 1010 cm-3 at 3000 K,
6.1 x 1012 cm-3 at 4000K, and 6.2 x 1013 cm-3 at 5000K. Once produced,
the thermal plasma can be sustained for an indefinite duration if placed in
a perfectly insulated container. In this ideal situation, no power would be
needed to sustain the plasma and therefore the power budget could be infini-
tesimally small. In practice, however, the thermal plasma is flowing into a
non-perfectly insulated container or into ambient air, where it undergoes
recombination by conductive and radiative cooling and by mixing with
entrained air. The power required to sustain the plasma depends on the
geometry of the device, the environment into which the plasma flows, and
the flow velocity. In this section, the goal is to determine the minimum
power required to produce and sustain an open-air plasma volume by
means of a typical, industrial-scale rf, inductively coupled plasma torch.
First, a baseline experiment was performed to determine the 'brute force'
un optimized power necessary to produce a plasma with an electron
number density greater than 1013 em -3, and with dimensions greater than
5 em in all directions. Section 7.3.2.2 describes the rf torch facility that was
used and the set-up for the optical diagnostics. Section 7.3.2.3 presents
measurements of the gas and electron density profiles produced by the
torch for various gas injection modes. Finally section 7.3.2.4 presents
measurements of the power required to sustain the plasma.
7.3.2.2
Radiofrequency plasma torch facility
The measurements presented here were obtained in the rf torch facility of the
High Temperature Gas dynamics Laboratory at Stanford University. This
facility is centered around a 50 k W inductively coupled plasma torch (T AF A
--- Page 412 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
397
Nozzle
(7 em diameter) -~--
Quartz
Thbe
Power and
<
Cooling Water
Coil
Plasma Exit Velocity: -10 mls
't'flow (S em) = -S ms
't'chemistry < 1 ms
Gas Injectors:
• Radial
• Swirl
• Axial
Figure 7.3.2.2. Schematic cross-section of torch head with 7 cm diameter nozzle.
Model 66) powered by an rfLEPEL Model T-50-3 power supply operating at
4 MHz. The power supply delivers up to 120 k V A of line power to the oscillator
plates with a maximum of 12kV dc and 7.5A. The oscillator plates have a
maximum rf power output of 50 kW. The basic design for inductively coupled
plasma torches has not changed much since their introduction by Reed (1961).
A schematic drawing of the plasma torch head is shown in figure 7.3.2.2. The
feed gas is injected at the bottom ofa quartz tube (inner diameter 7.6cm, thick-
ness 3 mm) surrounded by a coaxial five-turn copper induction coil (mean
diameter 8.6 cm) traversed by an rf current. The outer Teflon body acts as an
electrical insulator and electromagnetic screen. The coil is cooled with de-
ionized water to prevent arcing between its turns. The rf current produces an
oscillating axial magnetic field that forces the free electrons to spin in a radial
plane and thereby generates eddy currents. The energetic free electrons
produced by rf excitation can then ionize and dissociate heavy particles through
collisions. Further details on inductively coupled plasma torches can be found
in Eckert et al (1968), Dresvin et al (1972), Davies and Simpson (1979), and
Boulos (1985), and advanced numerical models in Mostaghirni et al (1987,
1989) and van den Abeele et al (1999).
The plasma torch can operate with a variety of gases (air, hydrogen,
nitrogen, oxygen, methane, argon, or mixtures thereof). For the baseline
experiments described here, the feed gas was primarily air with a small
amount of hydrogen (less than 2% mole fraction) added for purposes of elec-
tron number density measurements from the Stark-broadened H,aline shape.
The feed gas can be injected in axial, radial or swirl modes through a
manifold located at the bottom of the torch. Axial injection provides bulk
movement to the gas during the start-up phase. In normal operation, only
swirl and radial injectors are used. As will be seen below, the swirl-to-
radial feed ratio has a large impact on the temperature and concentration
profiles of the plasmas produced by the torch.
--- Page 413 ---
398
High Frequency Air Plasmas
Collecting Lens
Axial and Latera14-Mirror
(f = 50 em)
Translational System
with Iris (F/60)
Long Pass Filter
A>4oonm '\
SPEX Model 750 M
0.75 m Monochromator
Grating: 1200 glmm,
blazed at 500 nm
\1·Llt::
. ::: ... ::: . ~ . :.:.,,:c:c:;;,,»=
"
Imaging Lens
(f=20cm)
L...------'T "
Data Acquisition
Computer
TE Cooled CCD Camera
__ --' SPEX Model TE2000
2000x8oo pixels
15x15 ~
TAFA Model 66
Plasma Torch
LEPEL Model T-50
RF Generator
4MHz,50kW
Figure 7.3.2.3. Experimental set-up for emission diagnostics. (Laux et at 2003.)
The plasma generated in the coil region expands into ambient air through
a converging copper nozzle, 7 cm in diameter. At the nozzle exit plane, the
maximum axial velocity is estimated to be 10m/s, the maximum temperature
is measured at about 7000 K, the density p ~ 5.04 X 10-2 kg m -3 and the
dynamic viscosity JL ~ 1.6 x 1O-4 kgm- 1 S-I. Based on the nozzle diameter
of 7 em, the Reynolds number at the nozzle exit is about 220. The plasma
jet is therefore laminar at locations of 1 and 5 cm downstream of the nozzle
exit where our measurements were made. A few nozzle diameters downstream
of the nozzle exit, the plasma plume becomes turbulent as a result of mixing
with ambient air.
The radial profiles of temperature and electron number density were
measured by optical emission spectroscopy. The experimental set-up, shown
in figure 7.3.2.3, includes a 0.75m monochromator (SPEX model 750M)
fitted with a 1200lines/mm grating blazed at 500 nm and a backthinned,
ultraviolet-coated SPEX Model TE-2000 Spectrum One thermoelectrically
cooled CCD camera. The CCD chip measures 30 x l2mm and contains
2000 x 800 square pixels of dimension 15 x 151lm. Absolute intensity cali-
brations were obtained with an Optronics model OL550 radiance standard
traceable to NIST standards.
7.3.2.3
Plasma characterization
Figure 7.3.2.4 shows photographs of the plasma plume for three different
swirl/radial injection ratios. In the 'low swirl case', the flow rates were
67 slpm (standard liter per minute) in the radial mode and 33 slpm in the
--- Page 414 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
399
Figure 7.3.2.4. Air plasma plume for three conditions of the radial/swirl flowrates.
swirl mode. The 'medium' and 'high' swirl cases correspond to radial/swirl
flow rates of 67/50 and 67/67, respectively. In all three cases, the plate
power was kept constant at approximately 41.2kW, and a small quantity
of hydrogen (2.3 slpm) was premixed prior to injection into the torch. To a
good approximation the flow injected into the torch was thermodynamically
equivalent to humid air with 2.3 slpm of water vapor.
As can be seen from figure 7.3.2.4, the swirl/radial injection ratio had a
noticeable influence on the physical aspect of the plasma. The length of the
plume was approximately 35, 20, and 10 cm for the low (67/33), medium
(67/50) and high (67/67) swirl cases, respectively. In the low swirl case the
plasma luminosity exhibited a strong radial gradient, but in contrast it was
almost radially uniform in the high swirl case (it is not possible to observe
radial variations of the luminosity in figure 7.3.2.4 because the photographs
are intensity-saturated). Thus the plasma properties (temperature, electron
number density) were more uniform radially in the case with highest swirl
injection.
Measurements were made of temperature and electron number density
radial profiles at locations I and 5 cm downstream of the nozzle exit.
Temperature profiles were determined from the absolute intensity of the
atomic line of oxygen at 777.3 nm, using an Abel-inversion technique. The
temperature profiles measured at I and 5 cm downstream of the nozzle exit
for a plate power of 41.2 kW are shown in figures 7.3.2.5 and 7.3.2.6 for
both the low and high swirl cases. The radial profiles were found to be flatter
in the high swirl case (67/67) than in the low swirl case (67/33), in accordance
with the visual aspect of the plume.
--- Page 415 ---
400
High Frequency Air Plasmas
';m)
(00)
g (ill)
e
~
5~
<I)
S' ~
~
4~
4(0)
0
0.5
1.0
1.5
20
25
3.0
Rnus [an]
Figure 7.3.2.5. I cm downstream of the nozzle exit. Measured temperature profiles from
Abel-inverted absolute intensity profiles of the atomic oxygen triplet at 777.3 nm. Plate
power=41.2kW. Gas: air+2.3slpm H2.
Previous studies conducted at Stanford University (Laux 1993) had
shown that air plasmas generated by this torch under similar conditions of
temperature and velocity were close to local thermodynamic equilibrium
(LTE). This was because the characteristic chemical relaxation time was
about 10 times faster than the characteristic flow time between the coil
region, where the plasma was in a state of non-equilibrium, and the nozzle
exit where the measurements were made. Thus the relatively slow plasma
flowing through the 7 cm diameter nozzle was close to L TE both at 1 and
5 cm downstream of the nozzle exit. Under LTE conditions, electron
number densities were determined from the knowledge of the plasma
6500
-J:-~~
(ill)
g
()7!3.~
i
5500
i
5<XX)
~ 4500
4(0)
0
0.5
1.0
1.5
2.0
2.5
3.0
ROOius[an]
Figure 7.3.2.6. 5 cm downstream of the nozzle exit. Measured temperature profiles from
Abel-inverted absolute intensity profiles of the atomic oxygen triplet at 777.3 nm. Plate
power=41.2kW. Gas: air+2.3slpm H2 .
--- Page 416 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
401
1015
...L
~
1014
.[
67/67
r::,"
--Eq.Jilil:rium (0-m3 lire)
--Eq.Jilil:rium (0-m3 lire)
-Froml\
1013
0
0.5
1.0
1.5
20
2.5
3.0
Radius [cmJ
Figure 7.3.2.7. 1 cm downstream of the nozzle exit. Measured electron number density
profiles from Abel-inverted Ha line shapes and equilibrium electron number density
profiles based on the temperature profiles of figure 7.3.2.5. Plate power=41.2kW. Gas:
air+2.3slpm H 2.
temperature using chemical equilibrium relations (Saha equation). Figures
7.3.2.7 and 7.3.2.8 show the equilibrium electron number density profiles
based on the temperature profiles of figures 7.3.2.5 and 7.3.2.6. In order to
verify the L TE, direct electron number density measurements were also
made from the Stark-broadened atomic hydrogen Balmer (3 line at 486 nm,
using the spectroscopic technique detailed in chapter 8, section 8.3.
In air plasmas, the HiJ line sits on top of an intense emission background
that is mainly composed of bands of the second positive system of molecular
nitrogen. In order to extract the HiJ lineshape, spectral measurements were
10" r---------------------,
Radial/Swirl
10" ~~~~~~~~~~~~~~~~~~~
o
0.5
1.0
1.5
2.0
2.5
3.0
Radius [em]
Figure 7.3.2.8. 5 em downstream of the nozzle exit. Measured electron number density
profiles from Abel-inverted HiJ line shapes and equilibrium electron number density
profiles based on the temperature profiles of figure 7.3.2.6. Plate power=41.2 kW. Gas:
air+2.3slpm H2•
--- Page 417 ---
402
High Frequency Air Plasmas
,......,
::i
t'd
.......
. ~
rn
s:::
~
.....
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
483
-- Hp +Background
...... Background
• Hp
--Voigt
484
485
486
487
Wavelength [run]
Figure 7.3.2.9. Hp lineshape extraction procedure. I cm downstream of the nozzle exit.
Low swirl case (67/33 radial/swirl). Plate power=41.2kW. Gas: air+2.3slpm H2 . The
two spectra in the figure are those obtained after Abel-inversion at r = lOmm from the
plasma centerline.
made both with the mixture of air/hydrogen (spectrum labeled
'Hi3 + background' in figure 7.3.2.9) and with pure air (spectrum labeled
'Background'). Spectra measured at several lateral locations along chords
of the plasma were then Abel-inverted to provide local emission spectra as
a function of the radial location. At each radial location, the Hf3 lineshapes
were recovered by subtracting the background from the total signal. The
Hi3 lineshapes were then fitted with Voigt profiles, which represent the con-
volution of several broadening mechanisms including pressure (van der
Waals, resonance), Doppler, instrumental, and Stark broadening (see
figure 7.3.2.10). Pressure and Doppler broadening widths only depend on
the pressure and temperature of the gas. Instrumental broadening was
minimized by using a very small entrance slit on the monochromator
(30/lm). Radial electron number density profiles were determined with the
aid of the curves of figure 7.3.2.10. These curves were obtained as discussed
in chapter 8, section 8.5. The resulting electron density profiles are shown in
figures 7.3.2.7 and 7.3.2.8.
For the high swirl case shown in figure 7.3.2.8, the Hi3line intensity was
so weak relative to the nitrogen background (see figure 7.3.2.11) that it was
not possible to obtain a reliable series of Abel-inverted Hi3 lineshapes. Never-
theless, since the plasma temperature did not vary significantly over the
central part of the plasma, the electron number density determined from
the Hi3 lineshape measured along the diameter of the plasma provided an
estimate of the average electron density in the central region. As can be
seen from figure 7.3.2.8, the measured line-of-sight-averaged electron density
agreed well with the expected equilibrium value in the central region of the
plasma.
--- Page 418 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
403
0.10
0.08
E
!::: 0.06
'-'
~
:r:
~
0.04
0.02
0
10\3
1014
Electron Number Density [cm3]
Figure 7.3.2.10. H/lline broadening in atmospheric pressure, equilibrium air. Instrumental
broadening is well approximated by a Gaussian of half width at half maximum of
0.014nm.
The foregoing measurements demonstrated that the rf plasma torch
could generate steady-state open air plasmas with electron number densities
greater than 1013 em -3 over volumes with dimensions greater than 5 em in all
directions. The shape of the electron number density profiles could be
controlled by modifying the ratio of radial-to-swirl injection. The measure-
ments presented up to this point were obtained with a mixture of air and
hydrogen. Measurements were also made for dry air, in which case the
electron number density could only be determined by assuming chemical
equilibrium at the local temperature measured from the oxygen triplet at
777.3nm. Results of this series of experiments are shown in figures 7.3.2.12
1.4 ,...----------------------,
1.2
1.0
;:i
~ 0.8
.t 0.6
5
'E! 0.4
......
-- Hp + Background
...... Background
• Hp (x4)
-- Voigt Fit (x4)
0.2
O~~~~~~~~~~~~~~~~
969.5
970.0
970.5
971.0
971.5
Wavelength [nm]
Figure 7.3.2.11. Hi! lineshape extraction procedure. Line-of-sight Hi! lineshape at location
5 cm downstream of the nozzle exit. High swirl case (67/67 radial/swirl). Plate
power=41.2 kW. Gas: air + 2.3 slpm H2. Here the H/llineshape was measured in second
order so as to reduce instrumental broadening to approximately 0.007 nm. (Laux et al
2003.)
--- Page 419 ---
404
High Frequency Air Plasmas
6500
Radial/Swirl
~6000
~
~5500
-
e!
~5000
E
(1.)
1-4500
67167
4000
0
0.5
1.0
1.5
2.0
2.5
3.0
Radius [em]
Figure 7.3.2.12. Dry air. Temperature profiles 5 cm downstream of the nozzle exit as a
function of radial/swirl injection ratio. Plate power = 40.1 kW.
and 7.3.2.13. It can be seen that the profiles of temperature and electron
density are very similar to those measured in humid air.
7.3.2.4
The power budget
Power requirements can be defined either as the total 'wall plug' power
(which depends on the efficiency of the specific device utilized to generate
the plasma) or as the net power deposited into the plasma. In this work,
both measurements were made. The total wall plug power was determined
by directly measuring the current in each power lead of the 440 V, triphase
power supply, by means of a Fluke model 33 ammeter. The average
measured rms current was approximately 72A (70, 72, and 74A in each
phase). The rms voltage was Vrms = 440 V. The total wall power is then
"
c
1015 ~--------------------------------~
Radial/Swirl
~Eo-__
......... __
~6.7142
1013 ~~~~~~~~~~~~~~~~~~
o
0.5
1.0
1.5
2.0
2.5
3.0
Radius [em]
Figure 7.3.2.13. Dry air. LTE electron number density profiles at location 5 cm down-
stream of the nozzle exit as a function of radial/swirl injection ratio. Plate
power=40.1 kW.
--- Page 420 ---
Radiofrequency and Microwave Sustained High-Pressure Plasmas
405
given by the following expression:
P wall = V3Irms V rms cos cp ~ 48 kW
(7.3.2.1 )
where cos cp, the power factor, was approximately 0.9 according to power
supply specifications. The volume of plasma probed was well approximated
by a cylinder of diameter 6 cm and length 5 cm (140 cm3). Thus the total
volumetric wall power was about 340 W /cm3 .
To determine the power actually deposited into the plasma and, thereby,
the torch efficiency, a calorimetric balance was done on the cooling-water
circuit. To this end, the cooling circuit was instrumented with thermocouples
at the inlet and outlet of the generator, and turbine flow meters in the flow
lines. The total power removed by the cooling water was measured to be
Pcoolingwater = mep 6:..T ~ 33 kW.
(7.3.2.2)
The power deposited into the plasma is given by
P plasma = P wall - P cooling water ~ 15 k W.
(7.3.2.3)
The torch efficiency, defined as T/ = P plasmal P wall> was therefore about 31 %.
Thus, the minimum power required to sustain the thermal plasma volume
was lO5W/cm3.
The schematic plasma torch diagram presented in figure 7.3.2.14 shows
the power inputs and losses measured with the techniques described in the
Wall Power
48 kW
.. --...... " .
.
Electrical Circuit
_
_
_
_
I
Cooling Circuit
.. .. ..
Cooling water
• .... 33kW
J
= 105 W/cm'
Figure 7.3.2.14. Typical power flow diagram of the Stanford 50 kW rf torch.
--- Page 421 ---
406
High Frequency Air Plasmas
foregoing paragraphs. Approximately 15% of the total wall power was
dissipated as heat by the pumps and the filament, and about 54% by the
transformer/rectifier, oscillator, and torch head.
The total volume of plasma generated in the low swirl case (67/33)
depicted in figure 7.3.2.4 was actually larger than the probed volume of
140 cm3• The total volume with electron number densities greater than
1013 cm -3 was estimated to be on the order of 1000 cm3. This estimate
included the volume of plasma generated inside the torch head and the
volume extending 10cm downstream of the nozzle exit. Basing the power
requirements on this larger volume, the wall-plug power was about
48 W /cm3, and the minimum volumetric power for an ideal (100% efficient)
generator would be 15W/cm3•
7.3.3 Conclusions
Steady-state air plasmas with electron number densities greater than
1013 cm -3 and volumes with dimensions greater than 5 cm in all directions
were generated in both dry and humid air. The ratio of radial-to-swirl
injection controlled the shape of the electron number density profile, and
the power injected controlled the magnitude of the electron density profile.
The wall-plug power required to sustain an open volume of thermal air
plasma with electron density greater than 1013 cm -3 with a typical rf torch
was measured to be about 340W/cm3, or 105/rJW/cm3, where TJ represents
the efficiency of the specific device used to produce the plasma. Additional
experiments were conducted in the Stanford University High Temperature
Gas Dynamics Laboratory with an atmospheric pressure microwave torch
(model Litmas Red). This torch operated at a frequency of 2.45 GHz and
nominal power 5 kW, with up to 3.5 kW of microwave power deposited
Figure 7.3.2.15. Atmospheric pressure air plasma produced with a Litmas Red 5 kW
microwave torch. The nozzle exit diameter is 1 cm.
--- Page 422 ---
References
407
into the plasma. The torch could produce thermal air plasmas with tempera-
tures up to 5000 K, with a volume in open air of about 10 cm3• A photograph
of the plasma plume is shown in figure 7.3.2.15. The wall-plug power
required to produce electron densities greater than 1013 em -3 with the
microwave torch was about 200W/cm3, which is comparable to the power
requirements of the rf torch. It is important to emphasize again that the rf
and microwave torches produce plasmas that are thermal (i.e. in a state of
LTE) and accordingly that the gas temperature tends to be relatively high
(e.g. 4200 K for 1013 electrons/cm3). Reducing the plasma temperature
while maintaining a high electron number density requires the use of non-
equilibrium plasmas. This motivates the work presented later on de and
repetitively pulsed plasma discharges in section 7.4.
References
Boulos M I 1985 Pure Appl. Chem. 57(9) 1321
Davies J and Simpson P 1979 Induction Heating Handbook (London, New York:
McGraw-Hill)
Dresvin S V et a11972 in Dresvin S V (ed) Physics and Technology of Low-Temperature
Plasmas (Moscow: Atomizdat)
Eckert H U, Kelly F L and Olsen H N 1968 J. Appl. Phys. 39(3) 1846
Laux C 0 1993 'Optical diagnostics and radiative emission of air plasmas' PhD Thesis in
Mechanical Engineering, Stanford University, Stanford, CA
Laux C 0, Spence T G, Kruger CHand Zare R N 2003 PSST 12 I
Mostaghimi J and Boulos M I 1989 Plasma Chem. Plasma Proc. 9(1) 25
Mostaghimi J, Proulx P and Boulos M 11987 J. Appl. Phys. 61(5) 1753
Reed T B 1961 J. Appl. Phys. 32 821
van den Abeele D et al1999 Heat and Mass Transfer under Plasma Conditions 891340
7.3.3 Laser initiated and rf sustained experiments
7.3.3.1
Introduction
Near atmospheric pressure plasmas of higher densities (1013 cm-3) and larger
volumes (rv2000cm3) have a variety of applications. At higher pressures,
however, there is a decrease in the mean electron temperature at constant
rf power and fewer high-energy electrons are present. This effect, in addition
to the increasing collision frequency due to high gas pressures, makes the
energy cost per electron-ion pair created prohibitively high. A model
based on electron-beam delta function excitation and electric field sustain-
ment estimates a power density of 9 kW/cm3 for an air plasma density of
rv 1 013 / cm3 at sea level (Vidmar and Stalder 2003). In a classic experiment,
Eckert et al (1968) created an atmospheric pressure plasma in both argon
and air to study the emission spectrum given off by a high-pressure
plasma. Following the work of Babat (1947), he created a plasma using an
--- Page 423 ---
408
High Frequency Air Plasmas
inductive coil at a lower pressure of ",1 torr, and slowly increased the neutral
pressure and rf power until he could open the plasma chamber to the atmos-
phere. To protect the quartz chamber from heat damage and to help stabilize
the discharge, the gas was injected in a vortex, essentially forming a thermal
gas barrier between the hot plasma and the chamber wall. The coupled power
required to maintain the discharge was 18-S0kW at 4MHz to create the
plasma at lower pressure and sustain it up to atmospheric pressure with a
volume of about 2S00cm3 (7-IOW/cm3). Moreover, the time scale for
creating high-pressure plasma from the low pressure discharge is several
minutes and there is a great interest in the instantaneous creation of large
volume (> 1000 cm\ high density (1012_10 13 /cm3) discharges at atmospheric
pressures with minimum power.
In addition, the inductively coupled rf power required to ionize high-
pressure air is much higher than the rf power level (",9 kW /cm3) needed to
sustain the plasma at sea level. In an atmospheric pressure plasma torch, a
300 kV potential was required to initiate a discharge, whereas only 100 V
was needed to maintain the discharge with operating currents of 200-
600 A (Ramakrishnan and Rogozinski 1986, Schutze et alI998). Therefore,
there is a need for an alternative scheme to reduce the power budget required
to initiate and sustain the discharge at higher gas pressures. We envisioned
that if we could ionize a low ionization energy seed gas such as tetrakis
(dimethyl-amino) ethylene (TMAE) by (193 nm) ultraviolet laser or flash tube
photon absorption, then we could efficiently couple rf power to the plasma at
higher gas pressures and sustain the plasma at a much reduced rf power level.
A seed plasma can also be created by placing electrodes inside the chamber
where a small plasma formed by the spark is localized between the electrodes.
If the electrode is located close to the rf antenna so as to provide the required
plasma load, arcing from the rf source to the electrode can occur. In addition,
plasma bombardment of the electrode will result in deterioration and plasma
impurities over time.
Therefore, an electrodeless method for creating a large volume (SOO cm3)
seed plasma using ultraviolet photo-ionization is sought that will provide a
good plasma load for efficient rf coupling at lower power level via pulsed
inductively coupled sources. Previous experiments (Akhtar et al 2004,
Kelly et at 2002, Ding et at 2001) described in section 7.2.3, have shown
that a high initial density (",1013 cm-\ long axial extent (",100cm)
TMAE plasma can be efficiently created by a 193 nm laser in 760 torr of
nitrogen, air or argon. In addition, the long axial extent (100 cm) of the
laser seed plasma can allow enhanced rf penetration and ionization well
away from the IS-20 cm axial extent of the antenna. The possibility of
initiating a discharge by 193 nm laser photo-ionization of TMAE seeded in
high-pressure background argon gas that was later sustained by inductive
coupling of an rf wave has been demonstrated by Kelly et at (2002). This
section describes the experiments where laser-initiated seed discharge in
--- Page 424 ---
References
409
high-pressure background gas is sustained by the efficient coupling of rf
power with a reduced power budget.
7.3.3.2
Experimental set-up
A schematic of the experimental set-up is shown in figure 7.2.3.12. A uniform
intensity ultraviolet beam of 193 nm wavelength is produced using an
excimer laser (Lumonics Pulsemaster PM-842) that runs in the ArF (6.4eV
per photon) mode. The half-width of the laser pulse is 20 ± 2 ns with a 2 ns
rise/fall time and a maximum laser energy of 300 mJ. The laser output
cross-section of 2.8 cm x 1.2 cm is increased to 12.8 cm x 2.8 cm using a
lens system of fused silica cylindrical plano-convex and plano-concave
lenses in order to increase the plasma filling fraction of the vacuum chamber.
The laser beam enters a 5.4cm diameter by 80cm long alumina plasma
chamber through a 2.8 cm diameter Suprasil quartz window (98% transpar-
ency at 193 nm) at one end. Laser energy passing through the ultraviolet
window is measured using an energy meter Scientech (Astral AD30). In
order to account for the laser attenuation by the ultraviolet window, the
ultraviolet window is placed in front of the energy meter. A laser fluence
of 6 mJ /cm2 is maintained. Gas mass flow controllers along with a swirl
gas injection system are also located at the laser window end as shown in
figure 7.2.3.12. The plasma chamber is pumped down to a base pressure of
10-6 torr using a turbo-molecular pump. In the evacuated chamber, the
TMAE is either introduced by slowly raising the pressure to the optimum
values of 4--50 mtorr or by raising the chamber pressure to 5 torr with
argon pressurized TMAE admixture and then the air or noble gas is added
slowly over a minute to a pressure of760 torr while ensuring a laser-produced
TMAE plasma density> 1012 cm -3. The gas flow condition here is similar to
the static case and is used as a reference to measure the comparable efficiency
of the scheme.
The rfsource is a l3.56MHz single frequency generator and a maximum
output power of 10kW (Comdel CX-10000S) with variable duty cycle (90-
10%) and variable pulse repetition frequency (l00 Hz-l kHz) and very fast
(microsecond) turn-on/off time. Power is transmitted through a 500 cable
to an efficient capacitive matching network and to the antenna which
surrounds the plasma chamber. The rf power is coupled to the plasma
using a five-turn water-cooled helical antenna in conjunction with a capaci-
tive matching network. The equivalent series resistance of the antenna and
the capacitive match box are 1.50 and 300-400mO, respectively. We have
experimentally determined that a five-turn helical coil is the most effective
antenna for initiating and maintaining the plasma which excites the m = 0
TE mode field distribution. One interesting aspect that this antenna has
over the other antennas studied is that the dominant electric field lines,
which accelerate the electrons, have primarily an azimuthal component,
--- Page 425 ---
410
High Frequency Air Plasmas
and close on themselves. This eliminates the radial component of the current
density thought to be a major loss mechanism in the type-III antennas which
also excites m = 1 modes (Kelly et al 2002). The chamber and antenna are
enclosed in a screen shield at a 10 cm radius. The capacitive network consists
of two high-voltage vacuum variable capacitors and is shielded from the
plasma chamber by enclosing it in a conducting box. The lower plasma
radiation resistance (1-50) mandates special care required to reduce
ohmic losses in the impedance matching network and connections.
7.3.3.3
Experimental results
The hypotheses was confirmed in an earlier experiment (Kelly et al 2002)
where a laser-initiated seed discharge of 2-5 mtorr of TMAE in 150 torr of
argon is sustained by an rf coupling power of 2.8 kW, whereas with rf
power alone the maximum pressure at which plasma could be created was
80 torr. The line average plasma density scan versus pressure with different
rf sustaining power level is shown in figure 7.3.3.1.
We have recently improved the rf system by redesigning the capacitive
matching network and reduced the ohmic losses in the rf connections. A
very accurate, computer-controlled timing circuit sequences the seed gas
injection, laser firing, the rf turn-on and data acquisition. This exact timing
5
3.0
A
to ..
f::.
: .................
4
Argon:
•••••••••
2.5
:
.6.
•••
... ;
f
~
u
:
Argon+ TMAE
..
§"
-0
3
·
A
2.0
•
.¥
:!:.
·
l:'
•
~
•
;
• •
..
.
\
0
c:
•
IL
•
at
•
:;
0
2
.
f::.
1.5
•
Q.
II
.
Power
..5
E
• •
..
•
..!!
• •
A
D-
• •
••
•• •
f::.
1.0
• •
f::.
f::.
..
0
t~·5
tO~
10°
to'
t~
Pressure (Torr)
Figure 7.3.3.1. Collisionally corrected plasma density versus pressure for the five-turn
helical antenna in argon and a TMAEjargon mixture (Kelly et at 2002).
--- Page 426 ---
References
411
1.0E+14 r--------------------,
"
E
1.0E+13
.2-
~
Ui
~
\IS
E
~
1.0E+12
Q.
1.0E+11
10
20
30
40
60
60
70
80
Axial Distance (em)
Figure 7.3.3.2 Axial plot of the laser-initiated plasma density of 5 torr of argon-pressurized
TMAE with the addition of 760 torr of background gas.
sequence is very critical since the rf pulse must be enabled during the TMAE
plasma lifetime (T ~ I j.ts) where the seed plasma density is sufficiently large
(n > 1012/cm3) to provide sufficient plasma radiation resistance load
(Rpl > 10) for efficient rf coupling. Figure 7.3.3.2 shows the axial plot of
laser-initiated line-average plasma density of 5 torr argon pressurized
TMAE admixture to which 760 torr of background gas is slowly added.
The line-average plasma density is measured by the collisional plasma inter-
ferometry technique (Akhtar et at 2003). The long axial extent ('" 100 cm) of
high-density seed plasma acts as a good plasma load for efficient rf coupling.
Figure 7.3.3.3 shows photographs of argon plasmas at 760 torr. Part (a)
shows the plasma created by inductive coupling of 3.0 kW of rf power in a
Pyrex plasma chamber where the chamber pressure was raised to 760 torr.
In this case plasma is localized under the antenna. In contrast, as shown
in part (b), an axially uniform (",80 cm), high-density argon plasma
(1013 /cm3) is produced using rf sustainment of laser initiated discharge at
a substantially reduced rf power level of 700 W. A large volume plasma of
about 2000 cm3 is maintained at a density of '" 1 013 /cm3. The photograph
illustrates that the long axial extent of the seed plasma allows increased
axial penetration of inductive waves and helps maintain a plasma away
from the source region.
--- Page 427 ---
412
High Frequency Air Plasmas
(a)
(b)
Figure 7.3.3.3. 760 torr argon plasmas produced by (a) 3.0 kW ofrfpower alone and (b) by
rf sustainment of a laser initiated-discharge at 700 W.
Figure 7.3.3.4 shows a photograph of a laser-initiated and rf sustained
300 torr nitrogen plasma at a power level of 4.0 kW. The pressure variation
of the time-averaged plasma density and effective collision frequency of the
nitrogen plasma at a constant power of 4.0 kW is shown in figure 7.3.3.5.
A very bright plasma of high density (>1012 cm-3) fills the entire plasma
chamber. As can be seen from the photograph, the laser preionization has
a noticeable influence on the final rf sustained plasma density. It was also
observed that in the absence of a seed plasma or a low density seed
plasma, the background plasma could not be sustained even at higher rf
power levels. These results show that the laser initiation substantially
enhances the rf penetration and reduces the sustainment rf power levels.
Future research will examine air plasmas and higher rf power short pulses
for reduction of power densities for large-volumes high-density air plasmas.
Figure 7.3.3.4. Laser-initiated and rf sustained 300 torr nitrogen plasma at a coupled
power level of 4.0 kW.
--- Page 428 ---
References
413
5.0E+12
1.0E+12
-_.
r
-
4.0E+12
,
B.OE+11 ~
,
c?
I
(;
,
E
"
c
3.0E+12
6.0E+11
G)
.2-
:s
,
~
~
,
III
2.0E+12
4.0E+11
LL.
c
C
G)
0
c
:!!!
1.0E+12
2.0E+11 '0
0
O.OE+OO
O.OE+OO
50
150
170
220
300
Nitrogen Pressure (Torr)
Figure 7.3.3.5 Line average (d = 5 cm) plasma density and effective collision frequency for
a laser-initiated and rf sustained nitrogen plasma measured 10 cm from the antenna.
References
Akhtar K, Scharer J, Tysk S and Denning eM 2004 IEEE Trans. Plasma Sci. 32(2) 813
Akhtar K, Scharer J, Tysk Sand Kho E 2003 Rev. Sci. Insfrum. 74 996
Babat G 1947 J. Insf. Elec. Engineers (London) 94 27
Ding G, Scharer J E and Kelly K 2001 Phys. Plasmas 8 334
Eckert H U, Kelly F L and Olsen H N 1968 J. Appl. Phys. 3 1846
Kelly K L, Scharer J E, Paller E S and Ding G 2002 J. Appl. Phys. 92 698
Ramakrishnan S and Rogozinski, M W 1986 J. Appl. Phys. D 60 2771
Schutze A, Young J Y, Babayan S E, Park J, Selwyn G S and Hicks R F 1998 IEEE Trans.
Plasma Sci. 26 1685
Vidmar R J and Stalder K R 2003 'Air chemistry and power to generate and sustain
plasmas: plasma lifetime calculations', in Proc. AIAA 2003, pp. 1-8
7.3.4 Methods for spatial localization of a microwave discharge
7.3.4.1
Characteristics of microwave discharge
As discussed in section 1.2, at sea level, the molecular composition of air is
roughly 80% nitrogen (N2) and 20% oxygen (02), The ionization energies
Cj of O2 and N2 are 12.1 and l5.6eV, respectively. These molecules can be
ionized by ultraviolet radiation, for example, the earth's ionospheric
plasma is principally generated by solar ultraviolet radiation (see also section
1.3). Photon ionization requires that the wavelength AO of the radiation be
less than Ac = hc/cj. Thus the wavelengths of the ultraviolet radiation for
--- Page 429 ---
414
High Frequency Air Plasmas
ionizing O2 and N2 must be less than 102.6 and 79.6 nm, respectively. There-
fore, microwave wavelengths are too long to cause photon ionization. On the
other hand, the microwave electric field can accelerate background charge
particles. When the electric field intensity, E, of a high-power microwave
beam propagating in air exceeds the breakdown threshold field, Ecn of the
background air, avalanche ionization can occur through the impact process
(i.e. some of charge particles' (mainly electrons') kinetic energies can exceed
the ionization energies of O2 and N2). In each elastic collision with a neutral
molecule, an electron loses only a very small fraction of its total kinetic
energy, thus electrons can easily build up the thermal energy through
multiple collisions in the microwave field. However, as the electron energy
increases, the cross sections of inelastic collisions also increase. For electron
energies between 2 and 4 eV, the cross section for the excitation of vibrational
levels experiences a very large nearly step-like leap. This vibrational
excitation process hinders the continuous acceleration of electrons by the
microwave field toward the ionization energy level. It increases the required
field intensity for the microwave discharge, which occurs when the quiver
speed Vq of 'seed' electrons exceeds a critical value, Vqc = eEcr/mvc, where
Vc is the electron-neutral particle collision frequency. Then a significant
fraction of seed electrons can bypass the vibrational excitation loss band
and are accelerated continuously by the microwave field to the ionization
energy level. The breakdown threshold field, Ecn for a continuous wave or
long pulse microwave beam is given by (Lupan 1976)
Ecr = 3.684p(1 +w2/v~)1/2kV/m
(7.3.4.1)
where p is the background air pressure measured in torr; and wand Vc are the
microwave frequency and electron-neutral particle collision frequency,
respectively.
The density, n, of the microwave plasma is normally limited by the
microwave frequency. In the density range of n ~ 1017 m -3, the dominant
loss mechanism of free electrons in air is through their attachment with
neutral molecules. Avalanche breakdown occurs when the ionization rate,
Vi, is larger than the attachment rate, Va. The ionization frequency, Vi, is
given by (Yu 1976, Kuo and Zhang 1991)
Vi = 2.5 X 107p[8.8c:1/ 2 + 2.236c:3/ 2] exp( -7.546/c:)
S-I
(7.3.4.2)
where c: = E/Ecr . Equation (7.3.4.2) can be reduced to vi/va ~ c:5.3 for
1.3 < c: < 3.5 (Gurevich 1980).
This microwave-generated plasma attenuates the microwave beam
spatially, which in turn affects the volume and uniformity of plasma generation.
If the background is uniform, ionization tends to occur near the source, which
hinders the propagation of the microwave beam. Therefore, the electric field
intensity of a high-power microwave beam cannot be increased indefinitely.
Its power density has an upper bound set by the avalanche breakdown of air.
--- Page 430 ---
E
u
-..
!1
C
>
li:i
References
415
104 ..-----.---.--.--.-1 "-1 rll,nl"T1 '-1 --'--'-rrnl I"I""II..---.-"-.-TI TllnlTj '-1 --,--r-T""'rl 1 nr.1
102
4
3.3,us
o
1.1J4S
f -3.33Hz
::
Figure 7.3.4.1. Dependence of air breakdown threshold fields on the pressure for micro-
wave pulse lengths of 1.1 and 3.3I-1s. (Kuo et aI1990.)
It is noted that the breakdown process requires an initiation time
interval that depends on the number of seed electrons pre-existing in the
background. Normally, the breakdown threshold field increases as the
pulse length, T, of the microwave radiation decreases. This tendency is
demonstrated (Kuo and Zhang 1990) by the two Paschen breakdown
curves shown in figure 7.3.4.1, which show the dependence of the air break-
down threshold field on the air pressure for the cases of 1.1 and 3.3 ~s pulses.
In both cases, the minimum of the breakdown threshold appears at about the
same pressure, where Vc ~ w consistent with equation (7.3.4.1). In the
pressure region having vc» w, the breakdown threshold field, Ecn is
essentially independent of the pulse length and microwave frequency. Thus
Ecr = 3.684pkVjm, the same as in the de discharge case. In this pressure
region, it should be noted that the thermal ionization instability (Gildenburg
and Kim 1978) might become dominant in the discharge. This instability
arises due to mutual enhancements of the electron density and gas tempera-
ture. It evolves the discharge into filaments parallel to the wave electric field,
which form a fishbone structure (Vikharev et a11988) as can be seen from the
luminescence of the discharge.
To use microwaves to produce atmospheric pressure air plasma in
a designated region away from the source, it is necessary to avoid the
--- Page 431 ---
416
High Frequency Air Plasmas
undesirable ionization along the propagation path before reaching the
preferred ionization region. Such undesirable ionization causes attenuation
of the microwave radiation, which could then be left with insufficient
power density to cause air breakdown in the designated region. The
maximum power density of microwave radiation that propagates in the air
at atmospheric pressure without causing air breakdown is about 10GW/
m2. This thus determines an upper bound of the microwave power for the
application of air plasma generation at atmospheric pressure. Therefore,
additional arrangements are needed to achieve spatial localization of the
discharge. Several prominent approaches are discussed in the following.
1. Use a microwave resonant cavity to enhance the electric field intensity at
localized resonant peak-field regions. The plasma thus generated is
confined inside the cavity. An air jet can be introduced to blow the
plasma out of the cavity through a nozzle such as a microwave torch;
however, the volume of the plasma is usually small, and the generation
efficiency is low because most of the plasma is lost inside the cavity.
2. Add a lens to focus the microwave beam so that the electric field intensity
of the microwave beam in the region around the focal point can exceed the
air breakdown threshold. Again, the volume of the plasma is limited by
the size of the focal spot.
3. Add a seeding source to produce preliminary plasma, which can lower the
breakdown threshold field considerably in the region of space containing
the seed. The possible seeding sources include ultraviolet and x-ray radia-
tion, laser and electron beams, and dc and low frequency discharges (e.g.
plasma torches).
4. Use two intersecting microwave beams with parallel polarization. The
field intensity of each beam is below the breakdown threshold (Vikharev
et a11984, Kuo and Zhang 1990). However, in the intersection region of
the two beams, the field intensity can be doubled and can exceed the
breakdown threshold. This approach makes it possible to achieve better
spatial localization of the discharge and yet to produce plasma in a
large region (determined by the size of the intersection region). In fact,
this approach was first (Gurevich 1980) suggested to generate an artificial
ionospheric mirror in the lower ionosphere by ground-transmitted high-
power microwave beams for over-the-horizon (OTH) radar applications
(Kuo et at 1992). This is the approach to be described in detail in the
next subsection.
7.3.4.2 Plasma generated by two intersecting microwave beams
In the experiments discussed here, microwave power at a frequency of
3.27 GHz was generated by a single magnetron driven by a pulse forming
network, which had a pulse length of 1.I11s and a repetition rate of 60 Hz.
--- Page 432 ---
References
417
The peak output power of the tube was 1 MW. Since the power density of the
microwave radiation was too low to cause air breakdown at atmospheric
pressure, the experiment was conducted in a Plexiglas cube chamber, 2 ft
(61 cm) on a side, which was pumped down to a pressure of about 1 torr.
First, it was found that using a single pulse it was possible to generate a loca-
lized plasma only near the chamber walls. Therefore, a second pulse provided
by the same magnetron was fed into the cube through a second S-band
microwave horn placed at a right angle to the first. With such an arrange-
ment, the power of each pulse was reduced to below the breakdown threshold
for the low-pressure air inside the chamber. Hence, air breakdown could only
occur in the central region of the chamber, where the two pulses intersected.
The wave fields added to form a standing-wave pattern in the intersecting
region in a direction perpendicular to the bisecting line of the angle between
the two intersecting pulses. Thus parallel plasma layers with a separation
d = AI J2 were generated, where A was the wavelength of the wave. This is
shown in figure 7.3.4.2(a), in which seven such layers can be seen. The spatial
distribution of the plasma layers was measured with a Langmuir double
probe. This was accomplished by using a microwave phase shifter to move
the plasma layers across the probe. The peak density distribution for one
half of a spatial period was thus obtained and is presented in figure
7.3.4.2(b). It is shown that the plasma layers produced are well confined
with very good spatial periodicity.
Using the same approach but with much higher microwave power, a
plasma having similar characteristics to those presented in figure 7.3.4.2
can be generated in the open air. The volume of plasma generated by this
approach would depend on the dimensions, a and b, of the cross section of
the (rectangular) waveguide used (i.e. on the frequency band of the
microwave). Because the maximum field intensity has to be lower than the
breakdown threshold field inside the waveguide and slightly higher than
half of the breakdown threshold field in the intersecting region, the volume
of the resulting intersecting region could be estimated to be Sa2b and the
volume of the region containing plasma would be about 4a2b. Using S-
band microwave radiation and a standard rectangular waveguide having a
cross section of 7.2 cm x 3.4 cm, the cross section of the horn should not
exceed 14.4 cm x 6.S cm. Therefore, the volume of microwave plasma
layers is estimated to be about 2a2b = 350cm3•
Air plasma is very collisional and thus quite different from the more
widely investigated plasmas having low background gas pressures. The
collision frequency is much larger than the plasma frequency for plasma densi-
ties less than 5 x 1013 cm -3. In this density regime, the real part of the index of
refraction is positive for all wave frequencies, and there is no cutoff to the wave
propagation. Thus the applicable microwave field, rather than the microwave
frequency, limits the plasma density, which is estimated to have a maximum at
about 1013 cm -3. Inelastic collision processes dominate the microwave plasma
--- Page 433 ---
418
High Frequency Air Plasmas
(a)
.
I
10
"'
i
I
.
,
i
•
I
I
I
i
! I
lo.+-r--r-lo o.+----l ,~f---,--.-I ..!~.
It--.--.--t.
i J.t.
!
t I
x (eM)
(b)
Figure 7.3.4.2. (a) Plasma layers generated by two crossed microwave pulses having
parallel polarization, (Kuo et al 1990) and (b) the plasma peak density distribution
across the plasma layers, from the central point at x = 0 of one layer to the midpoint at
x = 3.24cm of the next layer. (Kuo et aI1990.)
produced. Thus the electron temperature is usually limited to about 2 eV by
the vibrational excitation loss.
The power required to maintain such a microwave discharge depends on
the electron-ion recombination rate and on the heating rate of the neutral gas
by the plasma (mainly through electron-neutral inelastic collisions). The elec-
tron-ion recombination rate decreases with the temperature of the plasma
(Christophorou 1984, Rowe 1993). The electron-neutral inelastic collision
rate can be significantly reduced either by elevating the electron temperature
to exceed 4eV or by limiting it to be well below 2eV. An auxiliary plasma
--- Page 434 ---
Repetitively Pulsed Discharges in Air
419
heating mechanism, such as could be provided by an auxiliary dc or low
frequency field, may be used to maintain a non-equilibrium microwave
plasma and to reduce the microwave power budget. However, it is not clear
if the overall power budget can be thus reduced.
References
Christophorou L G 1984 Electron-Molecule Interactions and Their Applications, vol 2
(Orlando: Academic Press)
Gildenburg V B and Kim A V 1978 Sov. Phys. JETP 4772
Gurevich A V 1980 Sov. Phys. Usp. (Eng!. Trans!.) 23 862
Kuo S P 1990 Phys. Rev. Lett. 65(8) 1000
Kuo S P and Zhang Y S 1990 Phys. Fluids 2(3) 667
Kuo S P and Zhang Y S 1991 Phys. Fluids B 3(10) 2906
Kuo S P, Zhang Y S, Lee M C, Kossey P A and Barker R J 1992 Radio Sci. 27(6) 851
Lupan Y A 1976 Sov. Phys. Tech. Phys. 21(11) 1367
Rowe B R 1993 Recent Flowing Afterglow Measurements, in Dissociative Recombination:
Theory, Experiment and Applications (New York: Plenum Press)
Vikharev A L, Gildenburg V B, Golubev S V et al1988 Sov. Phys. JETP 67724
Vikharev A L, Gildenburg V B, Ivanov 0 A and Stepanov AN 1984 Sov. J. Plasma Phys.
1096
7.4 Repetitively Pulsed Discharges in Air
7.4.1
Introduction
As we have seen in chapter 5, the power required to sustain elevated electron
densities with dc discharges is extremely large. Therefore, we have explored a
power reduction strategy based on pulsed electron heating. This strategy is
illustrated in figure 7.4.1. Short voltage pulses are applied to increase the
electron number density. After each pulse, ne decreases according to electron
recombination processes. When ne reaches the minimum desired value, a
second pulse is applied. The average electron density obtained with this
method depends on the pulse duration, pulse voltage, and the interval
between pulses.
As seen in chapter 5, dc discharges can maintain ne ~ 1012 cm -3 in
atmospheric pressure air with electric fields producing an electron tempera-
ture on the order of 1 eV. To produce the same average electron density
with short (1-10 ns) pulsed discharges, a higher electron temperature of
about 3-5 eV is required. Although the corresponding field is higher than
for a dc discharge, the ionization efficiency is much larger in the pulsed
--- Page 435 ---
420
High Frequency Air Plasmas
't Pulse
~.
time
Figure 7.4.1. Repetitively pulsed strategy. (Kruger et at 2002.)
case than in the dc case because the energy lost to nitrogen molecules, per
electron created, is several orders of magnitude smaller at Te = 3-5 eV
than at 1 eV. This increase in efficiency allows the power budget to be drama-
tically reduced with pulsed discharges. It may be shown (Nagulapally et al
2000) that the power reduction afforded by the repetitively pulsed approach
relative to dc is given by
R '" kion(Te,pulse)N
2 Q( Q 1)-2
(Te,dC )3/2
=
xo:e e-
x ---
kDRn~
Te,pulse
where 0: == kionN7J, and where kion is the species-weighed rate coefficient for
electron impact ionization of °2, N2, and 0, kDR is the rate coefficient for
dissociative recombination of NO+, N is the total number density of species,
71 is the pulse length, n; is the average electron number density produced by
the repetitively pulsed discharge, and Te,dc and Te,pulse represent the electron
temperatures produced by the dc and pulsed discharges, respectively.
Figure 7.4.2 shows the predicted inelastic energy losses of electrons by
collisions with N2, per unit number density of N2 and electrons. The losses
to nitrogen represent the main fraction of the losses in air. This is because
at electron temperatures below ",20000 K the resonant e-V transfer in
ground state N2 is by far the dominant loss channel (there is no such resonant
channel for O2 or NO). At electron temperatures above 20000 K, the
inelastic losses are dominated by electron-impact electronic excitation,
dissociation, and ionization, and the total losses per unit number density
of N2 and electrons are about the same as the total losses per unit number
density of O2 and electrons. Nitrogen losses dominate at Te > 20000 K
because the density of N2 is much higher than the density of 02. Figure
7.4.2 shows that the (useful) power into ionization represents an increasingly
large fraction of the total power as the electron temperature is increased. This
explains why pulsed discharges with electron temperatures of several eV are
--- Page 436 ---
Repetitively Pulsed Discharges in Air
421
-- Total Inelastic Losses
-- N2 Vibrational Excitation
--.t.- N2 Electronic Excitation
--- N2 Dissociation
N2 Ionization
10.29 l...-__
.L....J~....L..I..-__
.l..-__
.l..-__
-'--__
J.....J
o
10,000 20,000 30,000 40,000 50,000 60,000
Te (K)
Figure 7.4.2. Inelastic power losses by electron-impact vibrational excitation, electronic
excitation, dissociation, and ionization of N2• In these calculations, the vibrational
temperature is fixed equal to the gas temperature (Tv = Tg = 2000 K), and the electronic
temperature of internal energy levels is fixed equal to the electron temperature.
more efficient in terms of ionization than the dc discharges which operate at
about 1 eV.
7.4.2 Experiments with a single pulse
To test the pulsing scheme, experiments were conducted (Nagulapally et al
2000) in atmospheric pressure 2000 K air using a pulse forming line capable
of generating a lOns rectangular pulse with peak voltage up to 16kV. To
experimentally simulate the conditions of a repetitively pulsed discharge,
the initial elevated electron number density generated by the 'previous'
pulse is created by means of a dc discharge in parallel with the pulser. The
circuit schematic is shown in figure 7.4.3. With a dc voltage of 2 kV and
current of IS0mA, the initial electron density is 6.S x lOll cm-3. A lOkV,
10 ns pulse is superimposed to further increase the electron density. The
measured discharge diameter of about 3 mm is comparable with the diameter
of the dc discharge (figure 7.4.4). The temporal variation of plasma conduc-
tivity was measured from the voltage across the electrodes and the current
density through the plasma. The electron density increases from 6.S x lO"
to 9 x 1012 cm-3 during the pulse, then decays to 1012cm-3 in about 121-1s
(figure 7.4.5). The average measured electron density over the 121-1s duration
is 2.8 x 1012cm-3.
--- Page 437 ---
422
High Frequency Air Plasmas
DC
2kV -
150mA
Figure 7.4.3. Schematic of the combined pulsed and dc discharge experiments. (Kruger
et a12002.)
Figure 7.4.5 shows a comparison of the measured electron number
density with the predictions of our two-temperature model. The predictions
agree well with the measured electron decay time of l211S. This decay time is
consistent with the dissociative recombination time of NO+ predicted to be
1.0
-:- O.B
:::l
~0.6
?;o
.~ 0.4
2
E 0.2
-4
-2
0
2
4
Radius (mm)
Figure 7.4.4. Spatial extent of the plasma produced with pulsed and dc discharges. (Kruger
et a12002.)
1x1013
Air, P=1atm, T,,2300K
Electrode gap = 1.2 cm
rf'
\\
DC current = 150 mA
E
~
.,
c:
1 x1 012
\\
Pulse vo~age = 10 kV
"
~--MOdel
--Measured
----
-----
------
---
f---
--- -
--
o
10
20
30
Time (l1s)
Figure 7.4.5. Temporal electron density profile in the 10 ns pulsed discharge. (Kruger et al
2002.)
--- Page 438 ---
Repetitively Pulsed Discharges in Air
423
8.71ls without the dc background. Thus these results provide validation of
our chemical kinetic model of the recombination phase.
7.4.3 Experiments with 100 kHz repetitive discharge
The success of the proof-of-concept experiments conducted with the single
pulse discharge led us to investigate the generation of air plasmas with a repe-
titively pulsed discharge. A repetitive pulser capable of generating IOns
pulses, with peak voltages of 3-12 kV and pulse repetition frequencies up
to lOO kHz, was acquired from Moose-Hill/FID Technologies. This pulser
operates with a solid-state opening switch or drift-step recovery diode
(DSRD). The experimental set-up is shown in figure 7.4.6 and the electrical
circuit in figure 7.4.7. The discharge is applied to preheated, LTE air at
atmospheric pressure and about 2000 K. The dc circuit in parallel with the
pulser was used only to determine the electron number density from the
plasma conductivity. In regular operation, the dc circuit is disconnected
and the discharge operated with the pulser only.
Cooling
Watt-'T
Inlet
Nozzle
(7 em exit
diameter)
- .
/
LTE2000Kair
~~pmfuMo¢m
Cooling
......... ~---- Water
( )utlet
Mixing
Test Section
Mixing Ring
..IIIII!lJIIIIIIIIIPID"'''''' Injectors:
95 slpm
Gas Injectors:
71 slpm radial
34 slpm swirl
Figure. 7.4.6. Set-up for repetitive pulse discharge in air at 2000 K, 1 atm. (Kruger et at
2002.)
--- Page 439 ---
424
High Frequency Air Plasmas
DC +
Supply_
300Vmax
400Q
Generator
~fo()se-Ilill
Figure. 7.4.7. Repetitive pulse discharge circuit schematic (dc circuit applied only for
conductivity measurements). (Kruger et aI2002.)
A photograph of the repetitively pulsed discharge in operation in
atmospheric pressure preheated (2000 K) air is shown in figure 7.4.8. The
diffuse character of the discharge was confirmed with time-resolved (1.5 ns
frames every 2 ns) measurements of plasma emission during the pulse (see
figure 7.4.9). These measurements were made with a high-speed intensified
camera, Roper Scientific PI-MAX 1024. The diameter of the discharge is
approximately 3.3 mm. Additional time- and spectrally-resolved measure-
ments of emission during the pulse and the recombination phase show that
the pulse excites the C state of N2 and the A state of NO. After the pulse,
emission from the C state of N2 decays to a constant value within 30 ns,
and emission from the A state of NO shows a two-step decay, with first an
abrupt decrease by over four orders of magnitude from the end of the
pulse until 320 ns after the pulse, and then a slower decrease by one order
of magnitude until the next pulse.
Figure 7.4.8. Photograph of IOns, 100kHz repetitive pulse discharge in air at 2000K,
1 atm. (Kruger et aI2002.)
--- Page 440 ---
Repetitively Pulsed Discharges in Air
425
t==O
2m;
4ns
6ns
8ns
IOns
12ns
140s
16n5
18ns
Figure 7.4.9. Time-resolved images of 10 ns pulsed discharge in air at 2000 K, I atm.
(Dulen et al2002 (© 2002 IEEE).)
Figure 7.4.10 shows the measured temporal variations of the electron
density during three cycles of the pulsed discharge. The electron number
density varies from 7 x 1011 to 1.7 X 1012 cm-3, with an average value of
about 1012 cm -3. The power deposited into the plasma by the repetitive
discharge was determined from the pulse current (measured with a Rogowski
coil), the voltage between the electrodes (6 kV peak) minus the cathode fall
3x1012.......,....--------------...------.
%
~
1012
c.'" 9x1011
8x1011
7x1011
6x1011
5x1011
0
5
10
15
20
25
t Uts]
Figure 7.4.10. Electron number density measurements in the repetitive pulse discharge in
air at I atm, 2000 K.
--- Page 441 ---
426
High Frequency Air Plasmas
voltage (measured to be 1525 V by varying the gap distance), and the meas-
ured discharge diameter. The peak pulse current was 240 rnA. The power
deposited is found to be 12 W/cm3, consistent with the theoretical value of
9 W/cm3 for an optimized pulsed discharge producing 1012 electrons/cm3.
It is lower, by a factor of 250, than the power of 3000 W/cm3 required to
sustain 1012 electrons/cm3 with a de discharge.
More details about these experiments and modeling can be found in
(Packan 2003). In this reference, a study was made of the effect of the
pulse repetition frequency. Experiments were conducted with repetition
frequencies of 30 and 100 kHz. In both cases the power requirements were
close to lOW /cm3 for about 1012 electrons/cm3 . The main difference between
the plasmas produced is the amplitude of electron density variations. In the
30 kHz discharge, the amplitude varies by about a factor of 10, whereas in the
100 kHz the amplitude varies by a factor of two only.
The results of our research on de and pulsed electrical discharges are
summarized in figure 7.4.11, which shows the power required to generate
elevated electron number density in 2000 K, atmospheric pressure air, with
de and pulsed discharges. The experimental point represents the measured
power requirement of our repetitively pulsed discharge experiment. Power
budget reductions by an additional factor of about 5 are possible with
repetitive pulses of 1 ns duration. Such repetitive pulsers are already com-
mercially available. Therefore, power budget reductions by a factor of
1000 relative to the de case at 1012 electrons/cm3 can be readily obtained
with a repetitively pulsed technique.
10kVV/am3~------+--------r--~--~--~~
1VV/am3r-~~~~~~~~~~~~--~-rl
1010
Figure 7.4.11. Power budget requirements versus electron number density for dc and
pulsed discharges in air at I atm, 2000 K.
--- Page 442 ---
Electron-Beam Experiment with Laser Excitation
427
7.4.4 Conclusions
We have described a plasma generation technique using a repetitively pulsed
discharge in which electron number densities of more than 1012 cm -3 in air
are produced with approximately 12Wjcm3, more than two orders of
magnitude lower than the power required for a dc discharge. The basis of
the technique is to apply short (IOns), high voltage (rvlOkV) electric
pulses with a repetition frequency tailored to match the recombination
time of electrons. Both single-shot and repetitively pulsed diffuse discharges
at 100kHz have been demonstrated, with power reductions of over two
orders of magnitude for average electron densities greater than 1012 cm-3.
Power reductions of approximately three orders of magnitude are possible
with a 1 ns repetitive pulsing technique.
References
Duten X, Packan D, Yu L, Laux C 0 and Kruge C H 2002 IEEE Trans. Plasma Sci. 30(1)
178
Kruger C H, Laux C 0, Yu L, Packan D and Pierrot L 2002 Pure and Applied Chemistry
74(3) 337
Nagulapally M, Candler G V, Laux C 0, Yu L, Packan D, Kruger C H, Stark Rand
Schoenbach K H 2000 'Experiments and simulations of dc and pulsed discharges
in air plasmas' in 31st AIAA Plasmadynamics and Lasers Conference, Denver, CO
Packan D M 2003 'Repetitively pulsed glow discharge in atmospheric pressure air' PhD
Thesis in Mechanical Engineering, Stanford University, Stanford, CA
7.5 Electron-Beam Experiment with Laser Excitation
7.5.1
Introduction
In this section, we present a method of sustaining large-volume plasmas in
cold, atmospheric pressure air, using the optical pumping technique reviewed
in section 7.2.2.1 above, combined with an electron beam ionizer. The combi-
nation of these techniques was adopted in an effort to mitigate the most
critical problems of creating such plasmas: reducing the required power
budget and insuring stability. The techniques described in this section are
examples of 'non-self-sustained' electric discharges, in contrast to 'self-
sustained' discharges, in which ionization is provided by applying high
voltage to the electrodes maintaining the plasma. Typically, self-sustained
discharges, lacking an external ionization source, are usually only struck at
low gas pressures, well below even 0.1 atm, if a low temperature, diffuse,
glow-type plasma is required. As gas pressure is increased, higher voltages
--- Page 443 ---
428
High Frequency Air Plasmas
are required to strike. Operation at such higher voltages and pressures
usually leads to a marked transition, in which the plasma changes from a
diffuse, cool column of weakly ionized gas, a 'glow discharge', to a much
higher-temperature higher-conductivity plasma between the electrodes.
This transition is sometimes termed the 'glow-to-arc transition', and is
described in standard plasma references, e.g. [Rai9l]. After transition, very
high temperatures are reached, with a large fraction of the gas becoming
ionized, the resistivity of the plasma greatly decreasing, and the electron
temperature coming into near thermal equilibrium with the gas temperature.
Such discharges do not normally provide the relatively cold, large-volume
diffuse plasmas desired here. To circumvent this problem, various methods
have been used to extend the range of self-sustained glow-type discharges
to near atmospheric pressures, such as the use of individually ballasted
multiple cathodes, short duration rf high-voltage pulse stabilization, or
aerodynamic stabilization [Rai9l, Vel87, Gen75, Ric75, Zhd90]. The
energy efficiency of such discharges is, however, much lower than desirable
for large-volume plasmas, since the fraction of the input electrical power
going into ionization is often quite small.
An alternative approach is the use of non-self-sustained glow
discharges, in which some or all of the required volume ionization is provided
by an external source, such as an electron beam [Bas79, Kov 85]. Electron
beams are identified as having by far the lowest power budget among all
non-equilibrium ionization methods [AdaOO, MacOO, Mac99]. Further,
reliance on an external ionization source mitigates the glow-to-arc break-
down problem. The glow-to-arc transition, with subsequent plasma
thermalization, can be significantly delayed or avoided altogether. Even
when using this efficient ionization source, however, the power budget
required to sustain a relatively cold, large-volume air plasma remains
huge, greater than 1 GW 1m3. This is predominantly due to the rapid attach-
ment of electrons to oxygen molecules. Consequently, reduction of the air
plasma power budget mandates mitigation of electron attachment, and, for
further power reduction, lowering of the electron-ion recombination rate.
The method of the present section uses an electron beam to produce electrons
efficiently, and uses the optical pumping technique reviewed previously to
mitigate electron loss. In brief, we use the approach of section 7.2.2.1, i.e.
optical pumping by a CO laser, to modify the electron removal rates in an
electron beam sustained, CO-seeded high-pressure air plasma.
7.5.2 Electron loss reduction
There is recent experimental evidence that vibrational excitation of diatomic
species produced by a CO laser may reduce the rates of electron removal
(dissociative recombination and attachment to oxygen) in non-equilibrium
plasmas [PaIOla]. We give a brief discussion of this effect.
--- Page 444 ---
Electron-Beam Experiment with Laser Excitation
429
First, electron impact ionization of vibrationally excited molecules
produced by a CO laser can create vibrationally excited molecular ions
such as N! and O!,
N2(v) + ebeam -- N!(v) + ebeam + e;condary'
(7.5.1)
Vibrationally excited ions can also be created by a rapid resonance charge
transfer from vibrationally excited parent molecules, such as
(7.5.2)
Recent experimental data [Mos99] show that vibrational excitation of
molecular ions such as NO+ or O! can considerably reduce the rate of
their dissociative recombination, such as
(7.5.3)
Secondly, three-body attachment of secondary electrons produced by the
electron beam to vibrationally-excited oxygen molecules created by a CO
laser,
(7.5.4)
will produce vibrationally excited ions O2 (v). Since the electron affinity of
this ion is only about O.4eV [Rai91], vibrational excitation of oxygen
molecules to vibrational levels v ~ 2 can provide enough energy for auto-
detachment of an electron,
(7.5.5)
Since the three-body electron attachment to oxygen molecules is by far the
most rapid mechanism of electron removal in cold, high-pressure air
plasmas, reduction of the attachment rate greatly reduces the plasma
power budget. We now proceed to the details of an experimental demon-
stration of the use of this vibrational excitation technique, together with
an electron-beam ionizer, which produces cool, atmospheric pressure air
plasma with markedly improved efficiency.
7.5.3
Experimental discharge; electron beam ionizer
Figures 7.5.1 and 7.5.2 show schematics of the experimental set-up. An
electron gun (Kimball Physics EGH-8101) generates an electron beam with
energy of up to 80keV and a beam current of up to 20mA. The electron
gun can be operated continuously or pulsed. From the vacuum inside the
electron gun the electron beam passes through an aluminum foil window
into a plasma cell that can be pressurized up to atmospheric pressure. The
foil window with a thickness of 0.018 mm is glued onto a vacuum flange
with an aperture of 6.4mm. About 30keV of the electron beam energy is
lost in the window, which results in heating of the window. Pulsed operation
--- Page 445 ---
430
High Frequency Air Plasmas
electron gun
b",,;,W~_-Ie-beam sustained plasma
co laser
Figure 7.5.1. Schematic of the electron beam and laser set-up [PalOlb].
of the electron gun at a low duty cycle prevents overheating and failure of the
window. In the electron gun the electron beam has a relatively small diver-
gence that increases significantly (",90 0 full angle) due to scattering in the
foil window. A 12.7mm diameter brass electrode faces the window at a
distance of 10 mm. This defines a volume of the e-beam excited plasma of
'" I cm3 between the beam window and the electrode. The beam window
together with the entire chamber is grounded. For the current experiments
the electrode was usually also grounded. The electron gun was typically oper-
ated at beam energies between 60 and 80 keY and different beam currents
measured using an unbiased Faraday cup placed behind the beam window.
The plasma cell is pressurized with air at pressures between 100 torr and
I atm. A slow gas flow is maintained in the cell to provide flow convective
cooling and to remove chemical products. The residence time of the gas
mixture in the cell is of the order of a few seconds.
Perpendicular to the e-beam axis a CO laser beam is directed into the
e-beam excited plasma. The laser is used to vibrationally excite the diatomic
&-beam sumnecj plasma
Figure 7.5.2. Schematic of the plasma cell [PalO I b].
--- Page 446 ---
Electron-Beam Experiment with Laser Excitation
431
plasma constituents. The liquid nitrogen-cooled continuous wave CO laser
[PloOOa] produces a substantial fraction of its power output on the v = 1-0
fundamental band component in the infrared. In the present experiment,
the laser is typically operated at "-' 10 W continuous wave broadband
power on the lowest ten vibrational bands. The output on the lowest
bands (1-0 and 2-1) is necessary to start the optical absorption process in
cold CO at 300 K, 1-5% of which is seeded into the cell gases. The laser
beam is focused (f = 250 mm) to a focal area of ,,-,0.5 mm diameter to
increase the power loading per CO molecule, producing an excited region
,,-,5 cm long. As indicated in figures 7.5.1 and 7.5.2, the vibrationally excited
region is only a part of the total e-beam ionized plasma. Typically, the laser
pump maintains the gas molecules in this region with high energies in the CO,
O2 , and N2 vibrational modes. The energies in each mode would correspond
to a few thousand Kelvin if the gas were in equilibrium. These mode energies
are maintained in steady state in the plasma by the laser. The external gas
kinetic modes of translational and rotation molecular motion remain rela-
tively cold in this steady state. This gas kinetic temperature is easily measured
by monitoring the spontaneous infrared emission from the fundamental
vibrational bands of the vibrationally excited CO. From the relative intensity
of the spectrally-resolved vibrational-rotational lines, the rotational
temperature can be inferred from a Boltzmann plot. The rotational tempera-
ture is equal to the translational mode temperature in these high-pressure
collision-dominated plasmas. Since the emission arises only from the laser-
excited region of the plasma, this temperature inference is not compromised
by the surrounding e-beam-only excited region, and only reflects the
temperature of the laser-excited part of the plasma. Figure 7.5.3 shows
such an emission spectrum, from which a gas kinetic temperature of
T = 560 K is inferred.
The electron density in the e-beam/optically sustained plasma is
measured by microwave attenuation. The microwave experimental appa-
ratus consists of a v = 40 GHz oscillator, a transmitting and receiving
antenna/waveguide system, oriented perpendicular to the e-beam axis and
to the laser axis (figure 7.5.2), and a transmitted microwave power detector.
The receiving waveguide is positioned directly opposite the transmitting
waveguide, with the plasma located between them (figure 7.5.2). The micro-
wave detector produces a dc voltage proportional to the received microwave
power. From the relative difference of the transmitted power with and
without a plasma the attenuation of the microwave signal across the
plasma was determined.
7.5.4 Results and analysis of discharge operation
A reduction of the electron removal rates (i.e. the electron-ion recombina-
tion rate and/or the electron attachment rate) in the vibrationally excited
--- Page 447 ---
432
High Frequency Air Plasmas
2270
CO 1->0 R-Branch Emission
T=560 K
-1
wavenumber [em ]
Figure 7.5.3. Translational temperature in vibrationally-excited air at I atm measured by
Fourier transfonn emission spectroscopy.
region should manifest itself in two experimental observations: (i) the steady-
state electron density reached after an electron beam pulse is turned on
should rise, and (ii) the electron density decay after the beam is turned off
should become slower. In the present experiment, the average electron
density in the e-beam sustained plasma, n~aseline, is inferred from microwave
attenuation measurements using the relationship [PalOla]
nbaseline = (m cc li)v (8V) 2.
e
e
0
eoll
V
D
(7.5.6)
where
Veol!
is
the
electron-neutral
collision
frequency, 8V IV =
(Vtrans -
Vine) I Vine is the relative attenuation factor in terms of the forward
power detector voltage proportional to the incident and the transmitted
microwave power, and D ~ 0.8 cm is the size of the ionized region along
the microwave signal propagation (see figure 7.5.2). Note that equation
(7.5.6) assumes a uniform ionization across the plasma.
A CO laser beam propagating across the electron beam sustained
plasma creates a cylindrically shaped vibrationally excited region of
d ~ 2mm diameter (see figure 7.5.2). The analysis of the microwave
absorption measurements in electron beam sustained plasmas enhanced by
laser excitation is somewhat complicated by the fact that the plasma
volume affected by a focused CO laser is considerably smaller than the
--- Page 448 ---
Electron-Beam Experiment with Laser Excitation
433
volume ionized by the electron beam. For this reason, equation (7.5.6) should
be modified to take this effect into account. If one assumes that the electron
removal rate modification due to vibrational excitation is significant, and
that consequently the electron density in the optically pumped region,
n~odified, is much higher than in the e-beam ionized region, n~aseline, equation
(7.5.6) becomes
modified
(
1 2)
(8V) W
ne
= mecco e lIeon V
1fd2/4
(7.5.7)
where W ~ 0.33 cm is the width of the waveguide perpendicular to the laser
beam axis. In addition, inference of the electron density should account for
the change of the electron-neutral collision frequency, lIeol!> in the vibration-
ally excited plasma, which primarily depends on the electron temperature. In
the present paper, the dependence of the collision frequency on the average
electron energy is calculated by solving the coupled master equation for
the vibrational level populations of CO, N2, and O2, and Boltzmann
equation for the secondary (low-energy) plasma electrons [Ada98]. In the
laser-excited plasma, the electron temperature is strongly coupled to the
vibrational temperatures of the diatomic species due to rapid energy transfer
from vibrationally excited molecules to electrons in superelastic collisions
[Ale78, Ale79, Ada97]. The average electron energy in the optically
pumped plasma is about 5000 K, as determined by the modeling calculations
and recent Langmuir probe measurement in these laser pumped plasmas
[Plo02]. This gives a collision frequency of lIeon = 6.1 x 1011 S -I in air at
p = 1 atm and T = 560 K. In the purely e-beam sustained plasma, the
average electron energy is ",300 K, and the collision frequency is
lIeon = 1.1 X 1011 s-I at p = 1 atm and T = 300 K. Summarizing, the electron
densities in the electron beam sustained plasma and in the laser-enhanced
region are evaluated from equations (7.5.6) and (7.5.7), respectively.
The experimental results are compared with a kinetic model of the
electron production, electron removal, and charge transfer processes in the
investigated air plasmas. The model takes into account rates for electron
production by the e-beam, S, electron-ion recombination, /3, three-body
ion-ion recombination kR' electron attachment in three-body collisions to
02, k~2, and to N2, k~2, electron detachment from Oz in collisions with O2,
k~2, and in collisions with N2, k~2. Electron densities, ne, positive ion densities,
n+, and Oz densities are calculated integrating the differential equations
dne/dt = S -
k~2ne[02f -
k~2ne[02][N2]- /3nen+
+k~2ne[Oz][02] + k~2ne[Oz][N2]
(7.5.8)
d[Ozl/dt = k~2ne[02]2 + k~2ne[02][N2] - kR[Oz]n+N
(7.5.9)
--- Page 449 ---
434
High Frequency Air Plasmas
6c+11
-
Nt. T=300 K. c:x.pc.rimcnt
-
Nt' T=300 K. calculation
50+-11
40+-11
~
'? ! 30+-11
~
=>
~.cc9xl0-7 cm3/s
17
.J
k-_c2.7xlO
cm Is
1
=
2e+11
le+11
t[5]
Figure 7.5.4. Measured and calculated electron densities during and after a 20 IlS e-beam
pulse in I atm N2 . In the calculation the electron production rate ki and recombination
rate f3 were chosen to best fit the measurement.
(7.5.10)
In a first step, modeling results are fitted to the time resolved electron density
in I atm of pure N2 after a 20 j..ls e-beam pulse. Figure 7.5.4 shows the electron
density measurement and the calculated electron density that best agrees in
peak electron density and electron density decay. From the fit we obtain
an electron production rate of S = 2.7 X 1012 cm-3 s-I and, since the decay
in N2 is dominated by electron-ion recombination, the effective dissociative
electron-ion recombination rate for our e-beam ionized N2 plasma. The
determined recombination rate (3 = 0.9 X 10-6 cm3 S-I lies between the
known recombination rates for the expected dominant ions Nt
((3 = 2 X 10-7 cm3 S-I) and Nt ((3 = 2 X 10-6 cm3 s-I). Consequently, the
measurement suggests that about 50% of the positive ions in the plasma
are the faster recombining Nt that is produced in a conversion reaction.
Electron density measurements in the laser excited part of the e-beam
plasma are somewhat more uncertain than measurements in purely e-beam
sustained plasmas. This is due to (i) the uncertainty in the diameter d of
the laser excited region (see equation 7.5.7), (ii) the uncertainty in the trans-
lational temperature in the laser excited region, and (iii) the uncertainty in the
electron temperature Te in the laser excited region. From the size of the
visible glow of a laser-excited N2/CO plasma at p = I atm and, critically,
from Raman spectroscopic measurements [LemOO] the diameter of the
--- Page 450 ---
Electron-Beam Experiment with Laser Excitation
435
Se+l\
-
Air/CO + Laser. T=560 K. experiment (uncaJib.)
7e+1I
-
Nr T=560 K. calcuhllion
-
Air/CO + J.a!ler. T ... 16O K. experiment
~" .. """""""","""',"""'--,-""'--
6e+1I
51.>+11
.,..
! 4&:+11
r::"
3e+11
1e+11
tls1
Figure 7.5.5. Measured electron densities in I atm of laser-excited CO-seeded air before
and after calibration by comparison with N2. Assuming identical electron production
rates in I atm of air and I atm of N2 the slope of the initial electron density rise should
be identical for air and N2 . Very good agreement is achieved by changing the diameter
of the laser-excited region from d = O.2cm to d = O.185cm (equation 7.5.6).
laser excited region was estimated to be d = 0.2 cm. As noted previously
translational temperature in the laser region was measured spectroscopically
from a Boltzmann plot of the infrared emission intensities of CO 1 ----> 0
R-branch lines (figure 7.5.3). For 1 atm of air seeded with 5% CO and opti-
cally excited by a 10 W CO laser, the temperature was found to be 560 K.
Figure 7.5.5 shows the measured electron density assuming d = 0.2cm
and Te = 5000 K and a calculated electron density pulse in N2 at
T = 560 K. Assuming identical electron production rates in 1 atm of air
and 1 atm of Nz, the slope of the initial electron density rise in laser excited
air should be identical to the slope in Nz. Very good agreement is achieved by
changing the diameter of the laser excited region in equation 7.5.6 from
d = 0.2cm to d = 0.185cm, also shown in figure 7.5.5. The signal-to-noise
ratios for electron density measurements in the laser excited region are
much lower than purely e-beam excited plasmas. This is caused by the
much smaller size of the laser excited region and the consequently lower
MW attenuation. In fact, a microwave attenuation measurement in the
laser excited region is always accompanied by a measurement in the
surrounding, purely e-beam excited region. The illustrations of figure 7.5.6
show how the net signal is combined.
--- Page 451 ---
436
High Frequency Air Plasmas
Overall plasma
E-beam plasma
without laser
excitation
Laser excited
region of
e-beam plasma
n.
Figure 7.5.6. Illustration of how the e-beam-ionized region and the e-beam-ionized(laser
excited region contribute to the overall electron density signal recorded by the microwave
system. Note the different scales on the ne-axes [PalO I b].
Figure 7.5.7 shows the electron density pulse in the vibrationally excited
air plasma (the same data as figure 7.5.5, now calibrated), together with a
calculated pulse in N2 at T = 560 K and the assumed Te = 5000 K. Both
traces appear to be in very good agreement. Most notably, the decay of
the electron density in laser excited air is equally slow as in N2, i.e.
attachment of electrons to O2 does not seem to be a relevant process in
vibrationally excited air. The importance of attachment to oxygen in cold
equilibrium air can be seen in the dashed trace in figure 7.5.7 showing the
corresponding electron density measurement without laser excitation. This
experiment shows the markedly low level of ionization maintained by the
e-beam only. Note the 200-fold higher peak electron density in laser excited
air [(7.9 x 1011 cm-3)/(4.4 x 109 cm-3)].
As mentioned before, the CO laser excited air plasma is in a very strong
vibrational non-equilibrium. The vibrational temperature of the diatomic
species exceeds the translational temperature by at least a factor of 4.
--- Page 452 ---
Electron-Beam Experiment with Laser Excitation
437
8c}+JJ
--_. Air/CO, T::300 K. experiment
7e+ll
-
Air/CO + Laser, T=560 K. experiment
-
Nz' T=560 K. T.=5000 K. calc.
6e+11
3e+1I
2e+11
1e+11
o
t [s1
Figure 7.5.7. Measured electron density pulse in I atm of vibrationally excited air
compared with calculated electron density in N2 . In strong contrast to a plasma in cold
equilibrium air (dashed line) vibrationally-excited air does not seem to exhibit any electron
attachment to 02, i.e. peak electron density and plasma decay in vibrationally-excited air
seem to be purely caused by electron-ion recombination.
Nevertheless, the fraction of molecules in excited vibrational states is still
small compared to the population of the vibrational ground state. Therefore,
the apparent complete mitigation of electron attachment to oxygen in vibra-
tionally excited air cannot be caused by a vibrationally induced modification
of the attachment rate itself. This is because the ground-state O2 molecules
(>50%) would still be exhibiting the full attachment rate, i.e. the total
attachment rate could only be reduced by less than 50%. Consequently,
the vibrational excitation has to be acting on the electron detachment side.
On the other hand, the detachment rate shows a strong temperature
dependence that raises the question of whether the observed effect might
be due to the temperature rise (from 300 to 560 K) associated with the optical
excitation of our air plasma.
Figure 7.5.8 shows calculated and experimental electron densities in
a 3011S e-beam pulse in p = I atm air at slightly higher beam current
than in figure 7.5.7, there is no laser excitation of vibration in this
experiment. The modeling calculation, assuming S = 0.5 X 1018 cm-3 S-I,
(3 = 2 X 10-6 cm3 S-I, k?2 = 2.5 X 10-30 cm6 S-I, k~2 = 0.16 X 10-30 cm6 S-I,
k~2 = 2.2 X 10-18 cm3 S-I,
k~2 = 1.8 X 10-20 cm3 S-I,
kR = 1.55 X
10-25 cm3 S-I [Rai91] and T = 300 K shown in figure 7.5.8 agrees well with
--- Page 453 ---
438
High Frequency Air Plasmas
4c+10 -
I
I
3c+1O I-
.....
";l
§ 2c+l0 I-
....... ... =
lc+l0 I-
0""""-..........
1
I
-4e-OS
-2e-OS
I
I
o
I
I
T = 560 K, T. = 3000 K
T=560K,T.=560K
expennMKrt,mseroft
I
I
:!c-05
4e-05
t [s]
I
I
I
_
-
-
-
-
I
I
I
6e-05
8e-05
0.0001
Figure 7.5.8. Comparison of experimental data and kinetic modeling for different
translational and electron temperatures.
the experimental data. The two other traces in figure 7.5.8 show the calcu-
lated electron densities taking into account modified electron detachment
and electron-ion recombination rates due to increased electron and trans-
lational temperatures. The modified rates for increased translational
temperature only and increased translational and electron temperature
used are f3 = 1.5 X 10-6 cm3 S-I,
k~2 = 2.2 X 10-14 cm3 s-l, kN2 = 1.8 X
10-16 cm3 S-I,
and
f3 = 6.3 X 10-7 cm3 S-I,
k~2 = 2.2 X 1O-~4 cm3 S-I,
k~2 = 1.8 X 10-16 cm3 S-I, respectively [Rai9l]. It can be seen that the
change of electron and translational temperatures associated with the laser
excitation would not produce a very strong effect on the electron density
(x2) and the plasma decay time. Therefore, the strong effect observed in
the experimental data with laser excitation can be attributed to the
vibrational excitation, not temperature effects.
Figure 7.5.9 shows the measured electron densities for the conditions of
figures 7.5.4, 7.5.5, 7.5.7, and calculations for these conditions, using hugely
increased electron detachment rates. The experimental electron density
shown in this figure represents the best performance achieved in the 1 atm
air plasma, reaching high electron density with greatly increased plasma
lifetime. Increase of the detachment rates by five orders of magnitude fully
mitigates the effect of attachment and the calculated trace for laser excited
air practically coincides with the calculated trace for N2. The change of the
--- Page 454 ---
Electron-Beam Experiment with Laser Excitation
439
8.:+11
-
Air, T=S60 K. T.=5000 K. k..=k45bl:M. x. 10'. calc.
7e+11
Air/CO + i..aser. 1'z:..160 K. experiment
60+11
N;r j=$60 K, T.=SOOO K.!S=2.2x.IO·7 cm)/s. calc.
'?~
! 4e+11
3e+11
2.:+11
Figure 7.5.9. Experimental and calculated electron densities for the conditions of figures
7.5.4, 7.5.5 and 7.5.7 using hugely increased electron detachment rates. Increase of the
detachment rates by five orders of magnitude mitigates the effect of attachment and the
calculated trace for laser excited air practically coincides with the calculated trace for N2.
electron-ion
recombination
rate
from
(3 = 0.9 X 10-6 cm3 S-I
to
(3 = 2.2 x 10-7 is due to the increase of the electron temperature from
Te = 300 K in cold gas to Te = 5000 K in the vibrationally excited gas.
Finally, figure 7.5.10 shows the number densities for the negatively
charged species e- and O2, calculated from the rates determined from the
experiment using the analysis reviewed above. Due to attachment, the domi-
nant negative species in cold air is O2, whereas in vibrationally excited air the
O2 population is insignificant «2 x 109 cm -3) and the dominant negative
species is e-. Note the higher total number density of charged species in
vibrationally-excited air that is due to the reduced ion-ion recombination
channeL The experimental results and modeling calculations are consistent
with the hypothesis given in section 7.5.2, equations (7.5.1)-(7.5.5) for the
effect of vibrational excitation on electron attachment to oxygen and elec-
tron-ion recombination in electron beam sustained atmospheric pressure
air plasmas: (i) since the electron affinity of O2 is only about 0.4 e V
[Rai9l], vibrational excitation of O2 to vibrational levels v 2: 2 can provide
sufficient energy for the detachment of the attached electron
02(V 2: 2)[+M] -
O2 + e-[+M]
(7.5.11)
while charge transfer from O2 to vibrationally excited oxygen is sufficiently
rapid to make this process very efficient and (ii) superelastic collisions of
--- Page 455 ---
440
High Frequency Air Plasmas
8e+1I
-
e' (Air. T=560 K. 1'.=5000 K. kd=k..1IIJr. ll IO~)
- °2" (Air. 1'=300 K)
c" (Air 1'=300 K)
6e+11
-
0; (Air. 1'=560 K. Te=SOOO K. kd=k/flJK A 10')
Figure 7.5.10. Calculated number densities for the negatively charged species e- and
O2, Due to attachment, the dominant negative species in cold air is O2, whereas in
vibrationally excited air the O2 population is insignificant «2 x 109 cm-3) and the
dominant negative species is e-. Note the higher total number density.
the initially cold secondary electrons produced by the electron beam with
highly vibrationally excited molecules increase the electron temperature
significantly to Te ~ 5000 K, which reduces the electron-ion recombination
rate.
7.5.5 Summary; appraisal of the technique
These time-resolved electron density measurements in electron beam
sustained cold atmospheric pressure air plasmas demonstrate the effect of
vibrational excitation of the diatomic air species on electron removal
processes, notably dissociative recombination and attachment to O2,
Vibrational excitation of the diatomics is produced by laser excitation of
CO seeded into the air and subsequent vibration-vibration energy transfer
within the CO vibrational mode and from the CO to O2 and N 2 . The experi-
mental results are consistent with a model that assumes rapid vibrationally
induced detachment of electrons from O2 and vibrationally induced heating
of the free electrons to temperatures on the order of Te ~ 5000 K, thus
effectively mitigating the effect of electron attachment and electron-ion
recombination, respectively.
--- Page 456 ---
Electron-Beam Experiment with Laser Excitation
441
What is the overall influence of these electron loss mitigation effects on
the overall plasma power budget? This can be estimated as follows: In cold
air plasmas the dominant electron removal process is attachment to
oxygen. The minimum power budget (assuming 100% ionization efficiency)
to sustain a cold air plasma with an electron density of ne = 1013 cm-3 is
therefore given by Pa = Eionk a[02f For an average ionization energy in
air of Eion ::::::: l4eV this gives Pa = 1.4kW/cm3 = 1.4 GW/m3. In the case
of vibration ally-excited air, the electron loss by attachment is replenished
by detachment of electrons from O2 instead of O2 in the case of cold air.
With an electron affinity of Edel ::::::: 0.4 eV the minimum power budget to
overcome attachment decreases
to
Pa = Ede1ka[02l2 = 40 W /cm3 at
T = 300 K or Pa = 10 W /cm3 at the reduced gas density at T = 560 K. In
the case of mitigated attachment the main electron removal process in an
electron-beam-sustained air plasma is dissociative electron-ion recom-
bination. The minimum power budget to overcome recombination is
given by Pree = Eionf3n~. With an electron-ion recombination rate of
f3::::::: 1 X 10-6 cm3 s-1 we obtain Pree = 225 W /cm3. With the measured
recombination rate in vibrationally excited air, f3::::::: 2 X 10-7 cm3 s-l, the
mInimum power budget to overcome recombination decreases to
Pree = 45 W /cm3 .
In summary, the theoretical mlmmum power budget to overcome
attachment and recombination in our vibration ally excited air plasmas is
approximately 50 W /cm3, which represents a significant reduction compared
to almost 2000 W /cm3 in cold equilibrium air.
The 45 W/cm3 power budget estimate does not, however, include the
efficiency of the laser excitation process and the efficiency of the electron
beam ionization process. The laser power required is approximately
1 W /cm3. The laser used in the experimental demonstration is a continuous
wave, electrically-excited CO laser, which is the most efficient laser known
with demonstrated very high continuous wave powers. Several hundred
kW lasers of this type have been built, with 50% conversion of the input elec-
tric power into the beam. It is possible to project other means of achieving the
required vibrational mode excitation. For example, use of other lasers with
molecular seed ants other than CO could be possible. Auxiliary electrodes,
producing reduced electric fields operating at values to optimize vibrational
mode power loading are conceivable. These alternatives all have their own
problems. At the time of writing, the vibrational mode loading method
used here seems the most effective.
The electron beam as an ionization source is efficient, with perhaps 50%
of the beam energy going into ionization of the air. There are not major losses
in producing the beam. We estimate that perhaps total beam power require-
ments increase the power budget by another 1-2 W/cm3.
A feature of this method of plasma generation is its exclusive reliance on
beamed energy (laser, electron beam) to produce the plasma. This feature
--- Page 457 ---
442
High Frequency Air Plasmas
would be useful in applications in which it electrodeless plasma, or one
created at a distance from the power source, is desirable.
The principal limitations of the method should be noted, however:
1. The performance achieved here is only achieved in dry air. Moisture or the
presence of hydrocarbons in the air rapidly increases the rate of energy
loss from the excited vibrational modes, mandating higher laser powers,
and increasing plasma heating.
2. The system complexity and the attendant costs accompanying the electron
beam. The foil window is fragile, and vulnerable to heating from the high
pressure plasma; window failure leads to the air plasma contaminating the
electron gun. Improvement in window materials, window cooling, and,
even, electrodeless window development are subjects of on-going
research, but this remains a key problem in the use of large electron
beams for high pressure plasmas.
3. The systems complexity and the attendant costs accompanying the laser.
The CO laser achieves its high efficiencies when cooled to near cryogenic
temperatures. Large CO lasers have elaborate circulating gas systems with
heat exchangers, or use fast, even supersonic flows for convective cooling.
Research and development is also on-going in these laser systems.
References
[Ada97] Adamovich I V and Rich J W 1997 J. Phys. D: Appl. Phys. 30(12) 1741
[Ada98] Adamovich I V, Rich J Wand Nelson G L 1998 AIAA J. 36(4) 590
[AdaOO] Adamovich I V, Rich J W, Chernukho A P and Zhdanok S A 2000 'Analysis of
the power budget and stability of high-pressure non-equilibrium air plasmas'
Paper 00-2418, 31st Plasmadynamics and Lasers Conference, Denver, CO, 19-
22 June
[Ale78] Aleksandrov N L, Konchakov A M and Son E E 1978 Sov. J. Plasma Phys. 4 169
[Ale79] Aleksandrov N L, Konchakov A M and Son E E 1979 Sov. Phys. Tech. Phys. 49
661
[Bas79] Basov N G, Babaev I K, Danilychev V A et al1979 Sov. J. Quantum Electronics 6
772
[Gen75] Generalov N A, Zimakov V P, Kosynkin V D, Raizer Yu P and Roitenburg D I
1975 Technical Phys. Lett. 1431
[Kov85] Kovalev A S, Muratov E A, Ozerenko A A, Rakhimov A T and Suetin N V 1985
Sov. J. Plasma Phys. 11 515
[LeeOI] Lee W, Adamovich I V and Lempert W R 2001 J. Chemical Phys. 114(3) 1178
[LemOO] Lempert W R, Lee W, Leiweke Rand Adamovich I V 2000 'Spectroscopic
measurements of temperature and vibrational distribution function in weakly
ionized gases', Paper 00-2451, 21st AIAA Aerodynamic Measurement Technology
and Ground Testing Conference, Denver, CO, 19-22 June
[Mac99] Macheret S 0, Shneider M N and Miles R B 1999 AIAA Paper 99-3721, 30th
AIAA Plasmadynamics and Lasers Conference, Norfolk, VA, 28 June--l July
--- Page 458 ---
Research Challenges and Opportunities
443
[MacOO] Macheret S 0, Shneider M N and Miles R B 2000 'Modeling of air plasma
generation by electron beams and high-voltage pulses', AIAA Paper 2000-
2569, 31st AlA A Plasmadynamics and Lasers Conference, Denver, CO, 19-22
June
[Mae91] Maetzing H 1991 Adv. Chern. Phys. 80 315
[Mos99] Mostefaoui T, Laube S, Gautier G, Ebrion-Rowe C, Rowe BRand Mitchell J B
A 1999 J. Phys. B: At. Mol. Opt. Phys. 32 5247
[palO 1 a] Palm P, P16njes E, Buoni M, Subramaniam V V and Adamovich I V 2001 J. Appl.
Phys. 89 5903
[PalO 1 b] Palm P, Plonjes E, Adamovich I V, Subramaniam V V, Lempert W R and Rich J
W 2001 'High pressure air plasmas sustained by an electron beam and enhanced
by optical pumping', AIAA-Paper 2001-2937, 32nd AlAA Plasmadynamics and
Lasers Conference, 11-14 June, Anaheim, CA
[PloOOa] Plonjes E, Palm P, Chernukho A P, Adamovich I V and Rich J W 2000 Chern.
Phys. 256 315
[PloOOb] Ploenjes E, Palm P, Lee W, Chidley M D, Adamovich I V, Lempert W Rand
Rich J W 2000 Chern. Phys. 260 353
[PloOI]
Ploenjes E, Palm P, Lee W, Lempert W Rand Adamovich I V 2001 J. Appl. Phys.
89(11) 5911
[Plo02]
Plonjes E, Palm P, Adamovich I V and Rich J W 2002 'Characterization of elec-
tron-mediated vibration-electronic (V-E) energy transfer in optically pumped
plasmas using Langmuir probe measurements', AIAA-Paper 2002-2243, 33rd
AlAA Plasmadynamics and Lasers Conference 20-23 May, Maui, Hawaii
[Rai91] Raizer Y P 1991 Gas Discharge Physics (Berlin: Springer)
[Ric75] Rich W, Bergman R C and Lordi J A 1975 AlAA J. 13 95
[VeI87]
Velikhov E P, Kovalev A Sand Rakhimov A T 1987 Physical Phenomena in Gas
Discharge Plasmas (Moscow: Nauka)
[Zhd90] Zhdanok, SA, Vasilieva, EM and Sergeeva, LA 1990 Sov. J. Engineering Phys.
58(1) 101
7.6 Research Challenges and Opportunities
The air plasma research techniques discussed in this chapter have yielded
several important results and concepts that need further development. The
use of lasers producing optically pumped or low ionization energy seed
gases in atmospheric air to provide seed plasmas of high density (1012-
1013 fcm3) of small size (20 cm3) to larger (500 cm3) volume should be pursued
further. These techniques can overcome the high power densities required to
ionize atmospheric air and provide an initial condition for lower power
plasma sustainment by inductive rf waves or other techniques. The use of
a laser allows plasma production well away from material surfaces which
can be attractive for certain applications. Although some of these techniques
were examined utilizing lasers to concentrate on the air plasma chemistry
--- Page 459 ---
444
High Frequency Air Plasmas
issues, less expensive focused flash tubes with reflectors could also be
considered for these techniques.
An important issue in sustaining high density air plasmas is the
formation of negative oxygen ions, °2, at room temperature. By preheating
the air to provide a higher neutral temperature of 2000 K by means such as rf
heating, this process can be greatly reduced and plasma lifetimes and power
sustainment densities required to provide average plasma densities in the
1013 /cm3 range and larger volumes substantially reduced. Another important
experimental technique is to carry out individual air component experiments
where the nitrogen, oxygen and other components of air including residual
water vapor concentrations, H20, are isolated. Due to the complexity of
air plasma chemistry, the role of the individual and collective processes
can be examined in a more systematic way. Important optical spectroscopy
and millimeter wave interferometery techniques and associated analytic
codes that have been developed by the researchers in this area will make
important contributions to this field.
The use of inductive rf waves to provide a plasma torch in near local
thermodynamic equilibrium provides an analysis of baseline condition for
steady-state, high density (> 1013 /cm\ large volume (1000 cm\ atmospheric
air plasma wall plug power density that is quite high (P = 48 W/cm\ The
use of gas flow enhances these discharges, cools the source region and
allows plasma production remote from the material source region. Micro-
wave plasma torch power densities for smaller plasmas require power densi-
ties in region of 200 W /cm3. In both cases the gas temperature is fairly high,
at 4200 K with electron plasma temperatures of 5000 K. These parameters
are deleterious for materials in the plasma region and illustrate the need
for pulsed, non-equilibrium plasma that can reduce the plasma temperature,
yet maintain high plasma densities and large volumes (lOOOcm\ In
addition, further research on pulsed plasmas should be carried out in the
microwave range to obtain high plasma density remote from the microwave
source region. The use of short, repetitive pulsed power, high voltage plasmas
in preheated (2000 K) air has been demonstrated to produce high average
density, non-equilibrium plasmas with a higher ionization efficiency, with
100 times lower time-average power densities than in the steady-state case.
The decaying plasma provides a seed for the next pulse when the repetition
rate matches the electron recombination rate. The volumes of initial
experiments were quite small (0.3 cm3) and arrays and methods for creation
of these lower time averaged power density air plasmas and creating plasmas
remotely from electrodes should be pursued further.
The use of pulsed, moderate energy (60-80keV) electron beams can also
be used to provide plasmas with lower power density and optical pumping to
reduce electron attachment to oxygen is an interesting technique. Initial
experiments show that due to the increased electron and gas temperatures
of 5000 K, electron attachment to oxygen could be reduced so that minimum
--- Page 460 ---
Research Challenges and Opportunities
445
power densities of 50 W/cm3 could be obtained to offset electron recombina-
tion processes. Scaling of this technique to larger volumes and improvement
of electron beam window are areas that need to be developed further. The use
of pulsed dc, rf, microwave and electron beam power with seed gas and tech-
niques used to reduce electron recombination with oxygen as well as more
advanced aspects of air plasma chemistry are areas that need to be explored
further to obtain non-equilibrium plasmas with lower power density in the
atmospheric air for a variety of applications.
--- Page 461 ---
Chapter 8
Plasma Diagnostics
B N Ganguly, W R Lempert, K Akhtar, J E Scharer, F Leipold,
CO Laux, R N Zare and A P Yalin
8.1
Introduction
Measurements of plasma parameters in high-pressure plasma environment
offer challenges and opportunities which usually have to satisfy requirements
that are different compared to both partially ionized and highly ionized low-
pressure plasmas. The highly collisional nature of atmospheric pressure
plasma, compared to lower «lOtorr) pressure plasmas, can significantly
modify the data analysis procedure and, more importantly, sometimes
even the applicability of methods used to measure plasma characteristics in
diffusion-dominated lower pressure plasmas. Also, the scaling laws of
collision ally dominated self-sustained plasmas are usually bounded by ioniza-
tion and thermal instabilities, which impose different operating requirements
for maintaining self-sustained non-equilibrium plasmas at atmospheric
pressure compared to low-pressure plasmas. Well developed low-pressure
plasma diagnostics methods for both partially ionized (Auciello and
Flamm 1989, Herman 1996) and highly ionized plasmas (Fonck and den
Hartog 2002, Hutchinson 2002) can be adopted for collisionally dominated
plasmas. The examples of applicability of electron density measurement by
millimeter wave and mid infrared interferometric methods, with appropriate
modifications for collisionally dominated plasmas, are discussed in this
chapter in sections 8.3 and 8.4, respectively. Also, elastic and inelastic laser
light diagnostic methods which are better suited for characterizing plasmas
at elevated gas density are described in section 8.2. In section 8.2, both
theoretical and experimental descriptions of Rayleigh scattering, pure
rotational and ro-vibrational Raman scattering and Thomson scattering
measurements in air plasma are described.
In this section filtered (by resonance absorption of atomic optical
transition) laser light scattering techniques are discussed in detail which
446
--- Page 462 ---
Introduction
447
permit measurement of gas temperature from Doppler broadening of Rayleigh
scattering under conditions where stray light scattering is significantly greater
than the Rayleigh scattering intensity. Similarly, examples of filtered pure rota-
tional Raman and Thomson scattering in plasmas at elevated pressure are also
described in this section. Some of the Thomson scattering results discussed in
section 8.2 are more applicable to the conditions for near equilibrium plasmas
than highly non-equilibrium plasmas. The incoherent Thomson scattering data
are fitted to a Gaussian-shape intensity distribution (Hutchinson 2002), which
is appropriate if the EEDF is Maxwellian. The EEDF in many molecular gas
non-equilibrium plasmas are not Maxwellian (see chapter 3). The procedure
for obtaining non-Maxwellian EEDF measurement by incoherent Thomson
scattering in atmospheric pressure plasmas has been discussed in a recent
publication by Huang et al (2000).
Pure rotational Raman scattering of N2 can permit gas temperatures
measurement with high accuracy (±lOK). Such a measurement technique
can be very useful to quantify the operating conditions of a short pulse
excited, low average power DBD where the gas temperature rise may be
only be 100-200 K above the ambient gas temperature.
Electron density measurement by millimeter wave interferometry is
described in section 8.3. In atmospheric pressure plasmas, the 105 GHz
probe frequency is smaller than the electron-neutral collision frequency.
Under such a measurement condition both probe beam intensity attenuation
and phase shift need to be measured to estimate electron density. The details
of such measurement and data analysis procedures are described in section
8.3. The choice of microwave or millimeter wave probe frequency is
determined by the required resolution of the electron density measurement.
For most non-equilibrium atmospheric pressure plasmas the electron density
is ne :::; 1013 cm -3. The 105 GHz probe frequency permits electron line density
measurement with resolution net:::; 1014 cm -2, where I is the linear plasma
dimension.
The spatially resolved electron density measurement using mid-infrared
CO2 laser interferometry is described in section 8.4. This interferometric
approach is ideally suited for electron density measurement in micro hollow-
cathode and other atmospheric pressure boundary dominated discharges
with P D :::; 10 torr cm, where P is the gas pressure and D is the inter-electrode
gap (Stark and Schoenbach 1999).
In low-pressure plasmas, Langmuir probes are used to measure electron
density and EEDF (Auciello and Flamm 1989). Probes always perturb the
local plasma surrounding. The extent of such perturbation depends on
some characteristic lengths in plasma, namely, electron Debye length AD,
ionization mean free path Ae, and charge exchange mean free path Aex. If
the probe dimension is larger than these characteristic lengths, the probe
perturbs the local plasma properties and the validity of probe measurement
becomes questionable (Auciello and Flamm 1989).
--- Page 463 ---
448
Plasma Diagnostics
Plasma emission based measurements of rotational temperatures from
electronically excited states are widely used to infer gas temperature in
plasmas (Auciello and Flamm 1989, Herman 1996, Ochkin 2002). Measure-
ments of rotational temperatures in atmospheric pressure air plasmas are
described in chapter 8.5. It should be noted that such measurements would
be a valid indicator of gas temperature only if the excited states are produced
by direct electron impact excitation from the ground state. Since the electron
collision with molecules cannot impart any significant amount of angular
momentum, the rotational population distribution of the excited state
should replicate the ground state rotational population distribution. Other
factors which can impact such measurements include self-absorption of
radiation and rotational quantum number dependent collisional quenching.
If the excited states are formed through dissociative excitation or other
processes where a significant amount of internal energy can be deposited,
plasma emission from those excited molecular states cannot be used for
estimating the rotational temperature of the ground state. Even when these
conditions are met, in discharges where the EEDF is time modulated, such
as in rf discharge, additional complications can arise where time modulated
radiative cascade can modify the population distribution of the electronically
excited rotational states. A comparison of time resolved rotational tempera-
ture measurements from H2 Fulcher-a band and Nt B-X (0,0) plasma
emission showed a radiative cascade can influence the estimate of 'rotational
temperature' measurement from the H2 Fulcher-a band (Gans et aI200l).
The accuracy of this relatively simple measurement technique can be
compromised if all the necessary conditions are not met. In view of this,
the plasma emission based rotational temperature measurement should be
calibrated with rotational Raman or Doppler broadening of diode laser
absorption measurements (Penache et al 2002). Although Doppler broad-
ening measurement permits measurement of gas temperature with high accu-
racy in low-pressure plasmas, it may have limited accuracy in high-pressure
plasmas, since the Doppler broadening scale is tl.D = 7.16 x 1O-7YoVT/M,
where Yo is the line-center transition frequency and M is the mass of the
absorbing species in atomic mass units, whereas pressure broadening
increases linearly with gas pressure (Demtroder 1981). For atmospheric
pressure plasmas with a gas temperature rise ::;200 K from ambient, pressure
broadening may dominate over Doppler broadening. Under this condition,
the diode laser absorption line shape becomes a Voigt profile, which is a
convolution of Gaussian (Doppler broadened) and a Lorentzian (pressure
broadened) line shape (Demtroder 1981). The Voigt, Gaussian, and Lorent-
zian linewidths (FWHM) are approximately given by (Penache et aI2002):
tl.>.b = tl.>.~ - tl.>'v . tl.>'L
(1)
where tl.>'G is the Gaussian component width, tl.>'v is the Voigt linewidth,
and tl.>'L is the Lorenztian component width. The Lorentzian component
--- Page 464 ---
Introduction
449
width can be de-convolved from the total Voigt linewidth in the wings of
the absorption line, since the Lorentzian predominates in the wing, and the
Gaussian component width is then determined from equation (1). If the
pressure broadening becomes the dominating contributor to the Voigt
profile, the accuracy of the Doppler broadening estimate from equation (1)
becomes limited.
Plasma emission based measurement of electron density in air plasma
from Stark broadening H~ is described in section 8.5. More details of the
electron temperature and the electron density dependent H~ line shape fitting
information can also be found in a recent review of spectroscopic measure-
ments at or near atmospheric pressure plasma (Ochkin 2002).
The Nt and NO+ ion density measurements in atmospheric pressure air
plasmas by ring-down spectroscopy are described in section 8.6.
The diagnostics methods presented in this chapter allows quantification
of the fundamental plasma characteristics, which can be used to either
validate model calculations and/or experimentally demonstrate scaling
properties of high-pressure plasmas. Application specific diagnostics, such
as measurements of 0, H, or N atom or other radical densities in plasmas,
have not been included in this chapter since the end use of atmospheric
pressure non-equilibrium plasmas covers a wide scope, such as high flux radi-
cals for materials processing, surface properties modification, detoxification,
plasma display panel, and VUV /UV photon source. Some of the optical
spectroscopic based measurements of process control and optimization are
described in a recently published proceeding of the International Society
for Optical Engineering (Ochkin 2002). It should be noted that commonly
used one-
or two-photon allowed laser-induced fluorescence (LIF)
measurement of absolute radical densities in low pressure plasmas (Dreyfus
et a11985) may not be readily applicable to similar absolute density measure-
ment of radical species, at atmospheric pressure, which have high collisional
quenching rates, e.g. the H atom (Preppernau et aI1995). The LIF measure-
ment can still be used to measure radical production efficiency in atmospheric
pressure discharges, using methods similar to the combustion diagnostics of
reactive species (Eckbreth 1996). Under some conditions, where spatial
resolution is not required, ring-down spectroscopic measurement is very
well suited for sensitive laser spectroscopic measurement of line integrated
absolute density of radical (McIlroy 1998, Staicu et a12002) and ionic species
(see section 8.6) formed in an atmospheric pressure plasma.
References
Aucillo 0 and Flamm D L (eds) 1989 Plasma Diagnostics vo1s 1 and 2 (New York: Academic)
Demtroder W 1981 Laser Spectroscopy (Berlin: Springer)
Dreyfus R W, Jasinski J M, Walkup R E and Selwyn G S 1985 Pure and Appl. Chern. 57
1265
--- Page 465 ---
450
Plasma Diagnostics
Eckbreth A C 1996 Laser Diagnostics for Combustion Temperature and Species
(Amsterdam: Gordon and Breach)
Fonck R J and Den Hartog D J (eds) 2003 Proceedings of the 14th Topical Conference on
High Temperature Plasma Diagnostics, Rev. Sci. Instrum. 74(3). And other
previous conference proceedings published in Rev. Sci. Instrum.
Gans T, Schulz-von der Gathen V and Dobe1e H F 2001 Plasma Sources Sci. Technol. 10 17
Herman I P 1996 Optical Diagnostics for Thin Film Processing (New York: Academic)
Huang M, Warner K, Lehn Sand Hieftje G M 2000 Spectrochimica Acta B 55 1397
Hutchinson I H 2002 Principles of Plasma Diagnostics (Cambridge: Cambridge University
Press)
McIlroy A 1998 Chern. Phys. Lett. 296 151
Ochkin V N (ed) 2002 'Spectroscopy of nonequilibrium plasma at elevated pressure',
Proceedings of SPIE, vol 4460
Penache C, Micelea M, Brauning-Demian A, Hohn 0, Schossler S, Jahnke T, Niemax K
and Schmidt-Bocking H 2002 Plasma Sources Sci. Technol. 11 476
Preppernau B L, Pearce K, Tserpi A, Wurzburg E and Miller T A 1995 Chern. Phys. 196
371
Staicu A, Stolk R Land ter Meulen J J 2002 J. Appl. Phys. 91 969
Stark R Hand Schoenbach K H 1999 Appl. Phys. Lett. 74 3770
8.2 Elastic and Inelastic Laser Scattering in Air Plasmas
8.2.1
Background and basic theory
8.2 .1.1
Scattering intensities
Laser scattering is a relatively simple yet powerful optical diagnostic tool for
high pressure molecular plasmas, capable of quantitative determination of
heavy species rotational/translational temperature, vibrational distribution
function of all major species, and electron number density and electron
temperature. We begin this section by providing a brief overview of sponta-
neous scattering theory, emphasizing the essential elements relevant to
measurements in molecular, non-equilibrium plasmas. More detail can be
found in Long (2002), Eckbreth (1996), and Weber (1979). The discussion
assumes knowledge of the fundamentals of diatomic spectroscopy such as
Dunham expansions for calculating individual rotational and vibrational
transition frequencies, nuclear spin degeneracy, and the Boltzmann distribu-
tion for equilibrium partitioning of internal energy, from which rotational
temperature can be determined. If necessary a compact summary can be
found in chapter 6 of Long (2002).
Scattering can be explained, classically, as the result of an incident
electromagnetic wave inducing an oscillating electric dipole moment p(t)
--- Page 466 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
451
which is given by the product of the polarizability, a, of the medium and the
time-varying incident electric field, E(t).
p(t) = a· E(t).
(1)
The polarizability, which has units of volume, is a measure of the distortion
of the electron charge cloud in response to the applied electric field and is a
function of the relative coordinates of the nuclei. It is customarily expanded
with respect to the vibrational normal coordinates (or 'normal modes') (Q) of
the molecule as
a=ao+ (oa) Q+ ...
oQ 0
(2)
where ao and (oa/oQ)o are evaluated at the equilibrium internuclear dis-
placement. Note that for diatomic molecules, which dominate air plasmas,
there is only a single vibrational normal mode, corresponding to relative
motion parallel to the axis connecting the nuclei. Assuming harmonic oscil-
lation with natural frequency Wk> so that Q = Qo COS(Wkt), and sinusoidal
applied electric field, E, with frequency WI and amplitude Eo, the induced
electric dipole moment is given by
p(t) = [ao+ (;~)oQOCOS(Wkt)]EoCOS(Wlt)
= aoEocos(wlt) + (;~\ Q;Eo [COS(WI -Wk)t + cos (WI +Wk)t]. (3)
The first term in equation (3) contributes to two well known scattering
phenomena. The first is the quasi-elastic scattering from bound electrons,
commonly referred to as Rayleigh scattering, which can be used to extract
heavy species translational temperature and number density. As will be
discussed in section 8.2.4, the analogous quasi-elastic scattering from free
electrons is termed Thomson scattering, which can be used for determination
of electron density and temperature. The first term is also responsible for
pure rotational Raman scattering, an inelastic scattering process corre-
sponding to quantized molecular rotation which, as will be shown, can be
used to extract extremely accurate values of rotational temperature. The
second term represents vibrational Raman scattering, which can be used to
measure the vibrational distribution functions of all major species.
Raman scattering requires a change in the polarizability with respect to
motion of internal degrees-of-freedom. For pure rotational Raman scattering,
this requires the polarizability to vary with molecular orientation, so that there
must exist an anisotropic component to the molecular polarizability, generally
expressed as all -
a~. A spherically symmetric molecule, such as CH4, yields
no pure rotational Raman effect. For a vibrational Raman transition to occur,
the polarizability must change as the molecule oscillates or as part of it bends.
--- Page 467 ---
452
Plasma Diagnostics
Since Raman scattering does not require a permanent dipole moment, it is an
excellent diagnostic for air plasmas, which are dominated by the homonuclear
diatomic molecules N2 and 02. In general, the polarizability increases as the
number of electrons increases so that heavier molecules tend to have inherently
larger Rayleigh scattering intensities.
For quantized transitions between rotational-vibrational quantum
states, the quantum mechanical expression for the polarizability matrix
element, analogous to the classical expression given by equation (2), is
al"v",l''; = (]"v" I a
I J'v') = (]"v" I ao I J'v') + (;~)o (]"v" I Q I J'v')
(4)
where J" v" and J'v' are rotational-vibrational quantum numbers labeling
the initial and final states, respectively, and the brackets indicate integration.
In equation (4), the first term represents Rayleigh and pure rotational Raman
scattering, which vanish unless v' = v" due to the orthogonality of the
vibrational wave functions, and the second term is responsible for vibrational
Raman scattering. Assuming separation of the rotational and vibrational
parts of the wave functions, evaluation of the matrix elements in equation
(4) leads to the well known selection rules, which for linear molecules are
/j.] = 0, ±2
(5)
for pure rotational Raman scattering (where /j.] = ° corresponds to
Rayleigh scattering) and
/j.v = ±l,
/j.] = 0, ±2
(6)
for vibrational transitions between harmonic oscillators. Transitions with
/j.] = -2,0, +2 are called 0, Q and S branches, respectively. Overtone tran-
sitions (/j.v = ±2, ±3, ... ) are allowed for anharmonic oscillators, but their
intensities are very weak.
Figure 8.2.1 shows the basic geometry employed in most scattering
measurements. The incident laser beam is linearly polarized with the polari-
zation vector orthogonal to the plane defined by the propagation directions
of the incident and detected scattered radiation, commonly referred to as the
z axis. For such a geometry the detector, by definition, is located in the
scattering plane so that the angle {)z (see equation (49» is equal to 90 0 •
Sample
~
Incident
Scattered
Figure 8.2.1. Basic scattering geometry for polarized light.
--- Page 468 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
453
For this case the scattering intensity, I, or power (P) per unit solid
angle (!l), from an ensemble of scatterers in rotational level J, is given by
(Long 2002)
7[2 -4 [()2
4boo)2]
III = Eij Vs
aoo + bJ,J 45 NJh,
D.J = 0
(7)
7[2 -4 [
bOO)2]
h = Eij Vs bJ,J ~
NJh,
D.J = 0
(8)
for Rayleigh scattering
7[2 -4 [
4boo)2]
III = Eij Vs bJ±2,J 45 NJh,
D.J = ±2
(9)
7[2 -4 [
bOO)2]
h = Eij Vs bJ±2,J ~
NJh,
D.J = ±2
(10)
for pure rotational Raman scattering and, assuming harmonic oscillator
wave functions,
7[2 -4 [2
4blO)2]
III = Eij Vs (alO) + bJ,J 45 NJh,
D.v= 1, D.J=O
(11 )
7[2 -4 [
blO)2]
I~ = Eij Vs bJ,J ~
NJh,
D.v= 1, D.J=O
(12)
7[2 -4 [
4blO)2]
III = Eij Vs bJ±2,J 45 NJh,
D.v = 1, D.J = ±2
(13)
7[2 -4 [
blO)2]
I~ = Eij Vs bJ±2,J ~
NJh,
D.v = 1, D.J = ±2
(14)
for vibrational Raman scattering. In equations (7)--(13) the symbols II and ..1
correspond to scattering polarized parallel and perpendicular, respectively,
to the incident laser polarization direction, NJ is the number density of
scatterers in the level J, h the irradiance (power/area) of the incident laser
beam, and aoo and 1'00 represent the matrix elements for the mean and
anisotropic parts of the polarizability, respectively, given by
aoo=i(axx+ayy+azz)
(15)
1'00 = 4 [(a:ex - ayy )2 + (ayy - azz)2 + (azz - axx )2 + 6(a;y + a;z + a;x)]1/2.
(16)
Similarly, alOhlO represent the corresponding polarizability derivative
components.
In equations (7)-(14) the symbols bJ"J, known as the Plazeck-Teller
factors (or rotational line strengths), represent the part of the polarizability
--- Page 469 ---
454
Plasma Diagnostics
matrix elements in equation (4) which arise from summation over the
magnetic sublevels, mJ. For linear molecules which behave as rigid rotors
(or more precisely, for symmetric top wave functions with the 'K' quantum
number equal to 0), bJ',J" have the following form (Long 2002).
8.2.1.2
Cross sections
3(J + l)(J + 2)
bJ+2,J = 2(21 + 1)(2J + 3)
3J(J - 1)
bJ - 2,J = 2(2J + 1)(21 -1)
J(J + 1)
bJ,J = (21 -1)(2J + 3)
(17)
(18)
(19)
Scattering intensities are most commonly tabulated by combining the
constants and molecule dependent matrix elements that occur in equations
(7}-(l4) to form what is known as the differential scattering cross section,
(do/dO), which is defined as
( dO')
111/1-
dO 1111- = Nh
(20)
where II and ..L again refer to polarization of scattered light which is parallel
or perpendicular, respectively, to the incident z axis polarization. Note that
the cross sections scale as the scattering frequency, 1/, to the fourth power
(with the exception of Thomson scattering) and are independent of both
the incident laser intensity and the scatterer number density. Some selected
Rayleigh and Raman cross sections are given in table 8.2.1. More extensive
tables can be found in (Eckbreth 1996, Shardanand and Rao 1977, Weber
1979).
While not essential to the primary purpose of this chapter, it is worth
pointing out that the differential Rayleigh cross section is typically cast in
a form different than equations (7) and (8). First, since the scattering
originating from particles with different values of J spectrally overlaps, NJ
can be replaced by N, the total number density, and the bJJ sector can be
set to 1. More significantly, it is traditional to express a and 'Y in terms of
n, the index of refraction, and Po, the natural light depolarization ratio, so
that the cross sections become (Miles et a12001)
( dO' )
( 30') (2 - Po )
dO
II =
87r
2 + Po
(21 )
( :~ ) 1- = (~:) (2 ~o Po )
(22)
--- Page 470 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
455
Table 8.2.1. Selected Rayleigh, rotational and vibrational Raman differential cross
sections are listed. Excitation wavelength is 532nm. Values for Rayleigh and
vibrational Raman correspond to the sum of 11+ ~ contributions. Values for
rotational Raman correspond to the II contribution from specified values of
1" and 1'.
Molecule
Rayleigh differential
Rotational Raman
Vibrational Raman
cross section
differential cross section
differential cross
(x 1028 cm2 sr- I )
(1" ---> 1') at 488 nm
section, Q-branch
(from Shardanand
(x 1030 cm2 sr- I )
(x103I cm2sr-l)
1977)
(from Eckbreth 1996,
(from Weber 1979)
Penney 1974)
N2
3.9
5.4 (6 -> 8)
3.7
O2
3.4
14 (7 -> 9)
4.4
CO
0.61 (6 -> 8)
3.5
He
0.080
H2
0.81
2.2 (I -> 3)
8.0
CO2
12
53 (16 -> 18)
5.3 (VI mode)
CH4
8.6
29 (VI mode)
where (J' is the integrated cross section given by
(J'=327f3(n-1)2 (6+3PO).
3).4N2
6-7po
(23)
Note that Po is equal to zero for isotropic molecules and is of the order 0.01-
0.05 for typical diatomic gases. The relatively small term in parentheses in
equation (23) is known as the 'King correction factor' (Miles et aI2001).
8.2.1.3 Anharmonicityeffects
In the previous sections we have ignored the vibrational level dependence of
the Raman scattering cross sections. However, since non-equilibrium
plasmas are characterized by very substantial vibrational mode dis-
equilibrium it is important to assess the influence of anharmonicity and
rotation/vibration coupling on the matrix elements, defined by equation
(4). In particular, it is important to note that for harmonic oscillator wave-
functions, the polarizability derivative matrix elements scale as (v + 1) 1/2
for ~v = + 1 and vl / 2 for ~v = -1 so that the vibrational scattering cross
sections are predicted to scale as v" + 1 for Stokes scattering and v" for
anti-Stokes (Eckbreth 1996). Real molecules, however, exhibit anharmoni-
city which needs to be taken into consideration, particularly at high v. One
approach is to substitute Morse potential wave functions in equation (4).
Assuming vibrational transitions originating in level v with ~v = ±1, the
--- Page 471 ---
456
Plasma Diagnostics
result is (Gallas 1980)
1
[
(k-2V-1)(k-2V-3)]1/2
(w 1r1v)=aM(k_2v_2) (v+1)
(k-v-1)
,
~v=+1
(24)
(wlrlv) =
1
[v (k-2v-1)(k-2v+ 1)]1/2,
aM(k - 2v)
(k - v)
~v= -1
(25)
where
_ (2JLWeXe) 1/2
aM -
Ii
'
and v and ware vibrational quantum numbers, and We and WeXe are the first
two terms in standard Dunham expansions for vibrational frequency. If it is
assumed that (8a/8Q)o is constant with respect to vibrational quantum
number, then the vibrational Raman scattering cross sections will scale as
(k - 2v -l)(k - 2v - 3)
Iv ()( (v + 1)
2
(k - 2v - 2) (k - v - I)
(Stokes)
(26)
(k-2v-I)(k-2v+ 1)
Iv ()( v
2
(k - 2v) (k - v)
(anti-Stokes).
(27)
The influence of anharmonicity can be seen in figure 8.2.2 which plots the
relative scattering cross section as a function of vibrational quantum
number assuming harmonic oscillators (filled circles), and equation (26) for
carbon monoxide (squares) and hydrogen (triangles). It can be seen that
60
~
1/1 50
c
S
c
~ 40
c
.;:
! "
30
u
U)
i
20
~ 10
0 . -
0
• Hannonlc Oscillator
• Morse Potential (CO)
••
••
••
A Morse Potential (H2)
••
••
• ••
.-
.. -
.- .. -
•••••••
.- .. -
&
•• : •••
&
••••
& ,I··
A
,
AA,,'
••••
•••
10
20
30
40
Vibrational Quantum number (v)
Figure 8.2.2. Relative scattering cross section as a function of v for harmonic oscillator
(e), co (_), and H2 (A).
--- Page 472 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
457
for v less than ",5, the anharmonicity correction is quite small, even for
hydrogen which has the largest anharmonicity of any diatomic molecule.
For carbon monoxide, which is representative of other common diatomic
species, such as nitrogen and oxygen, the correction becomes appreciable
(",7%) for vibrational levels exceeding ",10, and reaches ",33% at level
v ~ 40. As will be seen below, such high levels of CO have been observed
in optically pumped as well as certain electric discharge plasmas. In such
cases, the anharmonicity correction to the vibrational cross sections cannot
be ignored.
In addition to anharmonicity effects, it is important to consider the effect
of rotation-vibration interaction, particularly for pure rotational Raman
scattering (Drake 1982). As stated previously, the Plazeck-Teller factors
given in equations (17)-(19) assume rigid rotor wave functions, which
while an excellent approximation at low J, can introduce significant uncer-
tainty at high J, even in v = O. The effect becomes even larger at high v,
due to the increase in the average internuclear separation and corresponding
increase in the polarizability anisotropy. Following the notation of Drake
(1982) and Asawaroengchai and Rosenblatt (1980), the matrix element for
the polarizability anisotropy can be expressed by
(28)
where C is a constant, S(J) are the rigid rotor Plazeck-Teller factors,f(J) is
a centrifugal distortion correction, and (3v is the change in the polarizability
accompanying rotation, which is a function of v and can be expressed as
(29)
where (3e' = (fJ(3/fJr)e' (3e" = (fJ2(3/fJr2)e, and the average value of inter-
nuclear displacement, from first-order perturbation theory (Wolniewicz
1966), is given by
(30)
In equation (30) Be is the first term in the standard Dunham expansion for
rotational frequency and D!e is the rotation-vibration spectroscopic coupling
constant. The significance of equations (28)-(30) is that they provide a
method for correcting pure rotational Raman cross sections, which are tabu-
lated for v = 0, for use in vibrationally non-equilibrium environments.
Figure 8.2.3, which is a plot of the square of (3v/ (30 (which is proportional
to the cross section) for H2, CO, and NO, illustrates the magnitude of the
effect. This can also be important for high resolution measurements in
high temperature equilibrium systems, such as flames, in which temperature
is determined by the ratio of intensities for fixed J and different v.
--- Page 473 ---
458
Plasma Diagnostics
(13./130) 2
H2
6.0
•
5.5
5.0
•
4.5
•
4.0
•
3.5
•
3.0
2.5
•
2.0
•
CO
•
1.5
•
~
~
~
~
~N
1.0
0
2
4
6
8
10
v
Figure 8.2.3. Vibrational level dependence of the square of the polarizability anisotropy
for H2, CO, and NO.
Finally, for highly non-rigid rotors, such as hydrogen, the j(J) factor,
while less significant than (3v needs to be considered, since it can impact
spectra of molecules in the v = 0 level. Again, from Asawaroengchai and
Rosenblatt (1980),1(1) for pure rotational Stokes scattering is given by
j(J)oo = [1 + (4/X) (Be/we)2(J2 + 3J + 3)]2
(31)
where X is defined as (3e/re(3~. (Note that for anti-Stokes scattering, J is
replaced by J - 2). Similarly, for Stokes rotation-vibration scattering j(J)
is given by
(D.J = +2)
(32)
(D.J = -2).
(33)
Figure 8.2.4 plotsj(J)oo for H2 and N2 pure rotational Stokes transitions. It
can be seen that for N2 the correction is essentially negligible, where as for H2
the correction factor is approximately 15% for J = 4, which corresponds to a
rotational energy of 1200cm- 1 (or characteristic temperature of ",1750K).
8.2.1.4
Spectral line shapes
For most, albeit not for all, diagnostic measurements extraction of quanti-
tative information requires accurate knowledge of the appropriate spectral
line shape function. We provide here a brief introduction to the subject
which will serve as a basic foundation. Additional details can be found in
the cited references.
--- Page 474 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
459
f(O)~1.7
H2
1.6
•
1.5
•
1.4
•
1.3
•
1.2
•
•
1.1
• •
1.0
N2
0
2
4
6
8
10
J
Figure 8.2.4. Centrifugal distortion correction to the pure rotational Raman cross section
as a function of J for H2 and N2.
We begin with a slight digression, pointing out an important distinction
between Raman and Rayleigh/Thomson scattering. For Raman scattering
from an ensemble of gas phase scatterers what is known as the 'random
phase approximation' is generally assumed valid since it is reasonable that
the relative phases of internal oscillation or rotation of individual 'particles'
are randomly distributed. The result is that the total scattering intensity seen
at the detector is the simple incoherent sum of the intensity from each scat-
tering particle. This leads directly to a total intensity which is proportional to
N, the particle number density, as per equations (7)-(14). However, Rayleigh
and Thomson scattering are inherently coherent so that the relative phases
seen at the detector are dictated by the differences in the total propagation
path, which depends upon the positions of the individual particles within
the scattering sample volume, as well as the scattering geometry. For the
idealized case of a perfectly ordered array of stationary scattering particles
the vector sum of the Rayleigh scattered electric fields at the detector is
identically zero, except for the trivial case of zero degree scattering angle
(or 'forward' scattering). In the gas phase, however, the random motion of
particles gives rise to instantaneous fluctuations in the local scattering
number density such that phase cancellation at the detector is not perfect.
This 'dynamic' light scattering mechanism was first described by Einstein
and is discussed in more detail in many standard textbooks on the subject
(Chu 1991, Berne and Pecora 1976). Without going through the details we
simply state that for almost all cases the total Rayleigh scattering intensity
is also proportional to the number density of scatterers. Exceptions occur
at very small scattering angle and/or long wavelength light (Gresillon et al
1990) or in the vicinity of critical points (Ornstein and Zernike 1926).
For Raman scattering in gases, therefore, we can ignore collective
motion and focus our discussion of spectral line shapes on mechanisms
which affect individual molecules. A central consideration, for both
Raman and Rayleigh/Thomson scattering, is the scattering wave-vector, k,
--- Page 475 ---
460
Plasma Diagnostics
Figure 8.2.5. Scattering diagram illustrating magnitude and direction of wave-vector.
defined as
(34)
where the subscripts i and s refer to the incident and scattered propagation
directions, respectively (see figure 8.2.5). It can be seen that the direction
of k is perpendicular to the bisector of the angle formed by the incident
and scattering directions, referred to a common origin. From simple
geometry (the law of cosines) it is easy to show that the magnitude of the
vector k, !:lk, is given, in general, by
(35)
where ks and kj are equal to 27f / ,\g and 27f / .\, respectively, A is the radiation
wavelength and B is the scattering angle.
Note that for Rayleigh and Thomson scattering it is easy to show (using
2 sin2 [B /2] = I - cos[B]), that equation (35) reduces to
!:lk ~ 21kol sin (~) = ~
sin (~).
(36)
From the perspective of spectral line shapes, the k vector dictates the
contribution to the phase of the detected scattering due to the position, r,
of individual scatterers, through the expression
Ectet(t) = Eo exp[-i(wst + k· r(t)]
(37)
where Ws represents the central scattering frequency and the k· r(t) term has
units of phase angle. Ifr(t) = vt, where v is the vector velocity, then equation
(37) becomes
Ectet(t) = Eo exp[-i(ws + k· v)t] = Eo exp[-i(ws + WDop)]
(38)
where the k . v term is the well known Doppler shift due to the vector velocity v.
We now introduce the parameter often given the symbol Y, defined as
(39)
--- Page 476 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
461
where I is the collision mean free path (Miles 2001). If Y « 1, then the
scattering particles, on average, traverse a distance such that the k . v term
in equation (38) oscillates through many cycles of 27r in the time interval
between collisions. This condition, which typically corresponds to low
density, results in the well known 'Doppler' spectral profile, is representative
of scattering from an ensemble of particles with Maxwellian velocity distri-
bution. The spectral profile, S(w), is given by
S(w) = _1_ [In(2)] 1/2 exp [-In(2);w - Ws)2]
1'nop
7r
1'Dop
(40)
where 1'Dop' the half width at half maximum (HWHM), is given by
= [~k] [2In(2)kBT] 1/2
1'Dop
27r
m
(41 )
and kB is Boltzmann's constant. Note that equation (40) is valid for Raman,
Rayleigh, and Thomson scattering so long as Y« 1. As we shall see in
section 8.2.4, however, the definition of Y is different than equation (39)
for Thomson scattering. Equation (41), in combination with equation (35),
represents the general expression for the Doppler scattering line width,
taking into account scattering geometry as well as, in the case of Raman
scattering, Stokes or anti-Stokes frequency shifts.
For Y» 1, the k· v(t) term in equation (38) evolves by much less than
27r in the time interval between collisions. In this limit, a spectral phenomena
known as Dicke narrowing (Dicke 1953) occurs, in which the Doppler
contribution to the line width goes to zero and is replaced by a Lorentzian
component due to mass diffusion given by
Sdw) =_1 [
1'2
]
7r1'Diff (ws - w)2 + 1'2
(42)
where 1'Diff IX Dm, Dm being the coefficient of mass diffusion which scales as
the inverse of pressure. In the case of Raman scattering an additional
'Lorentzian' contribution to the spectral line width also develops due to col-
lisions which limit the 'lifetime' of the oscillation at Ws. This phenomenon,
known as 'pressure broadening', has HWHM given by
1'P = a(T)P
(43)
where a(T) is the temperature dependent pressure broadening coefficient,
which is most commonly given in units of cm-I bar-I. A full conceptual
treatment of the determination of a(T) is beyond the scope of this chapter,
but we will simply state that it is typically of order 0.1 cm-I bar-I at room
temperature and is generally determined experimentally (Bonamy et al
1988, Rosasco et aI1983).
--- Page 477 ---
462
Plasma Diagnostics
In the intermediate Y regime, the most commonly employed approach
for Raman scattering is to utilize the Voigt profile, Sv(w), given by
with
( In2)1/2
1 (B) J [
e-'/
]
Sv(w) = --;:-
i'DoP;:
dy (D _ y)2 + B2
B = (In2)1/2 (~),
i'Dop
D = (In2)1/2 (w - ws)
i'Dop
(44)
which treats the simultaneous Doppler and Lorentz components as a
convolution integral (Demtroder 1998). In some cases, where very high
resolution data are available, more complex treatments employing line
shape functions such as the Galatry profile are employed (Galatry 1961).
For Rayleigh and/or Thomson scattering, collective motion begins to
influence the line shape as Y approaches'" 1. As will be described in some
detail in section 8.2.4, in this regime acoustic modes begin to propagate in
the fluid, inducing correlated density fluctuations scattering from which results
in the development of frequency shifted side bands, symmetrically displaced
from the 'narrowed' central component. For molecular scattering this
phenomenon is known as Rayleigh-Brillouin (or Mandelstem) scattering.
For completeness we note briefly one additional spectral effect that
occurs at elevated pressures. In the previous discussion we have assumed
that the intensities from a set of individual spectral transitions, for example
O/S branch Raman transitions, are independent of one another. However,
in cases where lines begin to spectrally overlap it is often the case that this
so-called 'isolated line' hypothesis fails so that the total intensity at any wave-
length is not equal to the simple sum of contributions from adjacent lines. In
particular, individual Q-branch Raman transitions overlap significantly for
pressures of order 1 bar or greater and it is well known that 'line-mixing'
techniques must be used to accurately fit experimental spectra. While the
details are beyond the scope of this chapter, the basic approach requires
incorporation of state-to-state J-dependent rotational energy exchange,
which constitutes the primary mechanism of pressure broadening in most
diatomic systems. As molecules begin to experience J changing collisions
with a frequency exceeding the difference frequency between adjacent transi-
tions, the individual lines begin to merge together. This 'rotational
narrowing' is analogous to the Dicke narrowing of the Doppler profile
described previously, and is well recognized in spectral models of coherent
anti-Stokes Raman spectroscopy (CARS) (Hall et aI1979).
8.2.2 Practical considerations
Figure 8.2.6 illustrates a somewhat generic scattering apparatus, typical of that
which would be employed for single spatial point scattering measurements.
--- Page 478 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
463
Nd:YAG Laser
Pulser
, ,
;,.. , , ,
, ,
IceD
~
Monochromator
, , , , , , ,
~
Power Meter
co Laser
, , , , ,
_______ ..1
Trigger
Figure 8.2.6. Schematic diagram of typical spontaneous scattering apparatus, in this case
used for CO laser optical pumping studies described in section 7.2.
The most common laser source for application to luminous environments is
the 'Q-switched' Nd:YAG laser, which is readily available from several
commercial vendors. Typical single pulse output energy at the second
harmonic wavelength of 532 nm ranges from ",0.3 to 1.0 J with pulse dura-
tion and repetition rate equal to '" 10 ns and 10-30 Hz, respectively. While
532 nm systems are most common, it can be useful, in some cases, to
employ the third (355 nm) or fourth (266 nm) harmonic or to use KrF
(248 nm) or ArF (193 nm) excimer lasers. Such systems take advantage of
the fourth power of frequency dependence of the cross section (equations
(7)-(14)), but require more expensive, and somewhat less robust, optics.
For non-equilibrium air plasmas, strong interferences from O2 laser induced
fluorescence must also be considered, particularly at 193 and 248 nm. This
generally requires the use of line-narrowed, tunable sources, which are
readily available but considerably more expensive. Nonetheless, if ultimate
sensitivity is essential, for example to capture instantaneous 'single laser
shot' data, shorter wavelength systems are often a necessity. It should
always be recalled, however, that in photon units the scattering cross section
scales as frequency to the third power, since the photon energy is propor-
tional to frequency.
Laser focusing into the scattering medium is straightforward but subject
to the dual constraints of dielectric breakdown, which limits the intensity at
the 'waist' of the focused laser beam, and damage to the scattering medium
access windows. For what are known as 'Gaussian' laser beams, these two
--- Page 479 ---
464
Plasma Diagnostics
constraints are coupled by the following expressions for the 'beam waist', wo,
and the beam confocal parameter, zo, given by
Wo = (2~) (~)
2
1fWo
zO=T·
(45)
(46)
The confocal parameter is the distance from the waist location, along the
laser beam propagation axis, after which the beam diameter grows to
V2wo (Yariv 1975). For ",IOns duration pulses, typical BK7 or fused silica
windows experience thermal damage at beam pulse fluences of order 1-
10 J /cm2 at 532 nm, depending upon cleanliness. Dielectric breakdown
occurs at ",5 x 103 J / cm2 at 1 bar pressure, corresponding to ",0.20 J per
pulse, for a typical", 1 cm beam focused with a 300 mm focal length lens.
Note that this value is based on experience and assumes a focal spot which
is substantially greater (",50 )lm) than that calculated from equation (45).
None the less, as can be seen from equations (45) and (46), if Wo is increased
in order to avoid breakdown, the accompanying increase in the confocal
beam parameter can lead to window damage.
For Raman scattering, signal is typically collected at 90° with respect to
the laser beam propagation direction. The 'etendue' of the resolving
instrument (in this case a spectrometer), which, for fixed resolution, is the
maximum product of the collection solid angle and 'source' (which in this
case is the scattering volume) cross sectional area, places some additional
constraints on the collection optics (Vaughan 1989). For moderate resolution
Raman spectra, the sampling volume is typically 1: 1 imaged onto the
entrance slit of an ",0.25--0.3 m focal length grating spectrometer with slits
set to 100 )lm, or ",2-4 Wo of the focused laser beam. The solid collection
angle is matched to that of the spectrometer optics, typically "'1/4,
where I is the ratio of the collection lens focal length to clear aperture,
and the cylindrical scattering volume is aligned with its long axis parallel
to the entrance slit. Faster collection can be performed, but only with
accompanying loss of spectral resolution. For example if ani /2 collection
lens is used with an 1/4 imaging lens the accompanying magnification
would require an increased slit size to pass all the collected light into the
spectrometer.
In general, the detector of choice for Raman measurements in air
plasmas is the microchannel plate intensified CCD (lCCD) camera, which
combines high quantum efficiency with fast gating capability. This is essential
in highly luminous environments, typical of such plasmas, where interference
due to spontaneous emission can be far larger than the desired scattering
signal, often by eight orders of magnitude or more.
--- Page 480 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
465
Anticipated scattering signal levels can be estimated by considering the
following simple expression
(47)
where ELi hvA is the fluence of a single laser pulse (in photons/cm2), N is the
number density of scatterers, da/dD is the scattering differential cross-
section, dD is the collection solid angle, V is the object plane measurement
volume, 'T] is the detector quantum efficiency, and ¢ is an optical collection
efficiency which accounts for window losses, spectrometer grating efficiency,
filters, etc.
As an example, we consider the vibrational Q-branch spectrum to be
given in the next section (figure 8.2.7). For N2, da/dD = ",5 X 10-31 cm2/sr
for v = O. If we assume that all of the molecules are in level v = 0 then
N = '" 1.6 X 1019 cm -3, corresponding to 1 bar pressure and 500 K tem-
perature. If we further assume E = 0.20J/pulse, the V, the object plane
cylindrical volume, is 0.5 cm in length x the focused beam cross sectional
area, dD = 0.049 sr(f /4), 'T] = 0.06, and ¢ = 0.1, then substitution into
equation (11) yields S :::::l 600 photoelectrons/laser pulse, or 3.6 x 105 photo-
electrons/min (at 10 Hz laser repetition rate). The actual N2 data in figure
8.2.7 was obtained by integrating for ",30 s, whereas the CO data, for
which the number density is lower, was integrated for 5 min.
8.2.3 Measurements of vibrational distribution function
As alluded to in the previous section, figure 8.2.7 shows a Q-branch vibra-
tional Raman spectrum obtained in a weakly ionized CO seeded N2
plasma, which has been created using the CO laser optical pumping tech-
nique discussed in section 7.2. The total pressure is 410 torr and the seed
fraction is 4%. Each peak represents an unresolved Q-branch Stokes
Raman shift from a vibrational level with different vibrational quantum
number. The left part of the spectrum shows vibrational levels of CO up to
v = 37 while the right part shows nitrogen vibrational levels 0-5. The
spectrum is obtained using a standard spontaneous Raman scattering
instrument, similar to that shown in figure 8.2.6, with Nd:YAG pulse
energy of ",0.20 J at 532 nm and a 0.25 m grating spectrometer equipped
with an ICCD detector. The cylindrical measurement volume had
dimensions of ",0.5 cm length and 0.01 cm diameter. Since at the employed
spectrometer resolution the ICCD detector can capture '" 10 nm, the
spectrum displayed is actually a composite of multiple spectra which were
obtained in immediate succession. As mentioned in the previous section,
the N2 signal was averaged for approximately 30 s at a laser repetition rate
of 10 Hz whereas the CO spectra were averaged for 5 min. More experimental
details can be found in (Lee et aI2001).
--- Page 481 ---
466
Plasma Diagnostics
8
v=O
6
v=O
/
v=20
v= 37
2
O+-------~--------~------~~~~~~--~
565
575
585
Wavelength (nm)
595
605
Figure 8.2.7. Q-branch vibrational Raman spectrum from optically pumped (see section
7.2) 4% CO seeded N2 plasma at 410 torr total pressure.
Figure 8.2.8 shows the corresponding vibrational distribution functions
(VDFs) of CO and N2, which are obtained by dividing the integrated indivi-
dual Q-branch intensities by the relative v-dependent cross sections given by
equation (26). Also included in figure 8.2.8 is the result of master equation
modeling, as discussed in section 7.2. In this regard it is important to point
out that Raman scattering, unlike infrared emission spectroscopy, provides
absolute population fractions for all observed levels, including v = o.
When comparing VDFs of multi-component mixtures, it is sometimes
useful to define a 'first level' vibrational temperature by
1.44(vl - vo)
Tv = ----,-:-"--,..----=..:...
In(Pol PI)
(48)
where Vo and VI are the vibrational energies of vibrational levels v = 0 and
v = 1 (in wavenumber units), and Po and PI are their fractional populations.
Predicted and measured first level vibrational temperatures, defined by
equation (48), are shown in figure 8.2.8.
As a second example, figure 8.2.9 shows a Q-branch Raman spectrum
obtained from an optically pumped mixture similar to that of figure 8.2.7
except that 15 torr of oxygen has been added and the total pressure increased
to 755 torr. The CO seed fraction is also increased somewhat, to ",5%. It can
be seen that the energy previously accumulated in the vibrational mode of
CO has been substantially transferred to O2, due, as discussed in section
--- Page 482 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
467
1.0E+0
l.OE·l
1.OE·2
l.OE·3
Relative population
•
o
CO, experiment (Tv =3500 K)
N2, experiment (Tv=2200 K)
CO, calculation (Tv=5300 K)
N2, calculation (Tv =2700 K)
•••••• •••••••• •
• • •••
I.OE·4 -+--,---r--.----.--,---.--,----.
o
10
20
30
40
Vibrational quantum number
Figure 8.2.8. VDFs extracted from data of figure 8.2.7, along with master equation
modeling predictions (see section 7.2).
7.2, to the lower vibrational mode spacing of O2, relative to CO. The top
spectrum shows six vibrational levels (v = 0-5) of nitrogen with corre·
sponding first level vibrational temperature Tv = 2500 ± 100 K. The
middle spectrum shows nine vibrational levels (v = 0-8) of CO with
Tv = 3400 ± 250 K. The bottom spectrum contains 13 vibrational levels
(v = 0-12) of O2 with Tv = 3660 ± 400 K. The vibrational distributions
are, again, non-Boltzmann.
As a final example, figure 8.2.10 shows a pair of pure H2 rotational
Raman spectra obtained from a recent pump/probe study of V-V transfer
rates (Ahn 2004). The system was initially prepared, via stimulated Raman
pumping, to a state in which about one third of the H2 molecules in the
v = 0, J =1 rotation-vibration level were excited to the v = 1, J = 1 level.
The displayed spectrum was obtained IllS after application of the pump
pulse, and shows that detectable population has been V-V transferred to
vibrational levels, in J = 1, as high as v = 6. As can be seen in figure 8.2.3,
ignoring rotation-vibration coupling effects on the value of {3v would
result in an overestimate of the v = 3, J = 1 level population by a factor of
approximately two and the v = 6 level population by a factor of approxi-
mately three.
We end this section by noting that vibrational Q-branch spectra have
also been widely utilized for temperature measurements, particularly in
combustion environments. In particular, N2 CARS thermometry is a well
established temperature diagnostic which can yield rotational and/or
--- Page 483 ---
468
Plasma Diagnostics
14
12
10
598
598
800
802
604
808
608
810
Wavelength(nm)
8
7
co
6
2
O+------r-----,------.------.-----,,-----,-----~
588
590
592
1194
598
598
800
602
Wavelength(nm)
10
8
2
568
570
572
574
576
578
580
582
Wavelength(nm)
Figure 8.2.9. Q-branch Raman spectrum from optically pumped synthetic air mixture with
2% °2 - Total pressure is I bar.
--- Page 484 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
469
3
~2
1/1
C
.2!
.E
r
a_up by 10
Of-----~--~--~~~~~--=---
545
546
547
548
549
Wavelength (nm)
550
551
Figure 8.2.10. H2 pure rotational Raman spectra from pump/probe v-v transfer study.
The spectrum corresponds to vibrational distribution IllS after initial excitation of
~33% of molecules to v = 1. Pressure/temperature is I bar/300 K, respectively.
vibrational temperature (Regnier and Taran 1973). As stated previously,
rotational temperature determination at pressures of order 1 bar or higher
requires incorporation of rotational narrowing phenomena into the spectral
model. In principal, high resolution nonlinear Raman 'gain/loss' techniques
can be used to obtain complete rotationally resolved spectra (Rahn and
Palmer 1986, Lempert et a11984) but the approach is, in general, somewhat
impractical as a diagnostic method due to the required slow spectral tuning
of a very narrow spectral line width single longitudinal mode (SLM) laser.
8.2.4 Filtered scattering
8.2.4.1
Basic concept
Small wave-number shift scattering diagnostics, such as Rayleigh/Thomson
or pure rotational Raman, have traditionally suffered from large inter-
ferences due to elastic scattering from window and/or wall surfaces, or, in
the case of Thomson scattering in weakly ionized plasmas, from molecular
Rayleigh scattering. Such interferences, which are typically orders of
magnitude more intense than the desired signal, can completely overwhelm
the measurement when performed with traditional instrumentation such as
grating spectrometers. In recent years, however, several optical diagnostic
techniques based on the use of atomic/molecular vapor filters as narrow
bandwidth filters and/or as spectral discriminators have been developed.
The basic idea, illustrated in figure 8.2.11, is to utilize a narrow spectral
line width laser which is tuned to a strong absorption resonance of the
--- Page 485 ---
470
Plasma Diagnostics
Particle, Window
..- and Wall Scattering
Molecular/Electron
Scattering
~ Light
~
Figure 8.2.11. Basic filtered Rayleigh scattering concept, specifically illustrating ther-
mometry diagnostic.
vapor. If a cell filled with the vapor is then inserted into the path between the
scattering volume and the detector, elastic scattering can be attenuated while
Doppler shifted and/or broadened scattering can be transmitted. In fact, the
use of such vapor filters for Raman scattering dates to near the discovery of
the Raman effect itself (Rasetti 1930), although it is only with recent
advances in laser technology that their true utility has been realized. In
addition to continuous wave (cw) Raman instruments incorporating mercury
vapor (Pelletier 1992) and rubidium vapor (Indralingan et a11991, Clops et al
2000), the availability of high power, narrow spectral line width pulsed laser
sources as common laboratory tools has enabled a wide range of new vapor
filter-based scattering techniques. Most of these have utilized iodine vapor,
which is particularly convenient because of strong absorption resonances
within the tuning range of injection-seeded, pulsed Nd:YAG lasers, as well
as the relative ease of filter construction, and availability of high quantum
efficiency detectors, both for point measurements and for imaging. A
recent special issue of the journal Measurement Science and Technology
(2001) contains a variety of molecular filter-based diagnostics, including
velocity imaging, in which Doppler-shifted Rayleigh or Mie scattering is
converted to velocity by determination of the fractional transmission
through a vapor filter, and temperature imaging, which is similar to velocity
--- Page 486 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
471
imaging but is based on Doppler broadening of molecular Rayleigh scat-
tering, as opposed to Doppler shift. Other examples include: high spectral
resolution light detection and ranging (HSRL) (Shimizu et al 1983) and,
most recently, Thomson and pure rotational Raman scattering.
A comprehensive discussion of filtered scattering-based diagnostics is
beyond the scope of this book. Instead, we will focus on three techniques,
ultraviolet filtered Rayleigh scattering, which has been used for temperature
field mapping in a glow discharge plasma, filtered rotational Raman
scattering, which can give extremely accurate rotational temperature, and
filtered Thomson scattering, for which electron density sensitivity as low as
order 5 x 1011 cm-3 and electron temperature sensitivity of '"'-'0.10 eV has
been demonstrated (Bakker and Kroesen 2000).
8.2.4.2 Filtered Rayleigh scattering temperature diagnostic
As can be seen from consideration of equations (7), (9), and (11), Rayleigh
scattering has the advantage that the signal depends, principally, upon the
isotropic part of the polarizability, aoo, as opposed to the anisotropic part
1'00 (rotational Raman scattering), or the polarizability derivatives, alO
and/or 1'10 (vibrational Raman scattering). Since the anisotropic part of
the polarizability is typically of order a few percent of the isotropic, and
the polarizability derivatives are only '"'-'0.1 % of the static polarizability,
Rayleigh scattering is inherently more intense, by two to three orders of
magnitude, than Raman scattering.
The traditional difficulty with Rayleigh scattering as a general quantitative
diagnostic technique has been, as stated above, the interference due to stray
scattered light. This has now been largely overcome through the use of vapor
filters, which enables the high inherent sensitivity of Rayleigh scattering to be
utilized in a variety of traditionally harsh environments. For example, iodine
vapor based filtered Rayleigh scattering has recently been utilized for two-
dimensional temperature field imaging in hydrogen-air and methane-air
flames (Elliott et aI200l). Sensitivity was sufficiently high that instantaneous
'single laser shot' images were obtained, in addition to mean field data. The
H2-air data were found to agree with coherent anti-Stokes Raman (CARS)
profiles to within '"'-'2%.
A particularly novel ultraviolet filtered Rayleigh temperature instrument
utilizes the third harmonic output of a single frequency, injection-seeded tita-
nium:sapphire laser at 253.7nm in combination with an atomic mercury
vapor filter (Miles et al 2001). This system, while somewhat more complex
than Nd:YAG-iodine systems, takes advantage of the sensitivity enhancement
realizable by shifting the measurement to shorter wavelengths. In addition to
the 4th power of frequency scaling of the scattering cross section, this system
takes advantage of the nearly ideal behavior of filters constructed from
atomic mercury vapor. In particular, exceedingly high extinction can be
--- Page 487 ---
472
Plasma Diagnostics
UVFRS Temperature Profile ofArP"sma, p=50 torr, i=20 mA
-0.3
o
0.3
0.6
0.9
1.2
1.5
1.8
radius (em)
Figure 8.2.12. Radial temperature profile from 50 torr argon glow discharge plasma
obtained by ultraviolet filtered Rayleigh scattering (UV FRS).
--- Page 488 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
473
plasmas. However, the temperature accuracy is somewhat limited by the
resulting relatively weak dependence of the filter transmission on tempera-
ture due to the inherent JT scaling of the Doppler line width (see equation
(41)). An alternative approach is based on rotational Raman scattering,
which has the advantage that the complete rotational distribution function
is determined so that the inherent temperature sensitivity is higher. The
disadvantage, as seen in table 8.2.1, is that the cross section for pure
rotational Raman scattering is a factor of rv 100 weaker than that for
Rayleigh scattering, and this lower integrated signal is also distributed
amongst the individual populated rotational levels. Fortunately laser and
CCD-based detector technology has developed substantially over the past
ten years so that high signal-to-noise spectra can be readily obtained. For
most practical purposes, however, the measurement is constrained to single
spatial points.
Figure 8.2.13 illustrates the enabling capability provided by filtered
scattering. Figure 8.2.13(a) is a scattering spectrum from a static cell of
500 torr of nitrogen at room temperature. The spectrum was obtained in
an apparatus similar to that illustrated in figure 8.2.6 except that an
injection-seeded, single frequency titantium: sapphire laser was employed,
in place of the Nd:YAG laser. The output energy was rv50mJ per pulse at
780 nm and the signal was integrated on a near-infrared sensitive ICCD
detector for 1 min. The cylindrical scattering volume has dimensions of
rvO.5cm (length) x 50 Il (diameter). The spectrum appears as a single central
component with apparent spectral line width of 0.20 nm FWHM, completely
determined by the resolution of the grating spectrometer, since the line width
of the laser is rv30MHz (or rv6 x 1O-5 nm). Figure 8.2.13(b) shows the
spectrum obtained under identical conditions except that a 5 cm path
length rubidium vapor filter, heated to 320 DC, has been inserted into the
detection path. Note that the intensity axis for the filtered spectrum is the
same as that for the unfiltered, so that the relative intensities are directly
comparable. It can be seen that the peak rotational Raman intensity is a
factor of rv800 weaker than the original elastic and Rayleigh scattering.
While difficult to determine directly from the figure, it has been shown that
the peak residual fractional intensity of the central components is
rv6 x 10-6 so that the peak rotational Raman intensity is now rv200 times
greater (rather than rv800 times weaker) than the peak central component
(Lee and Lempert 2002).
Figure 8.2.14 shows a spectrum (Stokes side only) similar to that of
figure 8.2.13(b) except that it was obtained in a CO laser optically pumped
N2/CO mixture at rv 1 bar total pressure, as described in section 7.2. Also
shown is a least squares fit to a simple sum of pressure broadened transitions
spectral model, including convolution with the instrumental spectral
response function. The inferred rotational temperature is 355 K with 20-
statistical uncertainty of ±7 K (Lee 2003).
--- Page 489 ---
474
Plasma Diagnostics
0.8
! 0.6
f
c
.!l
-= 0.4
0.2
O·~----~-------+----~~~----~------~----~
768
(a)
";'
~
1.6E-03
12E-03
t 8.0E-04
c i
4.01:-04
772
776
780
Wavelength (nm)
784
788
792
O.OEt-OO .,--=:o:::.:..c~r-----+----'1'L----r---~-'-'-'~
768
772
776
780
784
788
792
(b)
Wilvel8ngth (nm)
Figure 8.2.13. Illustration of rubidium vapor filtered pure rotational Raman spectra. (a)
From the static cell of pure N2 at 500 torr and 300 K, obtained without filtering; (b) is
identical except that a vapor filter was employed.
8.2.4.4 Filtered Thomson scattering
Thomson scattering is a well known technique for determination of spatially
resolved electron density and electron temperature (Hutchinson 1990, Evans
and Katzenstein 1969). Similar to Rayleigh scattering, Thomson scattering
results from laser-induced polarization of charged species, principally, at
--- Page 490 ---
25000
20000
I 15000
l:-
in
c
~ 10000
5000
Elastic and Inelastic Laser Scattering in Air Plasmas
475
-- Experimental
- - - - - Fit
O+----,----~----.---_.----,_--_,r_--_.----._--_,
781
782
783
784
785
786
787
788
789
790
Wavelength (nm)
Figure 8.2.14. Filtered pure rotational Raman spectrum of optically pumped N2/CO
mixture at I bar pressure and least squares spectral fit. Inferred temperature is 355 ± 7 K.
least in weakly ionized plasmas, from free electrons. While the cross section
for free electron scattering is approximately one hundred times greater than
that for Rayleigh scattering of common air species, the typically low free
electron number density in weakly ionized plasmas (rv 1 010_1013 cm -3) results
in extremely low scattering signals. Further aggravating this problem is the
fact that the electron temperature of molecular plasmas is typically quite
low (a few eV). The corresponding relatively low Doppler broadened line-
width complicates the use of grating-based instruments for spectral rejection
of stray scattering, although the reader is referred to a recently reported triple
grating instrument incorporating a physical central component blocking
mask in place of the normal slit separating the first two gratings (Noguchi
et aI2001).
Recently vapor filter-based Thomson scattering instruments, similar to
the filtered Rayleigh and Raman instruments discussed above, have been
developed and demonstrated in weakly ionized plasmas. The first reported
system utilized a commercial Nd:YAG pumped dye laser in combination
with a sodium vapor filter at rv580 nm (Bakker et a12000) and, shortly there-
after, independently developed rubidium vapor systems were also reported
(Miles et al 2001, Lee 2003). Compared to rubidium-based systems,
sodium systems have the advantage that the laser is relatively simple and is
readily available commercially. The sodium vapor filter, however, is some-
what more complex to fabricate.
--- Page 491 ---
476
Plasma Diagnostics
The theory of Thomson scattering is well known and will only be
summarized here. More detail can be found in Hutchinson (2000) and
Evans and Katzenstein (1969). We begin with the expression for the
Thomson scattering differential cross section for linearly polarized photons
given by
(49)
where ()z, again, is the angle between the incident light polarization vector
and the detection direction, and re is the classical electron radius equal to
2.818 x 1O-15 m. For
()::. = 90°, da/d!1 = r~ = 7.94 x 1O-26 cm2/sr and,
unlike the Rayleigh or Raman scattering cross section, is independent of
scattering frequency.
As discussed in section 8.2.2, the total scattering intensity is, in general,
the coherent sum of the individual contributions from each electron.
However, at low electron density, when the incident laser wavelength is
short compared to the average distance between electrons, the photon
'sees' the moving electrons as individual particles, randomly distributed in
the plasma. In this case, the phase from each scattering 'particle', as seen
at the detector, is completely uncorrelated from that of all other particles
and the total scattering intensity is just the summation of intensities from
each electron. This is called incoherent Thomson scattering. However,
if the average distance is short compared to the laser wavelength, the
phase differences are no longer random and individual scattering intensities
add in a coherent manner. Analogous to equation (39) we define a parameter
a as
1
a = tlkAD
(50)
where tlk, again, is the magnitude of the scattering wave vector (see equation
(36)), and An is the Debye length given by
An = (EokB Te)I/2 ~ 743( T(eV} )1/2 (cm)
e2ne
ne(cm 3)
(51 )
where ne and Te are the electron number density and temperature, respec-
tively. When a « 1, the effects of Coulomb interactions on the scattering
spectrum are negligible since the scattering length scale, 1/ tlk, is much
smaller than the Debye length, which is the characteristic length scale over
which significant net charge separation can exist. In this case, the scattering
is completely incoherent, provided that the electrons are randomly distrib-
uted in space. In the limit of a --+ 0, the scattering line shape is Gaussian,
corresponding to a Maxwellian velocity distribution of electrons, with ,,(,
--- Page 492 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
477
the half width at half maximum, for A = 780 nm, given by
A
')'(nm) =
780
C
2In(2)kTe .
() _ 2 57 ;-;p . ()
me
SIn"2-.
y Te sIn "2
where Te is in eV units and () is the scattering angle.
(52)
For 0: > 1, the incident wave interacts with the Debye-shielded charges
and the scattered spectrum depends on the collective behavior of groups of
charges. The Gaussian shape becomes distorted and a distinct symmetric
side-band peaks arise. Physically this coherent Thomson scattering is
analogous to Rayleigh/Brillouin scattering, mentioned in section 8.2.1,
except that the scattering originates from correlated fluctuations in charge
density due to what are known as 'ion-acoustic' waves. When the correlation
length for these fluctuations exceeds the reciprocal of the scattering wave
vector, the side-bands begin to appear.
A full treatment of coherent scattering is beyond the scope of this book.
However, a common approximation to the scattering spectrum is that given
by Salpeter (1960), which, strictly speaking, applies when Te/Ti, the ratio
of electron to ion temperatures, is approximately 1. In this case the total
scattering is the sum of components originating from correlated electron
motion and that from correlated ion motion, given by
2n1/ 2
2n1/ 2
(
0:2
)2
S(k, w) = ~
r a(xe) + ~
Z
1 + 0:2
r ,a(Xi)
(53)
where Xe = w/ka, a = (2kTe/me)I/2, Xi = w/kb, b = (2kTdmi)I/2, and
r a (Xe), r ,a(Xi) are identical line shape functions which are plotted in
figure 8.2.15 as a function of the non-dimensional parameter x. Note,
however, that for Te/Tj ~ 1 the ion average velocity b is much smaller
than a. This implies that, in frequency units, the ion scattering contribution
is located much closer to the un shifted laser frequency than the electron
contribution.
The significance of figure 8.2.15 is that, for 0: of order 1 or greater,
electron density can be determined from the shape of the Thomson scattering
spectrum, without the need for absolute scattering intensity calibration.
Figure 8.2.16 illustrates an example filtered Thomson spectrum of an atmos-
pheric pressure argon lamp, obtained with a rubidium vapor-titanium:
sapphire system very similar to that used to obtain the filtered rotational
Raman spectra in the previous section, except that a scanning mono-
chrometer and photomultiplier tube detector were used rather than an
ICCD (Miles 2001). This measurement is complicated by the limited optical
access, which was solved by employing a 1800 backscattering geometry. As
can be seen by comparison of the shape of the experimental and fit spectra
with those given in figure 8.2.15, the measurement clearly corresponds to
the onset of the incoherent scattering regime. The inferred electron density
--- Page 493 ---
478
Plasma Diagnostics
o
2
3
4
x
Figure 8.2.15. Saltpeter approximation to Thomson scattering profile as a function of the
non-dimensional parameter a.
600
'@'
10
400
:8-
(ij
c:
.gI
(J)
c: o
00 E
o
.s:::
I-
200
-200
Electron Number Density. 1.6*10
16/c.c
Electron temperature: 0.82 eV
2
3
4
•
Thomson Signal (data)
--ASE Sign .. ;
-------- Emission
5
6
Wavelength From CenterWavelength(nm)
7
Figure 8.2.16. Rubidium vapor filtered Thomson scattering spectrum from atmospheric
pressure argon lamp.
--- Page 494 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
479
0.006
~ 0.004
-
~
U)
c:
~ 0.002
Discharge Emission
/
Thomson Scattering Signal
I !
0+---~----4-----~---+----~--~
774
(a)
16000
12000
4000
776
778
780
782
Wavelength (nm)
784
786
o+-------~-------+------~------~
778
780
782
784
786
(b)
Wavelength (nm)
Figure 8.2.17. Rubidium vapor FTS spectrum from argon constricted glow discharge. (a)
Spectrum illustrates scattering signal relative to spontaneous emission detected despite
utilization of gated ICCD detector. (b) Least squares fit to incoherent scattering model.
and temperature are 1.61 x 1016 cm-3 and 0.82eV, respectfully, which from
equations (36), (50), and (51) corresponds to a value of a ~ 1.2.
As an example of filtered Thomson scattering at lower electron density
(Lee 2002), figure 8.2.17 shows a spectrum from a dc argon 'constricted' glow
discharge, obtained using the same instrument employed for the filtered
rotational Raman spectra in figures 8.2.13 and 8.2.14. The argon pressure
is 30 torr and the discharge current is 100 rnA. The constricted glow is rv 1-
2 mm in diameter and is stabilized by incorporation of a 500 n current
limiting ballast resistor in series with the dc discharge. Figure 8.2.l7(a)
shows the Thomson scattering signal superimposed upon the relatively
large argon spontaneous emission, which is many orders of magnitude
--- Page 495 ---
480
Plasma Diagnostics
more intense despite employing a gated ICCD camera. Figure 8.2.17(b) is a
least squares fit of the experimental spectrum in figure 8.2.17(b) to a simple
incoherent Thomson scattering model. The absolute intensity is calibrated
using a N2 pure rotational Raman spectrum similar to that of figure
8.2.13, taking advantage of the accurately known differential rotational
Raman cross section of 5.4 x 10-30 cm2/sr for the J = 6 ----; 8 transition
of nitrogen at 488.0nm (Penney et al 1974) (see table 8.2.1). From this
procedure the inferred values of electron number density and temperature
are (2.0 x 1013 ) ± (6 x 1011) cm-3 and 0.67 ± 0.03 eV, respectfully, corre-
sponding to a equal to ,,-,0.06. We note, however, that the inferred value of
electron temperature seems somewhat low for this plasma and may reflect
systematic error associated with spatial non-uniformity and/or temporal
unsteadiness, which was observed by the authors.
As noted previously, sensitivity of "-'lOll cm-3 has been reported for
the conceptually similar sodium vapor filter system (Bakker and Kroesen
2000).
8.2.5 Conclusions
Recent years have seen very significant advances in laser and detector
technology which has allowed spontaneous scattering-based methods to
evolve into routine diagnostic tools for molecular, non-equilibrium plasmas.
The emergence of novel diagnostic approaches, such as those based on
narrow pass band atomic and molecular vapor filters, has enabled several
orders of magnitude improvement in sensitivity, so that the techniques can
now be applied to weakly ionized plasmas, a feat which was previously
considered all but impossible. Clearly the future looks bright for the use of
elastic and inelastic laser light scattering techniques for plasma diagnostics.
References
Ahn T and Lempert W 2004 to be published
Asawaroengchai C and Rosenblatt G M 1980 J. Chern. Phys. 72 2664
Bakker L P and Kroesen G M 2000 J. Appl. Phys. 88 3899
Bakker L P, Freriks J M, deGroog F J and Kroesen G M W 2000 Rev. Sci. Instrurn. 71
2007
Berne B J and Pecora R 1976 Dynamic Light Scattering (New York: Wiley)
Bonamy L, Bonamy J, Robert D, Lavorel B, Saint-Loup R, Chaux J, Santos J and Berger
H 1988 J. Chern. Phys. 89 5568
Chu B 1991 Laser Light Scattering-Basic Principles and Practice 2nd edition (Boston:
Academic Press)
Clops R, Fink M, Varghese P L and Young D 2000 Appl. Spectroscopy 54 1391
Demtroder W 1998 Laser Spectroscopy 2nd edition (Berlin: Springer)
Dicke R H 1953 Phys. Rev. 89472
--- Page 496 ---
Elastic and Inelastic Laser Scattering in Air Plasmas
481
Drake M 1982 Optics Lett. 7440
Eckbreth, A C 1996 Laser Diagnosticsfor Combustion Temperature and Species 2nd edition
(Amsterdam: Gordon and Breach)
Elliott G S, Glumac N and Carter C D 2001 Measurement Science and Technology 12
452
Evans D K and Katzenstein J 1969 Rep. Progress in Phys. 32207
Galatry L 1961 Phys. Rev. 122 1281
Gallas J A 1980 Phys. Rev. A 21 1829
Gresillon D, Gemaux G, Cabrit B and Bonnet J P 1990 European J. Mechanics B 9
415
Hall R J, Verdieck J F and Eckbreth A C 1979 Optics Commun. 35 69
Hutchinson I H 1990 Principles of Plasma Diagnostics (Cambridge: Cambridge University
Press)
Indralingan R, Simeonsson J B, Petrucci G A, Smith B Wand Winefordner J D W 1991
Analytical Chern. 64 964
Lee W 2003 'Development of Raman and Thomson scattering diagnostics for study of
energy transfer in nonequilibrium molecular plasmas' PhD thesis, Ohio State
University, June
Lee Wand Lempert W R 2002 AIAA J. 40 2504
Lee W, Adamovich I V and Lempert W R 2001 J. Chern. Phys. 114 1178
Lempert W R, Rosasco G J and Hurst W S 1984 J. Chern. Phys. 81 4241
Long D A 2002 The Raman Effect (London: Wiley)
Macheret S 0, Ionikh Y Z, Chernysheva N V, Yalin A P, Martinelli L and Miles R B 2001
Phys. of Fluids 13 2693
Measurement Science and Technology 2001 12(4)
Miles R B, Lempert W R and Forkey J N 200la Measurement Science and Technology 12
Miles R B, Valin A P, Tang Zhen, Zaidi SHand Forkey J N 2001b Measurement Science
and Technology 12 442
Noguchi Y, Matsuoka A, Bowden M D, Uchino K and Muraoka K 2001 Japanese J. Appl.
Phys. 40 326
Ornstein L Sand Zernike F 1926 Phys. Z. 27 761
Pelletier M J 1992 Appl. Spectroscopy 46 395
Penney C M, St Peters R L and Lapp M 1974 J. Opt. Soc. America 64 712
Rahn L A and Palmer R E 1986 J. Opt. Soc. America B 3 1165
Rasetti F 1930 Nuovo Cimento 7 261
Regnier P Rand Taran J P E 1973 Appl. Phys. Letters 23 240
Rosasco G J, Lempert W, Hurst W S and Fein A 1983 in Spectral Line Shapes, vol 2
(Berlin: Walter de Gruyter) p 635
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--- Page 497 ---
482
Plasma Diagnostics
8.3 Electron Density Measurements by Millimeter Wave
Interferometry
8.3.1 Introduction
Interferometry is primarily a non-perturbing plasma density diagnostic
technique through the interaction of electromagnetic waves with plasma. It
measures the refractive and dissipative properties of the plasma which in
turn depend on the plasma properties including the plasma density and the
collision frequency. The interferometer works on the Mach-Zehnder
principle (Hutchinson 2002) in which the plasma is in one arm of the two-
beam interferometer. Phase and amplitude differences between the two
arms are the measures of the electron plasma density and the effective
collision frequency. However, the specific interferometric measurement tech-
nique depends on the choice of the wave frequency (w), relative to the plasma
(wp) and the effective collision (Veff) frequencies. If the probing wave
frequency is much greater than the plasma frequency and collision frequen-
cies (w» wp » Veff), the electromagnetic wave suffers almost little or no
attenuation as it travels through the plasma. Therefore, only phase change
data are needed for a density measurement. In this case a linear relationship
exists between the line-average plasma density and the phase shift for a
radially uniform plasma column (Wharton 1965). Also, if wp ;::;: w, in low
collisionality plasmas the ordinary wave mode (O-mode, EIIBo) is in cutoff
(Wharton 1965, Stix 1992) and interferometry data cannot be obtained.
On the other hand, for high-pressure discharges, where the collision
frequency can be higher than both the plasma and the millimeter wave
frequency (Veff;::;: w >=:::! wp), an electromagnetic wave propagating through
the plasma arm undergoes phase change as well as strong attenuation. The
wave attenuation is caused by the presence of high collisionality. In this
situation the plasma density has a complex dependence on phase change as
well as on amplitude change and, therefore, the correct evaluation of
plasma density can only be obtained if both phase-change and amplitude-
change data are used (Akhtar et al 2003). In addition, we experimentally
observe O-mode transmission for wp;::;: w as predicted by the theory
(Wharton 1965).
For atmospheric pressure air pressure discharges, the diagnostic tech-
nique will depend on the choice of the probing wave frequency. Choice of
a higher wave frequency such as a CO2 laser (w = 1.78 X 1014 Hz) satisfies
the condition (w » wp » Veff), where plasma density is linearly related to
phase change. However, the contribution of neutral particle density to the
refractive index and to the phase change which can be neglected for
microwave diagnostics becomes very important for infrared diagnostics
(Podgornyi 1971). A technique to infer phase contributions of the electrons
and those of heavy particles is described in detail in the section 8.4.
--- Page 498 ---
Electron Density Measurements
483
In this section we present a measurement and analysis technique where
both amplitude and phase change data are used simultaneously to uniquely
determine both plasma density and effective collision frequency. This treat-
ment does not limit the application of interferometry to the relative values
of collision frequency and hence can be used for measurements at both
low gas pressure (w » wp » Vefa and high gas pressure (Veff ;::: w, wp). The
analysis does not assume, ab initio, a particular value of the collision
frequency; rather, it calculates the collision frequency along with density
using the phase and amplitude change data.
8.3.2 Electromagnetic wave propagation in plasma
In order to calculate the refractive and dissipative properties of a collisional
plasma, we consider an electromagnetic wave propagating in an infinite,
uniform, collisional plasma. In this model, electron motion is induced by
the electromagnetic wave and the ions are assumed to form a stationary
background. The equation of motion for plasma electrons in the absence
of a magnetic field is written as (Wharton 1965)
mr = -eE -
veff mr
(1)
where r is the electron displacement vector, E is the electromagnetic field and
Veff is the effective collision frequency for momentum transfer. If the electric
field varies as exp(jwt), the displacement vector r is given as
eE
r - ---,-----,-
- mw(w - jVeff) .
(2)
Using the current density equation J = -enev = (J. E, the complex conduc-
tivity (J is given as
•
2 (
• )
_
.
neer
nee
Veff - JW
(J = (Jr + J(Jj = - -E = -
(2
2 ).
m
w + Veff
(3)
The complex relative dielectric constant for a linear medium is given by
(Wharton 1965)
(4)
where wp is the plasma frequency and co is the free space permittivity. The
complex refractive index (n) and the complex propagation b) constants are
c
.
1/2
n = - = f1r - JX = K,
,
v
'Y = a + j(3 = ::: (jf1) = ::: VK
c
c
(5)
where w/c is the phase velocity, a = xw/c is the attenuation constant in
Np/m and (3 = f1rw/ c is the phase constant in rad/m. The solution for the
--- Page 499 ---
484
Plasma Diagnostics
plane wave phase and attenuation constants in the plasma yields
W
1
wp
{ (
2)
f3p=c 21-w2+z1ff
+! [(1 _
W~
)2 + (
W~
Veff)2] 1/2}1/2
2
w2+v2
w2+v2
W
eff
eff
(6)
w{ l(
W~)
ap=c -2 l-w2+v~ff
+~ [(1 - w
2 ~
V~ffY + (w2 ~
V~ff V:ff Yf/2f/2
(7)
Assuming a plasma slab of uniform average density profile, the total change
in phase and amplitude for interferometric signal are given as
(8)
Here f30 and ao are the free space values and f3p and a p are the plasma
values. Simultaneous solution of plasma density and Veff are obtained from
experimentally measured 6.¢ and 6.A values.
The relative frequency condition w » wp » Veff is usually satisfied in
low pressure discharges (p :::; 10 mtorr), where most interferometry operates.
In this limiting case the phase constant and attenuation constant are given as
(
2 )1/2
(
2 )
W
wp
w
wp
f3p=c l-w2
~c 1-2w2
'
2 (
2 )-1/2
a = veffWp
1 _ wp
P
2w2c
w2
(9)
Therefore, in such low pressure discharges the electromagnetic wave suffers
almost little or no attenuation as it travels through the plasma and the
phase difference between the two arms with the plasma present to that
without the plasma is a measure of the plasma density. The plasma density
can be expressed in this limit for a uniform density profile using equation
(7) as
= ( 47rCEome) f 6.¢ = 2 073 f 6.¢
-3
ne
e2
d·
d
cm
.
(10)
Here the phase change is in degrees, the diameter in centimeters and wave
frequency is in S-I. It can be seen that a linear relationship exists between
the line-average plasma density and the phase shift for a radially uniform
plasma column. Also if wp ::::: wand w » Veff' the ordinary wave mode (0-
mode) is cut off and interferometry data cannot be obtained as shown in
the normalized plot (figure 8.3.1) of f3pc/w and apc/w versus wp/w using
equations (6) and (7). Also shown is the propagation of wave even when
wp > w, when the collision frequency is equal to the wave frequency. It
--- Page 500 ---
Electron Density Measurements
485
....
CCI.
]
II !
0.5
o
Z
0.2
0.6
0.8
1
1.2
1A
1.8
1.8
2
m /m
p
Figure 8.3.1. Plot of normalized propagation and attenuation constant for collision
frequency relative to the wave frequency.
should be noted here that this approximation depends on the values of wave
frequency relative to the collision and plasma frequencies. As described in
section 8.4, this approximation for highly collisional atmospheric pressure
air plasmas is obtained by choosing a CO2 laser wave frequency of
W = 1.78 X 1014 Hz.
For highly collisional plasmas at high gas pressures where the condition
Veff » W :::: wp is satisfied, the effect of collisions can be accounted for through
the phase function (Laroussi 1999). However, these approximations are
valid only for limiting cases. The propagation phase constant and the
corresponding density terms in this limiting case for a uniform plasma profile
are
W { 1
1 [
W~] 1/2}1 /2 W [
W~]
(3 =- -+- 1 +--
:::::- 1 +--
p
c
2
2
w2v~ff
C
8w2v~ff
(11 )
(f ~¢ )1/2
-5 (f ~¢ )1/2
-3
ne = 38.6veff ~ = 5.09 x 10
Veff -d-
cm.
(12)
However, for moderately to highly collisional plasma where relative frequency
condition Veff » W :::: wp is satisfied, wave undergoes a phase change as well as
amplitude change. Therefore, it is instructive to use both phase and amplitude
change data from equations (8) and (9) simultaneously to solve for both
--- Page 501 ---
486
Plasma Diagnostics
plasma density and effective collision frequency accurately. This treatment
does not limit the application of interferometry to the relative values of the
collision frequency and, hence, can be used for both low pressure discharges
(w » wp » Veff) and high pressure discharges (Veff » W, w p).
8.3.3 Plasma density determination
A 105 GHz quadrature mm wave interferometry system (QBY-lAlOUW,
Quinstar Technology) is used to measure the plasma density and the effective
collision frequency of an rf produced plasma. The rf source is a 10 kW solid-
state unit (Comdel Inc.) with variable duty cycle (90-10%), variable pulse
repetition frequency (lOOHz-lkHz) and very fast (IlS) turn-on/off time
and a 25 kW unit (Comdel Inc.). The rf power is coupled through a helical
antenna that excites the m = 0 TE (transverse electric) mode very efficiently
using a capacitive matching network. The helical antenna is a five-turn coil of
~ inch (6.35 mm) copper tube wound tightly over the 5 cm diameter Pyrex
plasma chamber. The coil is 10.0 cm long axially and has a 6 cm internal
diameter. Figure 8.3.2 shows the schematic of the experimental system.
The interferometer works by using an I-Q (in-phase and quadrature
phase) mixer to determine the phase and amplitude change of the 105 GHz
mm wave signal going through the plasma. The two outputs are transferred
to the computer through an oscilloscope with a GPIB interface and stored
Oscillosoope
Figure 8.3.2. Schematic of the laser-initiated and rf sustained plasma experiment.
--- Page 502 ---
Figure 8.3.3. Interferometer trace showing a nearly cut-off density of 9 x 1013 cm-3 in
10 torr argon plasma at 1.0 kW using a five turn helical antenna. The vacuum circle is
represented by the dotted line.
using a Labview program. In order to shield rf-sensitive Gunn and detector
diodes, the interferometer assembly is housed in a Faraday shielded
conducting box. In addition, cables with very high shielding (:2:90 dB,
Times Microwave Systems) have been used to reduce the noise level on the
interferometer signal. The interferometric trace shown in figure 8.3.3 illus-
trates that electromagnetic wave attenuates significantly for high-density
plasma even at low neutral pressures.
The results for the plasma density computation using equations (9), (10)
and (12) are presented in table 8.3.1, for typical phase change and collision
frequency data in an rf-produced air plasma at 10, 100, and 760 torr
maintained at different rf power. From the experimentally determined
phase and attenuation data, the plasma density and effective collision
Table 8.3.1. Air plasma density using a 105 GHz (w = 6.59 X 1011 S-I) interferometer for
5 cm diameter tube.
Air
,6.¢
Attenu-
Verr
ne (cm-3)
ne (cm-3)
ne (cm-3)
pressure (degrees) ation
(S-I)
Using phase
Collisionless Highly
(torr)
(dB)
and amplitude limit,
collisional
data,
equation
plasma,
equation (8)
(10)
equation (12)
10
200
0.94
2.1 x 1010
8.5 X 1012
8.7 X 1012
2.1 X 1012
100
239.2
16.31
2.91 x 1011
1.2 X 1013
1.03 X 1013
3.3 X 1013
760
16.7
5.8
1.6 x 1012
4.5 X 1012
7.25 X 1011
4.5 X 1013
760
25.1
14.79
2.5 x 1012
1.7 X 1013
1.1 X 1012
9.25 X 1013
760
50.4
35.3
2.8 x 1012
4.5 X 1013
2.2 X 1012
1.46 X 1014
--- Page 503 ---
488
Plasma Diagnostics
frequency are determined using the analysis presented above. The collision
frequency and phase change data are then used to calculate the limiting
plasma density using equations (10) and (12). The result clearly shows that
plasma density has a complex dependence on phase change and attenuation
data and, therefore, an accurate measurement of plasma density must involve
measurement of both phase change and amplitude change of the probing
electromagnetic wave.
At high gas pressure and collisionality, where optical diagnostics
including the Stark effect are used for plasma density and temperature,
characterizations require a minimum plasma density (ne ~ 1014_1015 jcm3)
(Griem 1997, Lochte-Holtgreven 1968). This simple diagnostic is particularly
valuable for collisional air plasmas of moderate densities (ne < 1014 cm -3) at
higher gas pressures where probe and optical emission diagnostics are not
suitable for density measurements.
References
Akhtar K, Scharer J, Tysk Sand Kho E 2003 'Plasma interferometry at high pressures'
Rev. Sci. Instrum. 74 996
Griem H R 1997 in Principles of Plasma Spectroscopy (Cambridge: Cambridge University
Press) p 258
Hutchinson I H 2002 Principles of Plasma Diagnostics (Cambridge: Cambridge University
Press) p 114
Laroussi M 1999 Int. J. Infrared and Millimeter Waves 201501
Lochte-Ho1tgreven W 1968 in Plasma Diagnostics ed. Lochte-Holtgreven W (Amsterdam:
North-Holland) p 186
Podgornyi I M 1971 in Topics in Plasma Diagnostics (New York: Plenum Press) p 141
Stix T H 1992 in Waves in Plasmas (New York: AlP Press, Springer)
Wharton C B 1965 in Plasma Diagnostic Techniques ed. Huddlestone R H and Leonard S L
(Academic Press, New York) p 477
8.4 Electron Density Measurement by Infrared Heterodyne
Interferometry
8.4.1
Introduction
The electron density, ne, determines to a large extent the refractive index of a
plasma. The complex refractive index in turn determines the phase shift and
the attenuation of electromagnetic waves of frequency w passing through the
plasma. Phase shift and attenuation can be measured by using inter-
ferometric techniques, and consequently allow us to obtain information on
the electron density.
--- Page 504 ---
Electron Density Measurement
489
10"
1017
Microwave
(105 GHz)
<? 1016
~
1()3
'-='
...
~ 1015
~
Ul
c:
Q)
Q)
...
C
:l
Ul
c: 1014
Ul
e
~
1)
11J2
a..
Q)
iIi 1013
1012
10'
102
103
104
Probing Frequency [GHz]
Figure 8.4.1. Probe frequency range (hashed area) for which an air plasma at room
temperature can be considered as transparent (w » wp) and lossless (w » lie). The collision
frequency, lie' for air was obtained from Raizer (1991).
The index of refraction of a plasma as shown in the next section is a
nonlinear function of probe wave frequency, w, the plasma frequency, wP'
which contains information on the electron density, and the collision
frequency, v. However, if the probing frequency is large compared to the
collision frequency (w ~ v) the attenuation of the probing beam can be
neglected. If, in addition, the probing frequency is large compared to the
plasma frequency (w ~ wp) the relation between phase shift and electron
density becomes linear, and the electron density can be obtained directly
from the phase shift. Figure 8.4.1 shows the frequency-dependent range of
electron densities and gas pressures for which the two conditions hold.
According to these conditions (probing frequency at least an order of
magnitude higher than plasma and collision frequency, respectively), a micro-
wave interferometer operating at a frequency of 105 GHz allows us to measure
electron densities up to 2 x 1012 cm -3 in a plasma with a heavy particle density
equivalent to 20 torr or less at room temperature. For high-pressure plasmas,
such as atmospheric pressure plasmas, the heavy particle density in plasmas
and consequently the electron collision frequency increases. Furthermore,
the plasma frequency in a high-pressure discharge may exceed the probing
frequency due to higher electron densities. To use an interferometric technique
in this case, and still stay in the range where the plasma can be considered
collisionless and transparent, requires an increase in probing frequency, e.g.
using a laser in the infrared range. For the interferometer operating at
10.6j..lm described in this chapter, an electron density of up to 1017 cm-3 can
--- Page 505 ---
490
Plasma Diagnostics
be measured and up to a heavy particle density equivalent to 6 atm at room
temperature, still satisfying the condition (w» wp ' v). Changes of the heavy
particle density in the plasma (caused by heating) contribute also to the
phase shift of the probing beam. While this contribution can be neglected
compared to the contribution of electrons for microwaves, it has a consider-
able contribution in the infrared and must be taken into account. A technique
how this can be accomplished is outlined in section 8.5.3.
8.4.2 Index of refraction
The index of refraction, N, for an optical thin plasma with a low degree
of ionization, contains contributions from electrons, ions and neutrals. The
refractive index can be obtained from the dispersion relation for a mono-
chromatic electromagnetic wave with an electric field E = Eo exp i(kr - wt)
in a conducting medium:
2
2.
w2
(
io-( w) )
k = €O€rJ-loJ-lrw + IJ-loJ-lrWo- = 2 J-lr€r 1 + --
C
W€O€r
(1)
with k being the wave number, W the angular frequency, 100 and lOr the
absolute and relative permittivity, J-lo and J-lp the absolute and relative
permeability, and c is the speed of light in vacuum. The conductivity 0-
depends on the wave frequency wand on the plasma frequency wp and is
given by the equation (Greiner 1986)
2
2
o-(w) =
Wp€o
=
e ne
(v - iw)
me(v - iw)
(2)
where v is the electron collision frequency, and e and me the electron charge
and mass, respectively. Substituting the conductivity in equation (1) by o-(w)
(equation (2)) the dispersion relation yields
k2 = w: J-lr€r (1 +
ie2~e. )).
C
W€O€rme V - lW
(3)
If the probe wave frequency w is much higher than the collision frequency v
in the plasma, equation (3) simplifies to
(4)
where N is the refractive index. The contribution of the heavy particles to the
refractive index can be expressed by the susceptibilities Ii (10 = 1 + Ii) of the
particles. The dispersion relation then reads
2
2
(
2)
2
W
2
W
~
k = 2 N = 2
J-lr
1 + liion + lineutral - 2
c
c
w
(5)
--- Page 506 ---
Electron Density Measurement
491
where "'ion and "'neutral are the contributions from ions and neutral particles,
respectively. They are small compared to 1. With f-lr = 1, and for wp/w
small compared to 1, the square root of the expression for N 2 can be
written as
(6)
The contribution to the refractive index from neutrals and ions, respectively,
can be described by (Duschin and Pawlitschenko 1973)
"'ion = N. _ 1 = (A. + B
ion )
nion
2
IOn
IOn). 2
nionO
(7a)
"'neutral _ N _ 1 - (A
+ Bneutral) nneutral
2
-
neutral
-
neutral
\ 2
/\
nneutralO
(7b)
where A and B are specific values for a specie, n is the density, no is the density
under standard temperature and pressure (STP) condition (T = 273 K,
p = 1 bar) and), is the wavelength. If A and B for ions are not available,
the values for neutrals can be used as a reasonably good approximation.
In the following, the notation for ions and neutrals are combined into one
expression for heavy particles. A and B for selected species are listed in
Duschin and Pawlitschenko (1973). Substituting all terms in equation (6)
yields
N - 1 _
i
).2 n + (A + ~) nheavy
-
2( c2meco4~)
e
).2
nheavyO
(8)
where nheavy and nheavyO are the heavy particle density (ions and neutrals) at a
given pressure and temperature and under STP condition (T = 273 K,
p = 1 bar), respectively. A and B are constants. The first term describes the
contribution of the electrons; the second term that of neutrals and ions.
Interferometry can be used to measure changes in the refractive index
and consequently provides information on changes of particle densities.
The phase shift Ail> (rad) of a laser beam with a wavelength), passing
through a non-homogeneous plasma of length L caused by changes in the
electron density and heavy particle density is
Ail> = 27r JL AN(l) dl
).
0
(9a)
--- Page 507 ---
492
Plasma Diagnostics
8.4.3 The infrared heterodyne interferometer
In order to measure the phase shift and consequently the refractive index, a
Mach-Zehnder heterodyne interferometer operating at a wavelength of
A = 10.6 11m (C02 laser) has been used (figure 8.4.2). The laser beam is sepa-
rated into two equal intensity beams by means of a beam splitter (ZnSe). One
beam passes through the plasma. In order to provide the required spatial
resolution it has been focused into the plasma, with a waist width of less
than 50 11m. The plasma can be shifted transverse to the beam direction,
allowing us to scan the plasma column. The second beam bypasses the
plasma and is frequency shifted by means of a 40 MHz acousto-optic
modulator. The beat frequency of 40 MHz, obtained by superimposing
both beams, is recorded by an infrared detector, which operates at room
temperature, and the signal is compared to the driver signal of the
acousto-optic modulator. The phase shift of the laser beam is transferred
to the high-frequency signal and is recorded by a phase detector, which
converts the phase shift into a voltage signal. The resolution of the inter-
ferometer is about 0.01°.
The characteristic of the phase detector is sinusoidal. In order to
calibrate the phase detector, the interferometer is tuned (manually) to a
phase of q> = 7r/2. The corresponding voltage V7r/ 2 at the phase detector is
recorded. For measurements, the interferometer is tuned to a phase of
q> = O. This is the preferred operation point q>o of the interferometer. The
relation between measured phase detector signal V( q» and the phase shift
~q> (rad) is given by the equation
. V(q»
~q> = q> -
q>o = arcsm -- - q>o.
(10)
V7r/ 2
Beamsplitter
Plasma
Beamsplitter
Driver
AOM
Amplifier
40 MHz t---+-I ....... _-,-_ ....
Figure 8.4.2. Schematics of the infrared heterodyne interferometer.
--- Page 508 ---
Electron Density Measurement
493
The correlation between phase detector signal and particle densities is
obtained by substituting the phase shift ~<I> in equation (9).
8.4.4 Application to atmospheric pressure air micro plasmas
The conditions for the validity of equation (10) are that (a) the electron
collision frequency is small compared to the probing wave frequency and
(b) the plasma frequency is small compared to the probing wave frequency.
The electron collision frequency for air, which is the gas of choice in our
experiments, at atmospheric pressure and 2000 K is 4.4 X 1011 Hz (Raizer
1991). For a probing frequency of w = 1.78 X 1014 Hz (C02 laser), the
expression for N (equation (8)) can be used to get information on the electron
density in air plasmas with heavy particle densities up to 1.4 X 1020 cm-3
(Vc/W < 0.1). The plasma frequency is determined by the electron density.
Assuming that wp / w needs to be less than 0.1 allows us to use equation (9)
to determine the index of refraction in ionized gases with electron densities
up to 1017 cm -3.
Since interferometry provides the total phase shift (~<I» of a plasma, the
contributions of electrons (~<I>e1) and heavy particles (~<I>heavy) need to be
separated. In general, separation of electron and heavy particle contribution
can be achieved by using a second wavelength, since the contribution of
electrons and heavy particles to the phase shift are frequency dependent
(equation (8)). This technique provides information on both the electron
density and the heavy particle density. However, under certain conditions
it is possible to separate the contribution due to electrons (in which we are
interested) using a single-wavelength interferometer. By using light sources
which provide long-wavelength radiation, the contribution of the heavy
particles to the refractive index can be disregarded compared to the contribu-
tion of electrons. These requirements are met for conditions of gas pressure
of several tens of torr (condition (a)) and an electron density corresponding
to a plasma frequency exceeding the probing frequency by a factor of 10
(condition (b)), using microwave interferometry. In this case, the measured
phase shift provides the electron density without the need to use a separate
diagnostic technique.
However, in order to probe micro plasmas with characteristic dimen-
sions in the lOO!lm range, light sources with wavelengths on the order of,
or less than, the characteristic dimensions need to be used, in order to provide
sufficient spatial resolution. This condition requires, for micro plasma studies,
the use of infrared light sources. For infrared illumination and with electron
densities on the order of 1013cm-3 in an atmospheric pressure gas, the contri-
bution to the phase shift caused by changes of the heavy particles may exceed
the one for electrons by more than one order of magnitude. In this case, the
different response time for electrons and heavy particles, when a pulsed voltage
is applied to the plasma, can be used to separate the phase shift signals ~<I>e1
--- Page 509 ---
494
Plasma Diagnostics
and ~<I>heavy. As discussed in the following, using a microplasma in atmos-
pheric air as an example, this method, which is based on the difference in
time constants, can be used in diagnosing dc plasmas (Leipold et al 2000)
and pulsed plasmas (Leipold et aI2002).
8.4.5 Measurement of the electron density in dc plasmas
The plasma that was studied is a cylindrically symmetric atmospheric
pressure air glow discharge column with a diameter of less than 1 mm and
a column length of 2mm (figure 8.4.3) (Stark and Schoenbach 1999). The
spatial resolution requires a wavelength in the infrared range. For this appli-
cation a CO2 laser with an operation wavelength of A = 10.6 J..lm has been
chosen. According to Raizer (1991), the collision frequency of an atmos-
pheric pressure air plasma for a heavy particle density of 3.6 x 1018 cm-3 is
v = 4.4 X 1011 Hz. Since this frequency is small compared to the laser
frequency of w = 1.78 X 1014 Hz, the simplified equation (4) can be used
for the evaluation of the refractive index. An electron density of 1017 cm-3
corresponds to a plasma frequency of 1.78 x 1013 Hz. Consequently, the
ratio w~/w2 is approximately 1 %.
The electrode system consists of a microhollow cathode electrode system
(MHCD) and an additional (third) electrode with a variable distance from
the MHCD. The electrode configuration and the plasma are shown in
figure 8.4.3. The MHCD geometry consists of two plane-parallel electrodes
with a centered hole in each electrode. The electrodes are made of 100 J..lm
thick molybdenum foils, and the cathode and anode hole size of the
plasma cathode is also 100 J..lm. The dielectric between the electrodes is
Figure 8.4.3. Atmospheric pressure air discharge.
--- Page 510 ---
Electron Density Measurement
495
alumina (A120 3, 96% purity) of 250 J..lm thickness. The anode of the micro-
hollow cathode geometry is connected to ground. The third electrode,
placed at a distance of 2 mm in front of the plasma cathode, is also made
of molybdenum and biased positively. The MHdc sustained glow discharge
(MCS) is operated in dc mode, optional with a superimposed high voltage
pulse (1600 V) of 10 ns duration. The time between pulses was on the order
of 100 ms. The discharge dc current was limited by means of a ballast resistor
of 300 kO to 16 rnA. The measurements were performed in air at a pressure
of 1000 mbar and a humidity of 30%.
For a wavelength of A = 10.6 J..lm and in air plasma (A = 2.871 x 10-4,
B = 1.63 X 10-18 m2 (Duschin and Pawlitschenko 1973), the ratio of the
contributions to the phase shift due to electrons and heavy particles is
given by
D.<I>el
= 4.5 x 103
D.ne
D. <I>heavy
D.nheavy
(11 )
The change of the heavy particle density D.nheavy after switching the discharge
on is estimated using the ideal gas law. The gas temperature varies between
room temperature when the plasma is off and a temperature of 2000 K when
the plasma is on (Leipold et al 2000). For a pressure of 1 atm,
D.nheavy = 2.3 x 1019 cm-3 at room temperature. With electron densities at
ignition of 1013 to 1015 cm -3, the ratio D.<I>el/ D.<I>heavy varies between 0.002
and 0.2. This means that the major phase shift during the switching transient
is still determined by the change of the heavy particle density. In spite of this
difficulty, the phase signal can be separated due to the different response
times for electrons and heavy particles to rapid changes in voltage (ignition
of the plasma) (Leipold et al 2000). Figure 8.4.3 shows the phase shift
signal through the center of the discharge. The fast rising part of the phase
shift signal is assumed to be due to the change of the electron density; the
slowly rising part is assumed to be due to the change of the heavy particle
density caused by gas heating.
The electron density decays to the dc value after breakdown, while the
gas heats up causing a change in the heavy particle density. At ignition,
the electron density provides a significant fraction of the total phase shift
d<I>ed (d<I>el + d<I>heavy) (at t = 5 ms in figure 8.4.4). When the plasma
approaches steady state conditions, the fraction decreases to approximately
0.2% (at t> lOms in figure 8.4.4). Therefore, the total amplitude of the
phase shift for t> 10ms after ignition can be considered the change in the
heavy particle density with an error of less than 1 %. In order to obtain
information on the electron density during this steady-state phase, where
the electron density is identical to that for a dc plasma, the plasma was
operated in a pulsed mode with time intervals between pulses continuously
decreasing. The electron density can be measured during the re-ignition
phase of each pulse. By reducing the time between pulses towards zero, the
--- Page 511 ---
496
Plasma Diagnostics
0.02
3
-- Phase Shift
--- Voltage
0.00
2
-:i
.!!!. -0.02
b.cJ>hooYy
~
!E
Q)
~
Cl
(J)
J!!
Sl -0.04
~
til
~
--..--
a..
-------
0
-0.06
b.cJ> ..
Off-Time
-0.08
--L........J...~..---J.-.-..J..~~~-'-...l-
-1
0
2
4
6
8
10
Time [ms]
Figure 8.4.4. Phase shift signal through the center of the discharge for an off-time of 4 ms.
electron densities measured for the re-ignition transients approach that of the
dc plasma.
This method has been applied to the discharge in atmospheric pressure
air. The discharge was operated in the dc mode and was switched off for a
specific time (off-time) (figure 8.4.4). The electron density in the center of
the discharge at ignition calculated from the phase shift ~lI>el and the
change of the heavy particle density in the center of the discharge calculated
from the phase shift ~lI>heavy were recorded and plotted versus various off-
times (figure 8.4.5). Shortening the off-time allowed us to approach the dc
mode (off-time=O). The extrapolation of the curve in figure 8.4.5 towards
zero change in heavy particle density provides the electron density in the
dc case.
In order to obtain absolute electron densities, the radial profile of the
electron density needs to be known. In side-on measurements the plasma
was shifted in the z direction (insert, figure 8.4.6) through the laser beam,
providing the spatial phase shift distribution. In order to obtain the radial
phase shift distribution, a parabolic radial profile was assumed and the
corresponding spatial profile was calculated. The parameters for the para-
bolic profile were varied for best fit of measured and calculated relative
spatial profiles. The results are shown in figure 8.4.6. This relative radial
profile was used for calculating the electron density from the spatially
resolved phase shift. The same procedure was applied for the relative
radial heavy particle density profile. The gas temperature was obtained by
--- Page 512 ---
Electron Density Measurement
497
<1 5 1.8
CD -0 1.6
~
•
Experimental Results
-- Best Fit
~
1.4
o Extrapolation
c:::
1.2
0
B 1.0
c:::
~
~ 0.8
is
~
0.6
c:::
~ 0.4
Q)
0.2
1:5
1::
m 0.0
a..
~
m -0.2
Q)
1012
:::c
1013
1014
1015
1016
Electron Density on Axis [cm-1
Figure 8.4.5. Electron density in the center of the plasma column after breakdown
versus the change in heavy particle density. The numbers along the curve indicate the
corresponding off-times.
1.1
1.0
;' 0.9
.!!. 0.8
!E:
J:: 0.7
en
Q) 0.6
III
m
J:: 0.5
a..
"C
.~ 0.4
iii E 0.3
0
Z 0.2
0.1
0.0
0.0
•
Calculation --
(parabolic profile -.med)
Experimental Results
•
•
0.1
0.2
0.3
0.4
Distance from Center z [mm]
Figure 8.4.6. Spatial distribution of the measured and computed relative phase shift t.<I>el'
--- Page 513 ---
498
Plasma Diagnostics
1.2
1.2
-- Electron Density
1.0
-
- Gas Temperature
1.0
07
/{\\
'""':"
5
/
\
:::J
...
0.8
0.8 .!!.
~o
/
\
~
~
:::J
~ 0.6
/
\
-
0.6
~
CD
c:
/
'\.
a.
CD
E
c
c:
/
"
{!!.
e 0.4 ;,.--/
........
0.4
fd
~
(!)
W
0.2
0.2
0.0
0.0
2
1
0
1
2
Distance from Center [mm]
Figure 8.4.7. Radial distribution of electron density and relative gas temperature
distribution.
using the information on the heavy particle density and assuming that the
ideal gas law holds. The electron density distribution and the relative
radial temperature profile are shown in figure 8.4.7.
8.4.5 Measurement of the electron density in pulsed operation
A strong increase in electron density can be obtained by applying a voltage
pulse with a duration on the order of, or less than, the dielectric relaxation
time of the electrons to a dc plasma. The application of such a pulsed voltage
causes a shift in the electron energy distribution function to higher energies,
with negligible gas heating, thus reducing the probability for glow-to-arc
transition. The shift in electron energy causes a temporary increase of the
ionization rate and consequently an increase in electron density (Stark and
Schoenbach 2001).
The same atmospheric pressure air plasma, which was studied in the
dc mode, was pulsed with a 10 ns pulse of 1.6 kV amplitude (superimposed
to the dc voltage), and the electron density was measured by means of
infrared heterodyne interferometry. The change of the electron density
caused by the high voltage pulse can, in this case, be obtained directly
from the phase shift signal. The spatially resolved relative phase shift
~<[>(z) for various times after pulse application is shown in figure 8.4.8.
The spatial profiles could be fit to a Gaussian profile with a width of
--- Page 514 ---
Electron Density Measurement
499
•
22ns
-::i
.!. 2
~
~
.&:
en
II)
(I)
CII
.&:
a...
-0.1
0.0
0.1
Distance z from Center [mm]
Figure 8.4.8. Spatially resolved relative phase shift ~<I>(z) for various times after pulse
application.
a = 0.056 mm. This means that the radial profile is also Gaussian with
the same width. Figure 8.4.8 shows the temporally resolved electron density
in the center of the discharge obtained from the measured phase shift signal.
The voltage pulse causes an increase in electron density to at least
2.8 x 1015 cm-3. The electron density decays hyperbolically to its dc value.
The temporal resolution of this diagnostic method, with the currently used
experimental set-up, is 20 ns.
..-o
~2
(I)
c:
CD o
c:
~
iIi
o
-
Measuntment
............ Hyperbolic Approxlmallon
50
100
150
200
Time [ns]
Figure 8.4.9. Temporally resolved electron density in the center (z = 0) of the discharge.
--- Page 515 ---
500
Plasma Diagnostics
8.4.6 Conclusions
Interferometry is widely used for measurements of the electron density in
partially ionized plasmas (Hutchinson 1991). The choice of the probing
frequency is determined by the range of electron density, by the gas pressure,
and the desired spatial resolution. Increasing the probing frequency allows us
to increase the range of electron densities and gas pressures, utilizing only the
measured phase shift of the probe radiation passing through the plasma.
Also, the spatial resolution, which is limited to dimensions on the order of
the probe radiation wavelength, is improved by increasing the probing
frequency, The drawback of moving from e.g. the microwave into the
infrared or even visible frequency range is the increasing effect of heavy
particles, atom, molecules, and ions on the index of refraction, which
determines the phase shift. For instance, for electron densities of 1013 cm-3
in an atmospheric pressure air plasma the contribution of the heavy particles
to the measured phase shift is four orders of magnitude higher than that of
the electrons. Extracting information on the electron component therefore
requires phase shift measurements at two wavelengths.
A method which does not require a second probing radiation source but
still allows us to obtain electron density distributions and gas temperature
distributions in atmospheric pressure air plasmas with a spatial resolution
of better than 100)lm (using a CO2 laser) makes use of the different time
constant for ionizing and for heating of the weakly ionized plasma (Leipold
et aI2000). This concept is not only applicable to pulsed plasmas, but also to
dc plasmas. In the second case, the dc electron density is obtained by a
process where the dc discharge is turned on and off with increasingly smaller
intervals between the on-state. Extrapolating the electron densities to the
case of diminishing time between off- and on-states allows us to obtain the
steady-state (dc) value of the electron density and the gas temperature.
Although the diagnostic procedure for obtaining electron densities with
this method in weakly ionized atmospheric pressure air or other high-
pressure plasmas is rather complex, the high spatial resolution makes this
diagnostic technique attractive for the study of microdischarges or micro-
structures in large-volume high-pressure discharges.
References
Duschin L A and Pawlitschenko 0 S 1973 Plasmadiagnostik mit Lasern (Berlin: Akademie-
Verlag) p 8
Greiner W 1986 Theoretische Physik (Frankfurt am Main: Verlag Harri Deutsch)
Hutchinson I H 1991 Principles of plasma diagnostics (Cambridge: Cambridge University
Press)
Leipold F, Mohamed A-A and Schoenbach K H 2001 'Electron temperature measure-
ments in pulsed atmospheric pressure plasmas' Bull. APS GEe 46(6) 22
--- Page 516 ---
Plasma Emission Spectroscopy
501
Leipold F, Mohamed A-A Hand Schoenbach K H 2002 'High electron density, atmos-
pheric pressure air glow discharges' Conf. Record, 25th lnt. Power Modulator
Symp. and 2002 High Voltage Workshop, Hollywood, CA, June, p 130
Leipold F, Stark R H, EI-Habachi A and Schoenbach K H 2000 'Electron density
measurements in an atmospheric pressure air plasma by means of lR heterodyne
interferometry' J. Phys. D: Appl. Phys. 33 2268
Raizer Y P 1991 Gas Discharge Physics 2nd edition (Berlin: Springer)
Stark R Hand Schoenbach K H 1999 'Direct current glow discharges in atmospheric air'
Appl. Phys. Lett. 74 3770
Stark R Hand Schoenbach K H 2001 'Electron heating in atmospheric pressure glow
discharges' J. Appl. Phys. 89 3568
8.5 Plasma Emission Spectroscopy in Atmospheric Pressure Air
Plasmas
8.5.1
Temperature measurement
Atmospheric pressure air plasmas are often thought to be in local thermody-
namic equilibrium (L TE) owing to fast interspecies collisional exchange at
high pressure. This assumption cannot be relied upon, particularly with
respect to optical diagnostics. Velocity gradients in flowing plasmas, or
elevated electron temperatures created by electrical discharges, or both can
result in significant departures from chemical and thermal equilibrium.
This section reviews diagnostic techniques based on optical emission spectro-
scopy (OES) that we have found useful for making temperature measure-
ments in atmospheric pressure air plasmas, under conditions ranging from
thermal and chemical equilibrium to thermochemical non-equilibrium.
8.5.1.1
Temperature measurements in LTE air plasmas
For plasmas in LTE, a single temperature characterizes all internal energy
modes (vibrational, rotational, and electronic). This temperature can be
determined from the absolute intensity of any atomic or molecular feature,
or from Boltzmann plots of vibrational or rotational population distri-
butions. Such measurements were made (Laux 1993) at 1 cm downstream
of the exit of a 50kW, rf (4 MHz), inductively coupled plasma torch
operating with atmospheric pressure air (Figure 8.5.1). Because the plasma
flows at relatively low velocity (10 m/s) in the field-free region between the
induction coil and the nozzle exit where the measurements are made, all
chemical reactions equilibrate well before reaching the nozzle exit and there-
fore the plasma is close to LTE. The experimental set-up for OES measure-
ments, shown in Figure 8.5.2, comprises a 0.75 m monochromator fitted with
--- Page 517 ---
502
Plasma Diagnostics
Nozzle
(5 em diameter)
Quartz Tube
RF Coil
Gas Injectors
(a)
(b)
Figure 8.5.1. (a) Schematic of 50 kW plasma torch head. The distance from the top of the
induction coil to the nozzle exit is about 10 cm. (b) Torch head and L TE air plasma plume.
either a 2000 x 800 pixel CCD camera (SPEX TE2000) or a photomultiplier
tube (Hamamatsu Rl104). Absolute calibrations of the spectral intensities
between 200 and 800 nm are made with radiance standards including a
calibrated tungsten strip lamp for the range 350-800 nm and a I kW dc
argon arc-jet in the range 200-400 nm. The optical train is constructed
with spherical mirrors or MgF2 lenses to minimize chromatic aberrations
in the ultraviolet. Long-pass filters inserted in the optical train eliminate
second- and higher-order light. Figure 8.5.3 shows the radial temperature
profiles obtained after the emission measurements are inverted with the
Axial and Lateral4-Mirror
Collecting Lens
1ational
(f= 50 em)
Trans
System
with Iris (F/60)
\
If@t::
.•• ::.:::::::;:~:,:." ... :
..
SPEX Model 750 M
0.75 m Monochromator
Grating: 1200 glmm,
blazed at 500 nm
TE Cooled CCD Camera
___ -' SPEX Model TE2000
Data Acquisition
Computer
2oo0x8oo pixels
15x15 J.tlTl
Figure 8.5.2. Experimental set-up for emission diagnostics.
TAFA Model 66
Plasma Torch
LEPEL Model T -50
RF Generator
4MHz,50kW
--- Page 518 ---
8000
7000
g
1
6000
~5000
4000
0
Plasma Emission Spectroscopy
503
r·· ......... .
I ... ·.
...• , T_
",T_,
--.- T"TE (0 line at TI7.3 run)
-o-Tm( 0 lioeat615.7 om)
--.-T, ........ (from 0 lines)
-+- T LTE ( N line at 746.8 run)
Air Flow Rate: 95 l/min
Plate Power. 69 kW
0.5
1.0
1.5
2.0
Radius(cm)
Figure 8.5.3. Measured electronic, vibrational, and rotational temperature profiles in L TE
alr.
help of the Abel transform. The 'L TE' and Boltzmann temperatures shown
in figure 8.5.3 are based on the absolute and relative intensities, respectively,
of various atomic lines of oxygen and nitrogen. The rotational temperature
profiles are obtained from measurements of the NO,!, (0,1) band shape,
using the technique proposed by Gomes et al (1992). The vibrational
temperature profile is measured from the relative intensities of the (0,0)
and (2,1) bandheads of Nt B-X (first negative band system) at 391.4nm
and 356.4 nm, respectively. As can be seen from figure 8.5.3, the measured
vibrational, rotational, and electronic temperature profiles are to within
experimental uncertainty in good agreement with one another, as expected
because the plasma is close to L TE.
8.5.1.2
Temperature measurements in non-equilibrium air plasmas
In non-equilibrium plasmas, the techniques described in the foregoing para-
graph may not provide reliable information about the gas temperature
because the population distribution of internal energy states tends to
depart from Boltzmann distributions at the gas temperature. This behavior
is especially the case for the electronic and vibrational population distribu-
tions, but the rotational populations tend to follow a Boltzmann distribution
at the gas temperature owing to fast rotational relaxation at atmospheric
pressure. Thus, the gas temperature can often be inferred from the intensity
distribution of rotational lines. Various transitions of O2, N2, Nt, and NO
(dry air) and OR (humid air) can be used, depending on the level of
plasma excitation. To illustrate the variety of emission bands available for
OES in air plasmas, figure 8.5.4 shows the ultraviolet emission spectra of
equilibrium, atmospheric pressure air with a water vapor mole fraction of
1.3%, for temperatures in the range 3000-8000K. Below about 5000K,
bands of NO, OR, and O2 dominate the spectrum. The second positive
--- Page 519 ---
504
Plasma Diagnostics
9000K
<lI" .... U • .," '""1- 5000 K
250
300
350
400
450
A [nm]
Figure 8.5.4. Ultraviolet emission spectra of L TE air at atmospheric pressure with 1.3 %
mole fraction of water vapor. These simulations were performed with SPECAIR, using
a trapezoidal instrumental broadening function of base 0.66 nm and top 0.22 nm.
band system of N2 (C-B), the first negative band system of Nt (B-X), and
atomic lines of ° and N appear at higher temperatures. Emission features
similar to those of figure 8.5.4 can also be observed in low-temperature
non-equilibrium air plasmas such as those produced by electrical discharges.
All spectral simulations presented here have been made with the
SPECAIR code (Laux 2002), which was developed on the basis of the NonE-
Quilibrium Air Radiation code (NEQAIR) of Park (1985). The current
version of SPECAIR models 37 molecular transitions of NO, N2, Nt, °2,
CN, OH, NH, Cb and CO, as well as atomic lines of N, 0, and C. The
model provides accurate simulations of the absolute spectral emission and
absorption of air from 80 nm to 5.5 ~m. As an illustration of the capabilities
of the model, figure 8.5.5 shows a comparison between absolute intensity
emission spectra measured in L TE air and SPECAIR predictions. The
plasma conditions are those corresponding to the temperature profile of
figure 8.5.3, with a peak centerline temperature of approximately 7500 K.
As can be seen in figure 8.5.5, the model is able to reproduce the line positions
and intensities of the experimental spectra.
We now turn our attention to techniques best suited for quantitative
temperature measurements in discharges. The rotational temperature can
be measured from N2 C-B rotational lines. At even higher temperatures or
higher electric field excitation, many molecular transitions appear in the spec-
trum and an accurate spectroscopic model is required to extract individual
lines of a particular system. For these conditions, we recently proposed a
--- Page 520 ---
2
0
180
4 •
1
3
.s
2
~
.!II
~
0
300
1.0
0.5
0
400
0.15
0.10
0.05
0
500
0.5
"iii 0.4
N~ 0.3
3: .s 0.2
~ 0.1
I 0
J
soo
10
0.1
0.Q1
700
Figure 8.5.5.
~7500K.
Plasma Emission Spectroscopy
505
--Measured
-SPECAIR
NO p. y. 5 ••• p'. y'
N.C-B
O2 SchJrnann-Runge
190
200
210
220
230
240
250
280
'00
280
290
300
CNB-X
N;B-X
N. C-B. N; B-X --Measured
--SPECAIR
310
320
330
340
350
380
370
380
390
400
N, C-B. N; B-X
-Measured
--SPECAIR
410
420
430
440
450
480
470
480
490
500
0
-Measured
N.B-A.O.N -SPECAIR
510
520
530
540
550
560
570
580
590
SOO
0
N,B-A.O. N
--Measured
-SPECAIR
_J. .....
l.
J.
I
I
.....
--
IV'
.~
610
620
630
640
650
660
670
660
690
700
--Measured
0
N
-SPECAIR
710
720
730
740
750
760
770
780
Wavelength (nm)
Comparison between SPECAIR and measured spectrum of L TE air at
--- Page 521 ---
506
Plasma Diagnostics
method based on selected rotational lines of Nt B-X (Laux et aI200l). The
N2 and Nt rotational temperature measurement techniques are described in
the following subsections.
8.5.2 NO A-X and N2 C-B rotational temperature measurements
At higher temperatures or higher plasma excitation the rotational tempera-
ture can be measured from the NO A-X (NO ,,-band system) or N2 C-B
(N2 second positive band system) transitions.
The NO " technique proposed by Gomes et al (1992) is based on the
width of the NO A-X (0,1) band. Gomes et al (1992) used the technique to
measure rotational temperature of atmospheric pressure air plasmas in the
range 3000-5000 K with a quoted accuracy of 250 K.
Spectroscopic measurements of the N2 C-B transition are illustrated in
figure 8.5.6, which shows a spectrum obtained in the dc glow discharge
experiments of Yu et al (2002) (see figure 8.5.7). The slit function is a
trapezoid of base 0.66 nm and top 0.22 nm. The rotational temperature
was determined by fitting the spectrum with SPECAIR in the range 260-
382 nm. This spectral range corresponds to the Av = -2 vibrational
sequence of the N2 C-B band system. The best-fit SPECAIR spectrum
yields a rotational temperature of 2200 ± 50 K. The best-fit vibrational
temperature, based on the relative intensities of the (0,2), (1,3), (2,4), and
(3,5) vibrational bands of the N2 C-B system, is 3400 ± 50 K. It should be
noted that the vibrational temperature of the C state of N2 is not necessarily
the same as the vibrational temperature of the ground state of N2.
Figure 8.5.8 shows the predicted spectral width of the (0,2) band of N2
C-B at 20 and 40% of the peak intensity, as a function of the rotational
30 -- Experimental Spectrum
(0,2)
---- Spectroscopic Model SPECAIR
Best fit
(1,3)
'"":' 20
T =2200±50K
:;
r
~
.~
!: ] 10
0
360
364
368
372
376
380
384
388
Wavelength (run)
Figure 8.5.6. Measured N2 C-B spectrum in the atmospheric pressure air glow discharge
(conditions of figure 8.5.7). SPECAIR best-fit provides a rotational temperature of
22DD± SDK.
--- Page 522 ---
Plasma Emission Spectroscopy
507
Figure 8.5.7. DC glow discharge experiments in air at 2200 K and I atm. The glow
discharge is created by applying a dc electric field (1.4 kV fcm 200 rnA) in fast flowing
(~450mfs) low-temperature (2200K) atmospheric pressure air. Interelectrode distance =
3.5 cm. The measured electron number density in the bright central region of the discharge
is approximately 101Z cm-3.
4
....... 3
E
5
:5
~ 2
e
W2O%/
/_./
.... ....... -.
._._e
./
;:;
/
~ 1.0 'e-ooo-K---------,
oj!! 0.8
5000K
.S!
.E 0.6
i .!l! 0.4 LL'-"","",=-:C
(U § 0.2
z
OU-__ ~
__ ~~~
__
L-~
376
377
378
379
380
381
O~~
__ ~~~~~~~~~_~~(~n~m~)~~~--u
2000
4000
6000
Rotational Temperature (K)
Figure 8.5.8. Spectral widths of the Nz C-B (0,2) band at 20 and 40% of the peak's height.
These calculations were made with SPECAIR assuming a trapezoidal slit function of base
0.66 and top 0.22 nm. The inset shows the (0,2) band spectra at various rotational tempera-
tures, normalized to the intensity of the peak at 380.4 nm.
--- Page 523 ---
508
Plasma Diagnostics
temperature. These simulations were made with SPECAIR, assuming a
trapezoidal slit function of base 0.66 and top 0.22 nm. The width curves
provide a quick way to estimate the rotational temperature if a full spectral
model is not available.
8.5.3 Nt B-X rotational temperature measurements
At higher excitation levels, the NO 'Y and N2 second positive band systems
suffer from increasing overlap by transitions from higher NO states (NO 8,
10), and by the O2 Schumann-Runge, CN violet, and Nt first negative
band systems. The Nt first negative band system (B-X transition) can be
used to measure the rotational temperature, provided that an accurate spec-
troscopic model is available to extract Nt lines from the encroaching lines of
CN and N2 that emit in the same spectral range. The modeling is complicated
by perturbations that affect the positions, intensities, and splittings of the Nt
lines. Recent spectroscopic analyses by Michaud et al (2000) have provided
accurate spectroscopic constants, incorporated in SPECAIR, that enable
the precise identification of high rotational lines of Nt B-X up to rotational
quantum numbers of about 100. We showed in (Laux et al 2001) that the
group of rotational lines R(70) and P(97) at 375.95 nm is well isolated
from lines of other transitions, and that the intensity of these two lines
relative to the bandhead of the Nt B-X (0,0) band at 391.55 nm is a very
sensitive function of the rotational temperature. This technique was
successfully applied to rotational temperature measurements in a non-
equilibrium recombining nitrogen/argon plasma (Laux et al 2001). The
rotational temperature was measured to be 4850 ± 100 K, an accuracy far
superior to that of other Nt rotational temperature measurement techniques
(see for instance the review by Scott et al (1998».
8.5.4 Measurements of electron number density by optical emission
spectroscopy
In plasmas with electron number densities greater than ",5 x 1013 cm-3,
spatially and temporally resolved electron number density measurements
can be made by emission spectroscopy from the lineshape of the Balmer {3
transition (4-2) of atomic hydrogen at 486.1 nm. This technique requires
the addition to the plasma of a small amount (typically 1 or 2% mole
fraction) of hydrogen, which may come either from dissociated water
vapor in humid air or from premixing H2 into the air stream. For detection
by emission spectroscopy, the population of the n = 4 electronic state of
atomic hydrogen must be high enough for the H,a line to be distinguishable
from underlying air plasma emission (mostly coming from the B-A or
second positive band system of N2). This condition is usually fulfilled in
equilibrium air plasmas with temperatures greater than 4000 K, or in
--- Page 524 ---
Plasma Emission Spectroscopy
509
non-equilibrium plasmas with sufficient excitation of hydrogen electronic
states.
8.5.4.1
Broadening coefficients of the H(3 lineshape
The lineshape of the H(3 transition is determined by Lorentzian (Stark, van
der Waals, resonance, natural) and Gaussian (Doppler, instrumental) broad-
ening mechanisms that result in a Voigt profile. The Lorentzian half-width at
half-maximum (HWHM) is the sum of the Lorentzian HWHMs. The
Gaussian HWHM is the square root of the sum of the squared Gaussian
HWHMs. If monochromator slits of equal width are used, the instrumental
slit function is well approximated by a Gaussian profile. Numerical
expressions for the Stark, van der Waals, resonance, Doppler, and natural
HWHMs are derived below for the case of an air plasma with a small
amount (a few percent) of hydrogen.
8.5.4.2
Stark broadening
Stark broadening results from Coulomb interactions between the radiating
species (here the hydrogen atom) and the charged particles present in the
plasma. Both ions and electrons induce Stark broadening, but electrons
are responsible for the major part because of their higher relative velocities.
The lineshape can be approximated by a Lorentzian function except at the
linecenter where electrostatic interactions with ions cause a dip. The Stark
broadening width is mostly a function of the free electron concentration,
and a weak function of the temperature. The Stark HWHM expression
given in table 8.5.1 corresponds to a fit of the widths listed by Gigosos and
Cardefioso (1996) for electron densities between 1014 and 4 x 1017 cm-3
and for reduced masses between 0.9 and 1.0, which covers all perturbers
present in the air plasma except hydrogen. (The Stark broadening of
hydrogen by hydrogen ions is neglected here because we assume that the
mole fraction of hydrogen is less than a few percent.) The fit is within
±5% of the values of Gigosos and Cardefioso for temperatures up to
10000 K, ± 13 % up to 20000 K, and ±20% up to 40000 K. If better
precision is needed, the actual values of Gigosos and Cardefioso can be
substituted for the present fit.
Table 8.5.1. Half widths at half maximum (in nm) for the Hf3 line at 486.132 nm. P is the
pressure in atm, T the gas temperature in Kelvin, ne the electron number
density in cm -\ and X H the mole fraction of hydrogen atoms .
.6.>"Stark
.6.>"resonance
.6.>"van der Waals
.6.>"natural
.6.>"Doppler
30.2XH (P/T)
1.8P/To.7
3.1 X 10-5
--- Page 525 ---
510
Plasma Diagnostics
8.5.4.3 Reonance broadening
Resonance broadening is caused by collisions between 'like' particles (e.g.
two hydrogen atoms) where the perturber's initial state is connected by an
allowed transition to the upper or lower state of the radiative transition
under consideration. Typically, the three perturbing transitions that must
be considered are g ---+ I, g ---+ U, and I ---+ U, where g stands for the ground
electronic state, and I and U for the lower and upper states of the radiative
transition. Using the expression given by Griem (1964, p 97), we obtain
3e2
.6.·\esonance = 16 2
2
7r comec
'-v--"
6.72 x 1O-16 m-2
Using
the
constants
of Wiese
et
al (1966)
(Aul = 486.132nm,
Alg = 121.567 nm, Aug = 97.2537 nm, gu = 32, gg = 2, gl = 8, fgl = 0.4162,
fgu = 0.02899, fiu = 0.1193), we obtain the resonance HWHM listed in
table 8.5.1.
8.5.4.4
Van der Waals broadening
Van der Waals broadening is caused by collisions with neutral perturbers
that do not share a resonant transition with the radiating particle. Griem
(1964, p 99) gives the following expression for a radiating species r colliding
with a perturber p:
~ ul
a
3/5
A2 (97r1i5 R2 )2/5_
.6.Avan derWaals ~ 2c
16m~E]
Vrp Np
(2)
where vrp is the relative speed of the radiating atom and the perturber, Ep is
the energy of the first excited state of the perturber connected with its ground
state by an allowed transition, Np is the number density of the perturber, and
the matrix element R~ is equal to
2" ~ 1
EH
[
z2 EH
]
Ra ~ 2. E _ E
5 E
_ E + 1 - 31a (ta + 1) .
00
a
00
a
(3)
In equation (3), EH and Eoo are the ionization energies of the hydrogen atom
and of the radiating atom, respectively, Ea is the term energy of the upper
state of the line, la its orbital quantum number, and z is the number of
effective charges (z = 1 for a neutral emitter, z = 2 for a singly ionized
emitter, ... ). For H(3, we have EH = Eoo = 13.6eV, Ea = 12.75eV, and
z = 1. The H(3 transition is a multiplet of seven lines (see table 8.5.2)
--- Page 526 ---
Plasma Emission Spectroscopy
511
Table 8.5.2. Components of the H(J transition multiplet and their properties.
Wavelength
Aul
Upper level
Lower level
gu
gl
Relative
air (nm)
(S-I)
configuration
configuration
intensity
(% of total
H(J emission)
486.12785
1.718 x 107
4d2D3/2
2p 2 P?/2
4
2
25.5
486.12869
9.668 x 106
4p211/2
2s2 SI/2
4
2
14.4
486.12883
8.593 x 105
4s 2 SI/2
2 20
p PI /2
2
2
0.6
486.12977
9.668 x 106
4p 2 P?/2
2S2 SI/2
2
2
7.2
486.13614
2.062 x 107
4d2D5/2
2p211/2
6
4
45.9
486.13650
3.437 x 106
4d2D3/2
2p211/2
4
4
5.1
486.13748
1.719 x 106
4s 2 SI/2
2p211/2
2
4
1.3
originating from upper states 4s, 4p, and 4d of orbital angular momenta
la = 0, 1, and 2. For la = 0, 1, and 2, (R~)2/5 takes the values 13.3, 12.9,
and 12.0, respectively. As listed in table 8.5.2, the components issued from
the 4s, 4p, and 4d states represent 1.9, 21.6, and 76.5% of the total H{3
emission, respectively. We use ~ese percentages as weighting factors to
determine an average value of (R;)2/5 = 12.2.
The relative velocity term v;P of equation can be related to the mean
speed as follows:
v;j,5 = (4/1f)2/1Or(9/5)(vrp)3/5 9:! 0.98(vrp )3/5 = 0.98(8kT /1fm;p)3/1O
(4)
where m;p is the reduced mass of the radiating species and its perturber.
Summing over all perturbers present in the plasma, and introducing the
mole fraction Xp of perturber p, equation becomes
,2 (9 1052 )2/5
[
X
]
~
Aut
1fn Ra
3/10 P
p
.6.Avan derWaals ~ 0.98 2c
16m3 E2
(8kT /1f)
kT L
4/5(. )3/10 .
e p
p
Ep
mrp
(5)
In air plasmas, 0, N, N2, °2, and NO represent 98% of the chemical
equilibrium composition for temperatures up to 10 000 K. We computed
the equilibrium mole fractions of these five species up to 10 000 K and
combined them with the Ep and m;p values listed in table 8.5.3 in order to
evaluate the summation term in equation (5). The value of this term is
found to be approximately constant over the entire temperature range and
equal to 0.151 ± 0.007. The final expression for the van der Waals HWHM
of H{3 in air plasmas with a small amount of hydrogen added is given in
table 8.5.1.
--- Page 527 ---
512
Plasma Diagnostics
Table 8.5.3. Constants needed in equation (5) when the radiating species is a hydrogen atom.
Perturber
M;p
Transition issued from the first
Ep
M;p -0.3 E;;0.8
(g/mole)
excited state optically connected to
(eY)
(g/mol)-0.3 ey-O.8
the ground state
0
0.94
3sO _
3p
9.5
0.17
N
0.93
4p _
4sO
10.3
0.16
O2
0.97
B3z:,;; -
X 3z:,i (Schumann-Runge)
6.2
0.23
N2
0.97
bIng _
X lz:,; (Birge-Hopfield I)
12.6
0.13
NO
0.97
A 2z:,+ _
X 2n (gamma)
5.5
0.26
8.5.4.5 Doppler broadening
For a collection of emitters with a Maxwellian velocity distribution
(characterized by a temperature Th ), Doppler broadening results in a
Gaussian lineshape with HWHM given by Griem (1964, p. 101):
1
D.ADoppler = "2 AUl
The Doppler HWHM of H(3 is given in table 8.5.1.
8.5.4.6 Natural broadening
Natural broadening gives a Lorentzian line profile of HWHM:
D.Anatural = :;~ (L Aun + LAin)
n<u
n<l
(6)
(7)
where the two summation terms represent the inverses of the transition's upper
and lower level lifetimes, which can be calculated using the Einstein A
coefficients tabulated by Wiese et al (1966). As can be seen from table 8.5.1,
natural broadening is negligible in comparison with the other mechanisms.
8.5.4.7 Fine structure effects
Because of fine structure spin-orbit splitting in the upper and lower levels,
the H(3 transition is in fact a multiplet of seven lines (see table 8.5.2). The
resulting lineshape is the sum of these lines, each of which can be calculated
with the broadening widths listed in table 8.5.1. The resulting lineshape will
be close to a Voigt profile only if the HWHM of each line is much greater
than 0.005 nm, half the separation between the extreme lines. The technique
presented below should only be used when the measured HWHM is much
greater than 0.005 nm. This condition is fulfilled in most situations of
practical interest.
--- Page 528 ---
Plasma Emission Spectroscopy
513
8.5.4.8
Electron density measurements in equilibrium air plasmas
We have applied the H(3 line shape technique to the measurement of electron
densities in the LTE air plasma characterized in section 8.5.1.1. Application
of the technique to non-equilibrium air and nitrogen plasmas (Gessman et al
1997) will be discussed in section 8.5.2.3. We used a 0.75m monochromator
with a l200-groove/mm grating, and entrance and exit slits of 20/lm. The
instrumental slit function was approximately Gaussian with HWHM of
0.011 nm. A small amount of H2 (1.7% mole fraction) was premixed with
air before injection into the plasma torch. The spatial resolution of the
measurements, determined by the width of the entrance slit and the magnifi-
cation of the optical train, was approximately 0.13 mm.
Figure 8.5.9 shows the line-of-sight emission spectrum measured along
the plasma diameter and the 'background' emission spectrum, mainly due
to the N2 B 3IIg-A 3~~ first positive system, which was measured after
switching off the hydrogen flow. Without hydrogen, the measured plasma
temperature is lower by approximately 200 K. The torch power was slightly
readjusted in order to return to the same temperature conditions by matching
the intensity of the background spectral features away from the H(3 line-
center. Figure 8.5.10 shows the H(3 line shape obtained by subtracting the
background signal from the total spectrum. The measured lineshape is
well fitted with a Voigt profile of HWHM = 0.11 nm. From the HWHMs
of the various broadening mechanisms shown in figure 8.5.11, we infer
an electron number density of approximately 1.0 x 1015 cm-3. Because
the intensity of the H(3 line is proportional to the population of hydrogen
in excited state n = 4, which is a strong function of the temperature
0.30
0.25
~ 0.20
j 0.15
v:l
~ 0.10
0.05
OLL~~~~~~~~~~~~~~~~~
485.4
485.6
485.8
486.0
486.2
486.4
486.6
Wavelength (nm)
Figure 8.5.9. Typical emission scan of the H(J line. The underlying emission features are
mostly from the N2 first positive band system.
--- Page 529 ---
514
Plasma Diagnostics
0.20
~ 0.15
1 0.10
tI.l
~ 0.05
•
Measured H~ Line
--Voigt Fit
485.4
485.6
485.8
486.0
486.2
486.4
486.6
Wavelength (run)
Figure 8.5.10. H(3lineshape obtained from the difference of the two signals shown in figure
8.5.9, and Voigt fit.
(n4 rv exp[-150000jT]), the 1ine-of-sight-integrated emission scan is domi-
nated by emission from the hot central plasma core and therefore provides
a good approximation of the electron density at the plasma center.
Radial profiles of electron density were obtained by an Abel inversion.
To this end, we scanned the H(3lineshape at 25 lateral locations along chords
of the 5 cm diameter plasma. Figure 8.5.12 shows the radial profile of elec-
tron densities determined from the Abel-inverted lineshapes. Figure 8.5.12
also shows the radial profile of chemical equilibrium electron densities
0.1
~
'-'
~ ~~=====~~
0.01
van der Waals
Electron Number Density (em
o3)
Figure 8.5.11. H(3 lineshape broadening as a function of the electron number density in
L TE air at atmospheric pressure. (Instrumental HWHM = 0.011 nm.) The resonance
broadening HWHM is less than 2 x 10-4 nm for present experimental conditions.
--- Page 530 ---
1.4x1015
1.2x1015
1.0x1015
.......
'7
8.0x1014
.[
.,
C
6.0x1014
4.0x1014
2.0x1014
0
0
0.5
Plasma Emission Spectroscopy
515
-
Measured Electron Density
····0···· Equilibrium Electron Density
··'O···"O·"a ... CJ. ••
1.0
1.5
Radial position (em)
2.0
Figure 8.5.12. Measured (solid line) and equilibrium (dashes) electron number density
profiles.
based on the measured LTE temperature of the oxygen line at 777.3 nm.
Because the plasma is expected to be in LTE, the excellent agreement
between the two profiles provides validation of the technique. Note that
the electron density of 1.0 x 1015 cm-3 determined from the line-of-sight
integrated lineshape is consistent with the Abel-inverted electron densities
in the central core of the plasma.
Additional examples of electron density measurements based on the
Stark-broadened H(3 lineshape can be found in chapter 7. In the latter
case (figure 8.5.13), the instrumental broadening was minimized using
the narrowest possible slit width (HWHM = 0.0 15 nm), but still was not
1.4 ,,-------------------,
~
1.2
1.0
=
~ 0.8
.j 0.6
]
0.4
0.2
-- H, + Background
. . . . .. Background
FWHM = 0.058 nm
• H, (x4)
-- Voigt Fit (x4)
o r-,w.,.""""'o.¥¥l¥-~~___;~6f!'o~~i""_'"IC'Y!
••
u.,..!;::~
969.5
970.0
970.5
971.0
971.5
Wavelength [run]
Figure 8.5.13. H{3lineshape in a low temperature (~4500K) LTE air plasma. Here the H{3
lineshape was measured in second order to reduce the instrumental broadening width by a
factor of 2 relative to other broadening widths.
--- Page 531 ---
516
Plasma Diagnostics
negligible relative to Stark broadening. To improve the sensitivity we meas-
ured the spectrum in the second order of the grating. This had the effect of
reducing instrumental broadening by a factor of 2 with respect to the other
broadening widths. CCD averaging times of 10 s were employed. The
inferred number density of 5 x 1013 cm-3 represents a lower detection limit
in equilibrium air plasmas because the intensity of the H(3 line becomes
very weak relative to the underlying N2 first positive signal.
Acknowledgments
The authors acknowledge Richard G. Gessman, Denis Packan and Lan Yu
for their contributions to the work presented here.
References
Copeland R A and Crosley DR 1984 'Rotational level dependence of electronic quenching
of hydroxyl OH (A 2E+, v' = 0)' Chern. Phys. Lett. 107(3) 295-300
Gessman R J 2000 'An experimental investigation of the effects of chemical and ioniza-
tional nonequilibrium in recombining air plasmas' Mechanical Engineering
Dept., Stanford University, Stanford, CA
Gessman R J , Laux C 0 and Kruger C H 1997 'Experimental study of kinetic mechanisms
of recombining atmospheric pressure air plasmas' 28th AIAA Plasmadynamics and
Lasers Conference, Atlanta, GA
Gigosos M A and Cardefioso V 1996 'New plasma diagnosis tables of hydrogen Stark
broadening including ion dynamics' J. Phys. B: At. Mol. Opt. Phys. 294795--4838
Gomes A M, Bacri J, Sarrette J P and Salon J 1992 'Measurement of heavy particle
temperature in a rf air discharge at atmospheric pressure from the numerical simu-
lation of the NO, system' J. Analytical Atomic Spectroscopy 7 1103-1109
Griem H R 1964 Plasma Spectroscopy (New York: McGraw-Hill)
Laux C 0 1993 'Optical diagnostics and radiative emission of air plasmas' PhD thesis,
HTGL Report 288, Mechanical Engineering, Stanford University, Stanford, CA
Laux C 0 2002 'Radiation and nonequilibrium collisional-radiative models' Special
Course on Physico-Chemical Modeling of High Enthalpy and Plasma Flows ed.
Fletcher T M D and Sharma S (Rhode-Saint-Genese, Belgium: von Karman
Institute)
Laux, CO, Gessman R J, Kruger C H, Roux F, Michaud F and Davis S P 2001 'Rotational
temperature measurements in air and nitrogen plasmas using the first negative
system of Nt' JQSRT 68(4) 473--482
Levin D A, Laux C 0 and Kruger C H 1999 'A general model for the spectral radiation
calculation of OH in the ultraviolet' JQSRT 61(3) 377-392
Michaud F, Roux F, Davis S P, Nguyen A-D and Laux C 0 2000 'High resolution Fourier
spectrometry of the 14Nt ion' J. Molec. Spectrosc. 203 1-8
Park C 1985 Nonequilibrium Air Radiation (NEQAIR) Program: User's Manual (Moffett
Field, CA: NASA-Ames Research Center)
Scott C D, Blackwell H E, Arepalli Sand Akundi M A 1998 'Techniques for estimating
rotational and vibrational temperatures in nitrogen arcjet flow' J. Thermophys.
Heat Transfer 12(4) 457--464
--- Page 532 ---
Ion Concentration Measurements
517
Wiese W L, Smith M Wand Glennon B M 1966 Atomic Transition Probabilities vol I.
Hydrogen through Neon (Washington, DC: US National Bureau of Standards,
National Standard Reference Series 1 153.
Yu L, Laux C 0, Packan D M and Kruger C H 2002 'Direct-current glow discharges in
atmospheric pressure air plasmas' J. Appl. Phys. 91(5) 2678-2686.
8.6 Ion Concentration Measurements by Cavity Ring-Down
Spectroscopy
8.6.1
Introduction
Measurements of ion and/or electron number density are needed to charac-
terize experiments and validate models for atmospheric pressure air and
nitrogen plasmas. As discussed in the previous section (on Stark broad-
ening), the electron density can be measured from the H(3 Stark-broadened
line shape down to densities of about 5 x 1013 cm -3. Below this value, more
sensitive measurement techniques are required. Physical probes tend to
disturb the plasma (see section 8.1), and techniques such as EM wave
interferometry (see section 8.3) does not readily provide results with high
spatial resolution. Optical techniques that measure ion concentrations are
widely used. Of these, emission provides information only on excited species,
fluorescence suffers from quenching effects, predissociation, and optical
interference that complicate interpretation, and absorption often lacks
sensitivity.
Cavity ring-down spectroscopy (CRDS), on the other hand, is a sensi-
tive line-of-sight averaged laser absorption technique that has been used to
measure species concentrations in low-pressure plasmas (Grange on et al
1999, Quandt et a11999, Booth et a12000, Kessels et a12001, Schwabedissen
et aI2001). The CRDS is additionally attractive as it enables measurements
of the speciation of the ion density. In particular, the Nt ion has been studied
in low-pressure hollow cathode sources (Kotterer et al 1996, Aldener et al
2000). In this section, we describe the use of CRDS to measure ion concen-
trations in atmospheric pressure discharges. By implementing CRDS in its
'standard' (i.e. not temporally-resolved) form, we perform spatially resolved
(by Abel inversion) ion concentration measurements. We also develop a
temporally resolved variant of CRDS, which we used to study ion recombi-
nation in pulsed plasmas. Measurements have been performed in both air
and nitrogen plasmas. In nitrogen plasmas, Nt tends to the dominant ion
at temperatures below ",6000 K, and under these conditions the CRDS
measurement of Nt enables one of the most direct measurements of electron
--- Page 533 ---
518
Plasma Diagnostics
number density. In LTE air, the concentration of Nt may be linked to that
of electrons through chemical equilibrium relations. In non-equilibrium
plasmas, a collisional-radiative model may be used to relate the ion and
electron concentrations. Alternatively, CRDS measurements of the NO+
ion can be performed.
An overview of the CRDS technique is provided in section 8.6.2,
including a discussion of temporally resolved CRDS. Section 8.6.3 presents
the experimental schemes used for spatially resolved ion concentration
measurements of the Nt ion in dc discharges, as well as temporally resolved
Nt ion concentration measurements in pulsed discharges. Measurement
results, and discussion, are provided. To aid in interpreting results, a col-
lisional radiative (CR) model is used to compute population fractions and
to relate the measured ion concentrations to electron number densities.
The inferred electron number density profiles are compared with electrical
measurements, and the non-equilibrium nature of the plasma is discussed.
Section 8.6.4 discusses CRDS measurements of the NO+ ion in air plasmas.
The experimental scheme and a discussion of results are presented. Conclu-
sions are provided in section 8.6.5.
8.6.2 Cavity ring-down spectroscopy
Cavity ring-down spectroscopy (CRDS) has become a widely used method in
absorption spectroscopy owing primarily to its high sensitivity. Detailed
reviews of the technique may be found in Busch and Busch (1999) and
Berden et al (2000). Essentially, a laser beam is coupled into a high-finesse
optical cavity containing a sample, where it passes many times between the
mirrors. As the light bounces back and forth inside the cavity, its intensity
decays (rings down) owing to sample absorption, particle scattering loss
(generally negligible), and mirror transmission loss. A photodetector is
used to measure the ring-down signal, which is fitted to yield the sample
loss. The technique affords high sensitivity owing to a combination of long
effective path length and insensitivity to laser energy fluctuations. Therefore,
CRDS is well suited to the detection of trace species in plasmas. Under
appropriate conditions, the laser lineshape may be neglected, and the ring-
down signal S(t) decays exponentially (Zalicki and Zare 1995, Yalin et al
2002) as:
S(t) = So exp[-tIT],
C
liT = I [/absk(vd + (1 - R)]
(1)
where T is the lie time of the decay (termed the ring-down time), c is the
speed of light, I is the cavity length, labs is the absorber column length,
k(v) is the absorption coefficient, VL is the laser frequency, and 1 - R is the
effective mirror loss (including scattering and all other empty-cavity
losses). Generally, the measured ring-down signal is fit with an exponential,
--- Page 534 ---
Ion Concentration Measurements
519
and the ring-down time T is extracted. Combining T with the ring-down time
TO measured with the laser detuned from the absorption feature allows a
determination of the sample absorbance, and hence absorption coefficient:
abs == labsk(vd = -
- -
-
.
I [1 1 ]
C
T
TO
(2)
We minimize any potential laser lineshape dependence by tuning the laser
frequency across an absorption line, and measuring the frequency-integrated
absorption coefficient (Yalin et al 2002). This approach is equivalent to
assuming that laser broadening causes an effective absorption lineshape,
found as the convolution of the symmetric laser lineshape with the actual
absorption lineshape (Yalin et al 2002).
The prior discussion of CRDS has implicitly assumed that the sample
concentration (and associated absorption loss) is independent of time, as
would be the case in a dc discharge. In pulsed discharges, however, the ion
concentration varies over the duration of the optical ring-down (decay of
light in the cavity). A more complex approach is then required. It might be
tempting to consider using lower reflectivity mirrors with shorter ring-
down times so that the losses may be treated as constant over the ring-
down, but the sensitivity of such an approach is inferior (Zalicki et al
1995). Although a number of kinetics studies have been performed with
CRDS, nearly all of these experiments study processes that are slow
compared to experimental ring-down times. An exception is the work of
Brown et al (2000), who perform gas-phase measurements in cases where
the populations do change over the duration of the ring-down. We follow
a related approach to measure ion recombination in a plasma over time-
scales comparable to the ring-down time (microseconds). For the case of a
time-dependent absorption, the ring-down signal S(t) may be written as
(Brown et al 2000)
S(t) = So exp [ -7 [t k(v, t)labs dt + (1 - R)t]]
(3)
where the absorption coefficient now has a time dependence. Rearranging
equation leads to an expression for the absorbance as a function of time:
abs(t) == k(v, t)labs = -~ :t [In (S12)] - (1 - R).
(4)
The derivative (local slope) of the logarithm of the ring-down signal is
proportional to the loss (sample plus empty cavity) at that time. To obtain
time-dependent concentrations directly, Brown et al analyzed their data
with this method. We choose to follow an alternative approach in which
the ring-down signal is divided into a series of time-windows, each of
which is fit to an exponential decay (ring-down time). We believe that this
approach is less noisy because it avoids differentiation.
--- Page 535 ---
520
Plasma Diagnostics
8.6.3 Nt measurements
8.6.3.1
Atmospheric pressure discharge
We have developed a compact atmospheric pressure plasma source for diag-
nostic development. The discharge may be operated with both nitrogen and
air. A photograph of the nitrogen discharge with a schematic representation
of the ring-down cavity is shown in figure 8.6.1. Nitrogen is injected through
a flow straightener and passes through the discharge region with a velocity of
about 20 cm/s. The discharge is formed between a pair of platinum pins
(separation 0.85 cm) that are vertically mounted on water-cooled stainless-
steel tubes. The discharge is maintained by a dc current supply
(imax = 250 rnA) in a ballasted circuit (Rb = 9.35 kD). The pins are brought
together to ignite the discharge, and are then separated using a translation
stage. The position of the discharge is observed to be stable and reproducible.
The discharge is contained within a Plexiglas cylinder (diameter 12 inches,
30.5 cm) that isolates it from room air disturbances. Small holes allow
weak ventilation by a fan through the top to avoid accumulation of undesir-
able by-products of the discharge (such as ozone or oxides of nitrogen), and
enable passage of the laser beam through the discharge. A second translation
stage is used to displace the entire discharge cylinder relative to the optical
axis in order to obtain spatial profiles.
To explore the repetitively pulsed approaches, we connect a high-voltage
pulser in parallel to the dc discharge circuit. The pulser is capacitively coupled
to the discharge so that it is isolated from the dc supply. The dc field serves to
give a baseline of ionization and to heat the gas. We operate the high-voltage
pulser (pulse width", 10 ns, pulse voltage ",8 kV) at 10 Hz so that it may be
synchronized relative to the laser. At this repetition rate the plasma equili-
brates between high-voltage pulses so that the behavior during and following
each pulse is not affected by the presence of other pulses.
8.6.3.2 CRDS measurements
We study the Nt ion by probing the (0,0) band of its first negative band
system (B2I.:~_X2I.:i) in the vicinity of 391 nm. We select this spectral
. OPO laser
PMT
R=O.9998+
to data
acquisition
Figure 8.6.1. Photograph of the atmospheric pressure nitrogen discharge and schematic
diagram of the ring-down cavity. Electrode separation: 0.85 cm. Discharge current:
l87mA.
--- Page 536 ---
Ion Concentration Measurements
521
Computer
HR - High reflector
IF - I nterference Filter
D - Diffuser
Ir - Iris
L - Lens
Plasma
IF
D
HR
HR
Ir
L
Figure 8.6.2. Schematic diagram of CRDS set-up. The ring-down cavity has a length of
0.75 m and uses 0.5 m radius of curvature mirrors. An OPO is used as the light source,
and a photomultiplier tube (PMT) detects the light exiting the cavity.
feature because it is comparatively strong and optically accessible. The
optical layout is shown in figure 8.6.2. An OPO system (doubled idler) is
used as the light source (repetition rate = 10 Hz, pulse width'" 7 ns, pulse
energy ",3 mJ, linewidth ",0.14cm-1). The output from the OPO passes
through a Glan-Taylor polarizer to attenuate the energy, and several
irises. Typically, about 100 IlJ per pulse is incident on the back face of the
entrance ring-down mirror. The irises serve to select a relatively uniform
portion of the beam and to reduce the beam diameter prior to cavity injection
(from ",6 mm to less than < '" 1 mm). Because the OPO laser light is multi-
mode, and spectrally broad (",4GHz) compared to the cavity free spectral
range (",400 MHz), we operate in a continuum-mode (meaning that many
transverse cavity-modes are active) rather than attempting to mode-match
the beam to the cavity. Exciting many transverse cavity-modes has the
advantage that mode-beating effects (interferences between different cavity
modes causing temporal 'beats' in the ring-down signals) are minimized.
Also, by averaging multiple ring-down signals, the mode-beating effects are
further reduced (averaged away) and a near single-exponential decay is
obtained (see Berden et al 2000 and references therein). We use a linear
cavity of 75 cm length with 50 cm radius-of-curvature (ROC) mirrors from
Research Electro-Optics. The spatial resolution and selection of cavity
geometry are discussed below. The ring-down signal is collected behind the
output mirror with a fast photomultiplier tube (Hamamatsu-Rl104),
which we filter against the pump laser and other luminosity with two
narrow-band interference filters (CVI-FlO-390-4-l). The PMT signals are
passed to a digitizing oscilloscope (HP 5451OA, 250 MHz analog bandwidth,
--- Page 537 ---
522
Plasma Diagnostics
8-bit vertical resolution) and are read to computer with custom data acquisi-
tion software. In a typical ring-down spectrum, 16 or 32 decay curves are
averaged at each wavelength (to minimize mode-beating effects), and the
resulting waveform is fitted with an exponential to yield the ring-down
time T. For the dc measurements, the portion of the ring-down signal used
in the fit is that in between 90 and 10% of the peak (initial) signal amplitude.
The detuned ring-down time TO is determined with the laser tuned off the
absorption features. Spectral scans use a step-size of 0.001 nm. When
performing spatial scans, we use step-sizes of 0.2 mm.
The CRDS set-up used for the pulsed measurements differs only in terms
of data fitting and timing. Because sample absorption loss is no longer
constant during the measurement, the time dependent equation (4) is used
to fit the data. Rather than computing derivatives we fit a series of line
segments to the logarithm of the ring-down signal. The fitting windows are
ll-ls in length. This time interval represents a good compromise in making
the window short compared to the timescale of the process studied yet
affording an acceptable signal-to-noise level. Because our time windows
are long compared to the pulse length ('" 1 0 ns), we do not resolve the
build-up of ionization that occurs during the time the pulse is on; yet we
are able to resolve the subsequent recombination. We synchronize the laser
relative to the firing of the discharge with an external timing circuit. In
order to obtain concentration information at different times relative to the
firing of the high voltage pulse, we vary the delay time between the firing
of the laser and the firing of the high voltage pulser. Delay times (Tpulse-
Tlaser) of -10, -8, -6, -4, -2, -1, 0, 1, and 2l-ls are used. Jitter from the
external timing circuit and triggering scheme are negligible compared to
the measurement temporal resolution. Again, to minimize mode-beating
effects, we average 16 or 32 ring-down decay signals.
Implementing CRDS in the atmospheric plasma requires special care in
the choice of cavity geometry. For a linear cavity formed with mirrors of
equal radius of curvature (ROC), the cavity geometry is determined by the
dimensionless g-parameter, defined as unity minus the cavity length divided
by the mirror radius of curvature (Siegman 1986). Initial attempts to form a
ring-down cavity with g = 0.875 (length 75 cm, 6 m ROC mirrors), resulted in
distorted and irreproducible profiles, owing to beam steering from index-of-
refraction gradients (similar to a mirage). Recent work by Spuler and Linne
(2002) simulates the effect of cavity geometry on beam propagation in
CRDS experiments. Their results indicate that a g-parameter of about
-0.5 represents a good compromise between beam waist and beam walk in
environments where beam steering may be present. Accordingly, we form
a cavity of length 75cm, with 50cm ROC mirrors (Research Electro
Optics). No beam steering is detected with this geometry. Qualitatively,
this geometry tends to recenter deviated beams, whereas the more planar
geometry is not as effective.
--- Page 538 ---
Ion Concentration Measurements
523
8.6.3.3
Conductivity measurements
We also determine the electron number density in the discharge by an
electrical conductivity approach. For the dc discharge, we measure the
time-independent discharge current and electric field, and use Ohm's law
to compute the product of the average electron number density and
column area. The electric field is found as the slope of the discharge
voltage versus electrode separation. We write Ohm's law as j = i/area =
(nee2/me L IJeh)E where IJeh is the average collision frequency between
electrons and heavy particles. Because of the low ionization fraction
«"" 10-5), IJeh is dominated by collisions with neutrals, so we can write
IJeh ~ nngeQen, where nn = P/kTg is the number density of neutrals,
ge = (8kTe/1fme)O.5 is the thermal electron velocity, and Qen is the average
momentum transfer cross-section for electron-nitrogen collisions. We
determine Te by means of a collisional radiative model (Pierrot et al1999),
with input parameters (vibronic ground state population and rotational
temperature) obtained from the CRDS measurements. Qen is determined
as a function of Te from tabulated values (Shkarofsky et alI966).
We follow an analogous approach to determine the time-varying
electron number density in the pulsed discharge. In this case we measure
the time-dependent current and electric field, and use these to determine
temporally resolved electron number densities. The time-dependent electric
field is found (after subtracting the cathode fall) from the discharge voltage,
which we measure using fast probes (time response ",,3 ns). The pulsed
discharge has the complication that the shape of the profile is altered
following the high-voltage pulse, because higher concentrations near the
center recombine more quickly. We model these effects based on chemical
kinetic considerations (see Yalin et al2002).
8.6.3.4 Nt ring-down spectra
Nt ring-down spectra are recorded as a function of discharge current
and position. We discuss the spectra in terms of measurement accuracy
and detection sensitivity.
Figure 8.6.3 shows measured and simulated absorption spectra in the
vicinity of the (0,0) bandhead of the Nt first negative band system. Rotation-
ally resolved lines from the P and R branches are visible. The lines are
identified using tabulated line locations (Michaud et al 2000, Laux et al
2001), and are labeled with the angular momentum quantum number Nil
of the lower state. The displayed spectrum is recorded along the discharge
centerline, at a current of 187 mA, and averages 16 shots at each wavelength.
The experimental spectrum is plotted in terms of single-pass cavity loss and
illustrates the high sensitivity attainable with the CRDS technique. The
cavity loss is the sum of mirror reflective loss and sample absorptive loss.
--- Page 539 ---
524
Plasma Diagnostics
........
500
E
Experiment I
a. .e
UI
400
_N
r;-~
-'"
~e
~~
UI
"'"-
~it'
"'"-
0
...J
.?;o
300
.s;
cu
()
200
I Simulation I
390.6
390.8
391.0
391.2
391.4
A (nm)
Figure 8.6.3. Measured and simulated Nt absorption spectra near the (0,0) bandhead of
the first negative band system. Lines from the P and R branches are identified.
(The Rayleigh scattering losses are computed to be negligible.) Near the
bandhead, the signal is ",,280 ppm/pass, the baseline reflective loss is
",,200 ppm/pass, and the baseline noise is ",,5 ppm/pass, so that the signal-
to-noise ratio is ",,56. This ratio suggests an absorbance-per-pass sensitivity
of about 1 ppm, which corresponds to a detection limit of about
7 x 1010 cm-3 for Nt ions at our experimental conditions. The baseline
reflective loss of ",,200ppm/pass corresponds to a mirror reflectivity of
",,0.9998 which is in accord with the manufacturer's specifications.
Figure 8.6.4 shows an expanded view of the P(28) and R(1) lines after
baseline subtraction. Fitted Voigt peaks (constrained to have the same
shape and width) are shown with solid lines, and their sum is shown with a
dotted line. For the P(28) lines, the doublet structure arising from the
unpaired electron is apparent. The fit yields a doublet spacing of 0.005 nm,
in good agreement with the literature (Michaud et al 2000, Laux et al
2001). The R(1) lines are close to the detection limit and correspond to a
Nt X state population of about 1010 cm -3. Their splitting is much less
than the linewidths and is not resolved. The fitted FWHM of each peak is
0.0042 nm, or 7.9 GHz, which is consistent with an expected thermally
broadened linewidth of ",,7 GHz and a measured laser linewidth of
",,4 GHz. Similar to conventional laser-based absorption, the use of an
effective line shape in CRDS is only rigorously valid in the optically thin
(weakly absorbing) limit. However, our calculations indicate that for the
linewidths and absorption parameters used in these experiments, the laser
line shape will have a negligible effect on the area of the measured absorption
features (Yalin et at 2002).
--- Page 540 ---
Ion Concentration Measurements
525
140
..•. .
E 120
Co
S: 100
II)
II)
III
80
Co
...
Q)
60
Co
Q)
u
40
R1(1 )
c:
III
.0
20
R2(1 )
...
0
II)
.0
0
or:(
. . . ...
390.89
390.90
390.91
390.92
390.93
A. (nm)
Figure 8.6.4. Expanded view ofP(28) and R(l) lines from figure 8.6.3. Background absorp-
tion has been subtracted. Voigt profiles fitted to the doublet are shown with solid lines,
while their sum is shown with a dotted line.
8.6.3.5
Spatial profiles of ion concentration and electron number density
We obtain spatial profiles of the Nt concentration by displacing the
discharge perpendicularly to the optical axis. CRDS is a path-integrated
technique and the discharge has axial symmetry. We verify the symmetry
of the discharge by performing measurements with the plasma rotated by
90°, and find that the cases have <2% deviation. We use an Abel inversion
to recover the radial Nt concentration profile. The concentration measure-
ments are based on the (frequency integrated) area of the lines P(9)-P(17)
in the (0,0) band head vicinity. We use tabulated line strengths from Michaud
et al (2000) and Laux et al (2001).
Figure 8.6.5 shows concentration profiles determined for different
values of current (i = 52, 97, 142, and 187mA). We find peak (centerline)
Nt
concentrations
of
7.8 x lOll,
1.5 X 1012,
2.4 X 1012,
and
3.6 x 1012 cm-3 for i = 52, 97, 142, and 187 rnA respectively. The shape of
the concentration profile remains approximately uniform at the different
conditions, though we observe that the radial half-maximum values increase
slightly with current. We find radial half-maximums of 0.80, 0.82, 0.93, and
1.05mm for i = 52, 97,142, and 187mA respectively.
The error bars on the Nt concentrations represent one standard devia-
tion (1 a). They primarily arise from the uncertainties in relating the measured
population of several rotational levels in the ground vibronic state, to the
overall population of Nt. Because the discharge is out of equilibrium, this
relationship depends on how the rotational, vibrational, and electronic
energy levels are populated. The rotational levels are equilibrated at the
--- Page 541 ---
526
Plasma Diagnostics
4.5
4.0
3.5
....... 3.0
'?
E 2.5
0
N
0
2.0
.....
...... - 1.5
+ N
~ 1.0
0.5
0.0
0
_i=187rnA
_i=142rnA
-+-i=97 rnA
-A-i=52 rnA
2
Radius (mm)
3
•
4
Figure 8.6.5 Radial concentration profiles of Nt measured by CRDS in an atmospheric
pressure glow discharge. Experimental data points are joined with line segments for
visual clarity.
gas temperature owing to fast collisional relaxation. The rotational tempera-
tures used in the analysis are obtained from Boltzmann plots, and are
Tr = 3100, 3600, 4150, and 4700K for currents of i = 52, 97, 142, and
187 rnA, respectively. The vibrational and electronic energy levels are out
of equilibrium, and a collisional-radiative (C-R) model (Pierrot et al 1999)
is used to determine the fraction of the population in the ground vibronic
state, and predicts 0.37 ± 0.02, 0.35 ± 0.02, 0.33 ± 0.02, and 0.31 ± 0.02
for i = 52, 97, 142, and 187 rnA, respectively. Combining the rotational
temperature uncertainties with those from the C-R model and those from
the Abel inversion (rv4%) results in an overall experimental uncertainty in
concentration of rv 10%.
The spatial resolution of our measurements is determined by the spatial
step-size (0.2 mm). To justify this claim, we need to verify that the dimension
of our laser beam waist does not influence the measured spatial profiles. The
simulations by Spuler and Linne (2002) indicate that our expected beam
waist is approximately 160-320 !lm, depending on the level of mode matching
achieved. Deconvoluting the broader case has an effect of only about 1 %
(0.02 mm) on the measured profiles, which is negligible compared to the
spatial step-size. Therefore the resulting spatial resolution is about 0.2 mm.
We incorporate the electrical measurements by comparing the electron
number density inferred from the CRDS ion measurements, to the
electron number density from the electrical conductivity approach. To
infer electron number densities from the CRDS, we need to know the frac-
tion of positive ions that are Nt. At our conditions, the C-R model predicts
--- Page 542 ---
Ion Concentration Measurements
527
Table 8.6.1. Comparison of electron number densities (at the radial half-maximum)
inferred by CRDS to those found by electrical measurement, for the dc
discharges. The last column is the ratio of the electron number density
inferred by CRDS to that found from electrical measurement.
i (rnA)
ne.CRDS (cm-3)
ne.Elec (cm -3)
CRDS/electrical
52
4.1 ± 0.4 x lO"
3.8 ± 0.4 x 10"
1.08 ± 0.16
97
8.2 ± 0.8 x 10"
7.8 ± 0.8 x 10"
1.05 ± 0.16
142
1.4 ± 0.1 x 1012
1.4 ± 0.1 x 1012
0.96 ± 0.14
187
2.1 ± 0.2 x 1012
2.0 ± 0.2 x 1012
1.06 ± 0.16
that 96, 93, 89, and 85% of ions are Nt, and the remainder is N+, for i = 52,
97,142, and l87mA, respectively. By charge balance, the sum of the Nt and
N+ concentrations equals the electron number density. We convert the Nt
concentration profiles (found by CRDS) to electron number density profiles
using these percentages. In order to determine electron number densities
from the conductivity measurements (which yield the product of average
electron number density with area), we assume that the shape of the electron
number density profile is the same as that for the ions. The electron number
densities (at the radial half-maximum) found in this way from electrical
measurements are compared with those inferred from the CRDS ion
measurements in table 8.6.1. The values are plotted in figure 8.6.6. The
2.4
I
I • eROS
I
2.0
• Electrical
,..... 1.6
i
"I
E
0
:::!
1.2
0 :s ..
c 0.8
0.4
I
40
60
80
100 120 140 160 180 200
i (rnA)
Figure 8.6.6. Electron number densities (at the radial half-maximum) as a function of
discharge current. Number densities are derived from CRDS ion measurements (squares),
and from electrical measurement (circles).
--- Page 543 ---
528
Plasma Diagnostics
-12,------------------------------,
_
-10
>
E
-
-8
iii
C
C)
en
-6
en c
-4
a:: o
-2
10
15
20
25
30
Time (J.IS)
Figure 8.6.7. Experimental ring-down traces with the laser tuned to the Nt absorption
bandhead (inset) with the high-voltage pulse (solid line) and without the high-voltage
pulse (dashed line).
uncertainty in the electrical measurement (10%) is primarily from uncer-
tainties in the momentum transfer cross-section (5 %), the discharge area
(4%), and the average gas temperature (8%). Column 4 of table 8.6.l
shows that the electron number densities found from optical and electrical
measurements overlap within their error bars. This excellent agreement
gives us confidence in our results for the electron number density.
8.6.3.6
Temporal profiles of Nj concentration and electron number density
Figure 8.6.7 shows ring-down traces obtained with and without firing the
high voltage pulse, and with the laser tuned to the Nt B-X (0,0) bandhead.
In the absence of the high-voltage pulse (dashed line) the absorption losses
are constant in time, and the signal decays as a single-exponential. In the
trace with the pulse (solid line), the light decays more steeply after the
pulse, reflecting an increased concentration of Nt. The spike in the latter
trace coincides with the firing of the pulse, and is caused by rf interference
generated by the pulser. To verify that we are observing changes in the Nt
concentration, we examine the analogous traces but with the laser de tuned
from the absorption band (see figure 8.6.8). These traces confirm that the
only effect of the high voltage pulse on the ring-down system is to generate
the interference spike. We analyze these traces to determine over what
region the interference spike affects the data. We vary the delay of the
high-voltage pulse relative to the laser shot so that we can obtain ion concen-
trations at different times.
--- Page 544 ---
Ion Concentration Measurements
529
-12
-
-10
>
E -
-8
C; c
CJ
-6
en
tn
C
-4
a::
0
-2
IHV
-.......... -
- -, Pulse
o
5
10
15
20
25
30
Time (JJS)
Figure 8.6.8. Experimental ring-down traces with the laser tuned away from the Nt
absorption (inset). We slightly scale «5%) the amplitude of the traces for visual clarity.
The detuned trace (dashed line) is offset by 0.2 m V to make it more visible.
We quantify the time-varying Nt concentration using equation (4) with
a 1 ~s window. This time interval represents a good compromise in making
the window short compared to the timescale of the process studied yet
affording an acceptable signal-to-noise level. The empty-cavity losses
(mirror reflectivity) are found from the ring-down signals with the laser
detuned, and these losses are subtracted in the analysis. Using tabulated
line strengths and the discharge dimensions, we find the absolute Nt center-
line concentrations as a function of time. Figure 8.6.9 presents the time-
varying concentrations (symbols). The error bars reflect uncertainties in
the population fractions, as well as uncertainty associated with a possible
change in shape of the concentration profile. The latter uncertainty is
estimated by chemical kinetic considerations (see Yalin et aI2002). One micro-
second after the pulse, the Nt concentration is '" 1.5 x 1013 cm -3, and then Nt
recombines to the dc level in about 1 0 ~s. The dc level is found by analyzing the
pulsed data at sufficiently long time delays after the pulse, and its value is
consistent with that found in the dc plasma without the pulser.
For the pulsed discharge, we also determine the electron concentration
by measuring the electrical conductivity. The temporally resolved electron
concentrations are shown with a swath in figure 8.6.9. The uncertainty in
the dc electron concentration reflects uncertainties in the profile shape, the
momentum transfer cross-section, and the gas temperature. The colli-
sional-radiative model predicts that Nt is the dominant ion produced by
the pulse. Thus, the agreement between the time-dependent electron and
Nt concentrations during plasma recombination verifies the temporally
--- Page 545 ---
530
Plasma Diagnostics
16 -
'1
E
(,) 12
... ... o
"I:""
-
8
....
+
~ 4
S' -4,,.----------,
til
'-" -5
00-6
o
0:::
~ -7
------------"_._----
5 -8h10-.."...I!--~=--.,..4.-,8,-1
O+-~~_r~~~~_y~~~~~
o
2
4
6
8
10
12
14
Time after Pulse (~)
16 -
'1
12 E
(,)
...
"'0
8 ~
CD
C
Figure 8.6.9. CRDS measurements of Nt concentrations (circles) and conductivity
measurements of electron densities (swath) versus time following the firing of a high-
voltage pulse in an atmospheric pressure nitrogen dc plasma. The dc level of Nt concen-
tration found by CRDS is shown with a hatched bar. The inset shows the ring-down signals
(plotted on a semi-log scale) with the HV pulse (solid), and without the HV pulse (dotted).
resolved CRDS measurement. The measured recombination time is consis-
tent with reported (Park 1989) dissociative recombination rate coefficients
for Nt (approximately 5 x 10-8 cm3/s).
8.6.3.7 Non-equilibrium discharge
To have a measure of the degree of non-equilibrium in the dc discharges, we
examine the ratio of the measured electron number density (at the radial half-
maximum) to the LTE electron number density at the corresponding
gas temperature. These ratios are given in column 3 of table 8.6.2 for
the four conditions studied in the dc discharge. The measured ion and
electron concentrations in the discharge are significantly higher than those
Table 8.6.2. Ratio of the measured dc electron number density
to the concentration corresponding to a L TE
plasma at the same gas temperature.
i (rnA)
Tg (K)
ne-CRDS/ne-LTE
52
3100
2.8 x 104
97
3600
980
142
4200
48
187
4700
5.6
--- Page 546 ---
Ion Concentration Measurements
531
corresponding to LTE conditions at the same gas temperature. The results
quantify the degree of ionization non-equilibrium in the discharges. At
higher values of discharge current the LTE concentration of charged species
rises steeply, so that the ratio of measured concentration to LTE concentra-
tion reduces. Related work in our laboratory has shown that by more rapidly
flowing the gas, comparable electron densities may be achieved with lower
gas temperatures. Clearly, additional non-equilibrium is generated in the
pulsed discharge. The high voltage pulse has a negligible effect on the gas
temperature (and hence corresponding LTE number density) yet the
measured electron number density in the discharge increases by a factor of
at least 4 immediately following the high voltage pulse.
8.6.4 NO+ measuremeuts
8.6.4.1
RF air plasma
The experimental set-up is shown schematically in figure 8.6.10. Atmospheric
pressure air plasmas are generated with a 50 kW rf inductively coupled
plasma torch operating at a frequency of 4 MHz. The torch is operated
with a voltage of 8.9 kV and a current of 4.6 A. The torch has been
extensively characterized at similar conditions, and the plasma is known to
be near LTE with a temperature of about 7000 K (Laux 1993).
8.6.4.2 CRDS measurements
Unlike the Nt ion, the NO+ ion does not have optically accessible electronic
transitions. To perform CRDS measurements, the ion must be probed by
accessing its infrared vibrational transitions. The strongest vibrational tran-
sitions are the fundamental bands, and for these transitions one finds that the
Nozzle
(7 em diameter)
Quartz
Tube
Power and
___
Cooling Water .........
Coil
Plasma Exit Velocity: -10 mls
't:tlow (5 em) = -5 ms
't:cllemistry < I ms
Gas Injectors:
• Radial
• Swirl
• Axial
Figure 8.6.lO. Schematic cross-section of torch head with 7 cm diameter nozzle.
--- Page 547 ---
532
Plasma Diagnostics
9.0><10.5
8.0><10.5
70x10·5
6. 0x10 5
fl 5. 0x10 5
r:::
til -e 4.0><10.5
0
UI
.c « 3.0><10.5
2.0x10·5
1.0><10.5
0
3.8
4.0
4.2
4.4
4.6
4.8
A. (Il-m)
Figure 8.6.11. Modeled absorbance of the air plasma at LTE temperature of 7000K over
pathlength of 5 cm. Absorption by NO, OH, and NO+ are included. Rotationally resolved
lines of the vibrational transitions are shown.
absorbance per NO+ ion is about 20000 times less than that of the electronic
transitions of the Nt ion. Figure 8.6.11 shows the modeled absorbance, as a
function of wavelength, for the air plasma at the conditions used. The simu-
lation is performed with SPECAIR and assumes a pathlength of 5 cm, and
LTE conditions at a temperature of 7000 K (Tg = Tr = Tv = Telectronic =
7000 K). The simulation includes the infrared absorption features of NO,
OH, and NO+. The absorption by NO and OH is relatively weak, while
the various fundamental bands ofNO+ have stronger predicted absorbances.
It is evident that the NO+ absorption begins at a wavelength of about
3950 nm, and is a maximum at about 4lO0nm. Accessing these infrared
wavelengths is challenging in terms of available laser sources. The current
measurements have been performed using a Continuum-Mirage OPO
system. The Mirage laser is designed to operate at a maximum wavelength
of 4000 nm; however, we optimized the alignment in a manner that enabled
operation in the vicinity of 4lO0 nm, in order to be nearer to the peak NO+
absorption. Ring-down cavity alignment at these wavelengths is challenging,
since the beam (and its back-reflections) are not readily observable. The ring-
down cavity was aligned using a combination of LCD (liquid crystal display)
paper to locate the beam, and a helium-neon laser to act as a reference. With
the plasma off, ring-down times of about 1.2 jlS were obtained, corresponding
to mirror reflectivities of about 0.998 (approximately an order of magnitude
worse than the mirrors used for the Nt experiments).
--- Page 548 ---
Ion Concentration Measurements
533
Our initial attempts to perform CRDS measurements in the plasma
torch used the same cavity-geometry as was used in the Nt experiments-
a g-parameter of 0.5. With the plasma off, this geometry yielded excellent
stability in the ring-down times: 1 % standard deviation in ring-down time
for single shot ring-down signals. However, with the plasma on, the beam
steering reduced the stability significantly. In the rf plasma, as compared
to the smaller nitrogen plasma, the cavity-geometry considerations are
different. In the smaller nitrogen plasma, we wanted to minimize simulta-
neously the cavity beam-waist and the beam-walk, leading to a g-parameter
of -0.5 (see discussion above). On the other hand in the rf plasma, the
plasma dimension (about 5 cm) is significantly larger than the beam dimen-
sion (about 1 mm). Therefore, the exact beam dimension is not critical,
and the cavity-geometry may be selected solely to minimize beam-walk.
The numerical modeling of Spuler and Linne (2002) indicates that mini-
mizing the beam-walk may be accomplished with a g-parameter of about
0.25, which we implemented by using a cavity of length 75 cm, and mirrors
of radius-of-curvature of 1 m. This geometry did indeed reduce the beam-
walk and enabled improved stability (about 2% standard deviation in
empty cavity ring-down times).
As will be discussed, the identification of spectral lines in the analysis of
the air plasma spectra is challenging. In order to assist in identifying NO+
spectral features, we also collected CRDS spectra with the plasma running
with argon and nitrogen (as opposed to air), conditions that are not expected
to have any significant NO+ concentration.
8.6.4.3
Results and discussion
Figure 8.6.12 shows a measured absorbance spectrum along the centerline of
the air plasma. The experimental data were obtained by averaging 16 laser
shots at each spectral position. The plotted CRDS data have been converted
to absorbance, and fitted with a peak-fitting program. (Fitted peaks are
shown in black, while raw data are shown with blue symbols.) Also shown
is the modeled NO absorbance assuming the expected plasma conditions
of path length 5 cm, and L TE at 7000 K. The modeled contributions from
OH and NO absorption are negligible on this scale. Comparing the CRD
spectrum in the air plasma to the CRD spectrum in the argon/nitrogen
plasma provides information as to line identities. The largest spectral feature
(at "-'4127.7nm) is present in both spectra, and therefore is presumed not to
be NO+. Comparing the other observed spectral features with the model does
not yield good agreement. To the best of our knowledge, the spectroscopic
constants used in our modeling are the most recent and accurate ones
available (Jarvis et aI1999). The exact locations of the rotationally resolved
lines are largely determined by the rotational constants B, which have a
quoted uncertainty of ±0.005 cm- 1 (or about 0.25%). Based on the quoted
--- Page 549 ---
534
Plasma Diagnostics
0.0004 .,------------"11""""-----------,
~ 0.0002
Data~
s::: as
.
.0
.
...
0
I/)
.0 «
0.0000
-0.0002 -I--r---.--..,.--..----,---T""-,---.---,--.--,-----.---i
41220
41240
41260
41280
41300
41320
41340
~(A)
Figure 8.6.12. Experimental and modeled absorbance spectrum from the air plasma near
4100 nm. Raw data (blue symbols) as well as fitted peaks (top black line) are shown, as well
as the modeled NO+ lines (plotted negative for visual clarity). The precision of the spectro-
scopic constants used in the model is insufficient to predict accurately the locations of the
rotational lines.
uncertainty we performed an uncertainty analysis, and found that with this
level of precision it is not possible to accurately predict the locations of
the rotational lines. Therefore, any match between the experimental data
and model would be fortuitous. Our experimental features are repeatable
(to within experimental uncertainty) and have approximately the correct
integrated area, so we do believe they belong to NO+.
8.6.5 Conclusions
Spatial and temporal profiles of Nt concentration have been measured in dc
and pulsed atmospheric pressure nitrogen glow discharges by cavity ring-
down spectroscopy. Special care in the selection of cavity geometry is
needed in the atmospheric pressure plasma environment. Sub-millimeter
spatial resolution, microsecond temporal resolution, and sub-ppm concen-
tration sensitivity have been achieved. The signal-to-noise ratio suggests a
dc detection limit of about 7 x 1010 cm-3 for Nt ions at our experimental
conditions (corresponding to an uncertainty in column density of about
1.4 x 1010 cm -2). Using a collisional-radiative model we infer electron
number densities from the measured ion profiles. The values of electron
number density found in this way are consistent with those found from
--- Page 550 ---
Ion Concentration Measurements
535
spatially integrated electrical conductivity measurements. The spectroscopic
technique is clearly favorable, because it offers spatial resolution and does
not require knowledge of other discharge parameters. Furthermore, the
spectroscopic technique enables measurements of the speciation of the ion
density, information not available from direct electrical measurements.
Measurements of the NO+ ion in air plasmas have also been demon-
strated. The accessible spectral features of NO+ are vibrational transitions,
considerably weaker than the ultraviolet electronic transitions used to
probe Nt. Nevertheless, CRDS data from air plasmas were obtained, and
spectral features attributed to NO+ were observed. This technique shows
promise for the measurement of NO+ concentrations once more accurate
spectroscopic constants of NO+ become available.
References
Aldener M, Lindgren B, Pettersson A and Sassenberg U 2000 'Cavity ringdown laser
absorption spectroscopy: nitrogen cation' Physica Scripta 61(1) 62-65
Berden G, Peeters R and Meijer G 2000 'Cavity ring-down spectroscopy: experimental
schemes and applications' Int. Rev. Phys. Chern. 19(4) 565-607
Booth J P, Cunge G, Biennier L, Romanini D and Kachanov A 2000 'Ultraviolet cavity
ring-down spectroscopy of free radicals in etching plasmas' Chern. Phys. Lett.
317(6) 631-636
Brown S S, Ravishankra A R and Stark H 2000 'Simultaneous kinetics and ring-down:
rate coefficients from single cavity loss temporal profiles' J. Chern. Phys. A 104
7044-7052
Busch K Wand Busch A M (eds) 1999 Cavity-Ringdown Spectroscopy (acS Symposium
Series) (Oxford: Oxford University Press)
Grangeon F, Monard C, Dorier J-L, Howling A A, HoUenstein C, Romanini D and
Sadeghi N 1999 'Applications of the cavity ring-down technique to a large-area
RF-plasma reactor' Plasrna Sources Sci. Technol. 8448-456
Jarvis G K, Evans M, Ng C Y and Mitsuke K 1999 'Rotational-resolved pulsed field
ionization photoelectron study of NO+ X lI;+, v+ = 0-32) in the energy range of
9.24-16.80eV' JCP 111(7) 3058-3069
Kessels W M M, Leroux A, Boogaarts M G H, Hoefnagels J P M, van de Sanden M C M
and Schram D C 2001 'Cavity ring down detection ofSiH3 in a remote SiH4 plasma
and comparison with model calculations and mass spectrometry' 1. Vac. Sci.
Technol. A 19(2) 467-476
Kotterer M, Conceicao J and Maier J P 1996 'Cavity ringdown spectroscopy of molecular
ions: A 2rrux 2I;; (6-0) transition of Nt Chern. Phys. Lett. 259(1-2) 233-236
Laux C 0 1993 'Optical diagnostics and radiative emission of air plasmas' Mechanical
Engineering. Stanford University, Stanford, CA, p 232
Laux C 0, Gessman R J, Kruger C H, Roux F, Michaud F and Davis S P 2001 'Rotational
temperature measurements in air and nitrogen plasmas using the first negative
system of Nt JQSRT 68(4) 473-482
Michaud F, Roux F, Davis S P, Nguyen A-D and Laux C 0 2000 'High resolution Fourier
spectrometry of the 14Nt ion' J. Molec. Spectrosc. 203 1-8
--- Page 551 ---
536
Plasma Diagnostics
Park C 1989 Nonequilibrium Hypersonic Aerothermodynamics (New York: Wiley)
Pierrot L, Yu L, Gessman R J, Laux C 0 and Kruger C H 1999 'Collisional-radiative
modeling of non-equilibrium effects in nitrogen plasmas' in 30th AIAA Plasma-
dynamics and Lasers Conference, Norfolk, VA
Quandt E, Kraemer I and Dobele H F 1999 'Measurements of Negative-Ion Densities by
Cavity Ringdown Spectroscopy' Europhysics Lett. 45 32-37
Schwabedissen A, Brockhaus A, Georg A and Engemann J 2001 'Determination of the
gas-phase Si atom density in radio frequency discharges by means of cavity ring-
down spectroscopy' J. Phys. D: Appl. Phys. 34(7) 1116-1121
Shkarofsky I P, Johnston T Wand Bachynski M P 1966 The Particle Kinetics of Plasmas
(Addison-Wesley)
Siegman A E 1986 Lasers (Mill Valley: University Science Books)
Spuler S and Linne M 2002 'Numerical analysis of beam propagation in pulsed cavity ring-
down spectroscopy' Appl. Optics 41(15) 2858-2868
Yalin, A P and Zare R N 2002 'Effect of laser lineshape on the quantitative analysis of
cavity ring-down signals' Laser Physics 12(8) 1065-1072
Yalin A P, Zare R N, Laux C 0 and Kruger C H 2002 'Temporally resolved cavity ring-
down spectroscopy in a pulsed nitrogen plasma' Appl. Phys. Lett. 81(8) 1408-1410
Zalicki P and Zare R N 1995 'Cavity ring-down spectroscopy for quantitative absorption
measurements' J. Chem. Phys. 102(7) 2708-2717
--- Page 552 ---
Chapter 9
Current Applications of Atmospheric
Pressure Air Plasmas
M Laroussi, K H Schoenbach, U Kogelschatz, R J Vidmar, S Kuo,
M Schmidt, J F Behnke, K Yukimura and E Stoffels
9.1
Introduction
High-pressure non-equilibrium plasmas possess unique features and charac-
teristics which have provided the basis for a host of applications. Being
non-equilibrium, these plasmas exhibit electron energies much higher than
that of the ions and the neutral species. The energetic electrons enter into
collision with the background gas causing enhanced level of dissociation,
excitation and ionization. Unlike the case of thermal plasmas, these reactions
occur without an increase in the gas enthalpy. Because the ions and the
neutrals remain relatively cold, the plasma does not cause any thermal
damage to articles they may come in contact with. This characteristic
opens up the possibility of using these plasmas for the treatment of heat-
sensitive materials including biological tissues. In addition, operation in
the high-pressure regime lends itself to the utilization of three-body processes
to generate useful species such as ozone and excimers (excited dimers and
trimers).
Low-temperature high-pressure non-equilibrium plasmas are already
routinely used in material processing applications. Etching and deposition,
where low-pressure plasmas have historically been dominant, are examples
of such applications. In the past two decades, non-equilibrium high-pressure
plasmas have also played an enabling role in the development of excimer
VUV and ultraviolet sources (Elias son and Kogelschatz 1991, EI-Habachi
and Schoenbach 1998), plasma-based surface treatment devices (Dorai and
Kushner 2003), and in environmental technology such as air pollution
control (Smulders et at 1998). More recently, research on the biological
and medical applications of these types of plasmas have witnessed a great
537
--- Page 553 ---
538
Current Applications of Atmospheric Pressure Air Plasmas
interest from the plasma and medical research communities. This is due to
newly found applications in promising medical research such as electro-
surgery (Stoffels et al 2003, Stalder 2003), tissue engineering (Blakely et al
2002), surface modification of bio-compatible materials (Sanchez-Estrada
et al 2002), and the sterilization of heat-sensitive medical instruments
(Laroussi 2002). These exciting applications would not have been possible
were it not for the extensive basic research on the generation and sustainment
of relatively large volumes of 'cold' plasmas at high pressures and with rela-
tively small input power. However, as seen in the previous chapters of this
book, in the case of air several challenges still remain to be overcome to
arrive at an optimal generation scheme that is capable of producing large
volume of air plasmas without a prohibitive level of applied power. Nonethe-
less, as will be shown in this chapter, success in this research endeavor will
potentially bring with it substantial economical and societal benefits. In
particular, the semiconductor industry, chemical industry, food industry,
and health and environmental industries, as well as the military stand to
be great beneficiaries from the novel applications of 'cold' air plasmas.
In this chapter, several applications of non-equilibrium air plasma are
covered in details by experts who have extensively contributed to this
research. The selected applications are of the kind that have had or poten-
tially will have a significant impact on industrial, health, environmental, or
military sectors. The first two sections (9.2 and 9.3) discuss electrostatic pre-
cipitation and ozone generation. This choice is motivated by the fact that
historically these two applications of electrical discharges were the first to
have been applied on a large industrial scale: electrostatic precipitation for
the cleaning of air from fumes and particulates, and ozone generation for
the disinfection of water supplies. Section 9.4 discusses the reflection and
absorption of electromagnetic waves by air plasmas. This has direct applica-
tions in military radar communications, and opens the possibility of using
plasmas as a protective shield from radar and high power microwave
weapons. Section 9.5 introduces the concept of using air plasmas to mitigate
the effects of shock waves in supersonic/hypersonic flights. Plasma has been
shown to reduce drag, which leads to lower thermal loading and higher fuel
efficiency. Section 9.6 discusses the use of air plasma to enhance combustion.
Ignition delays can be reduced and the combustion of hydrocarbon fuels can
be increased by the presence of radicals generated by the plasma. Section 9.7
gives an extensive coverage of material processing by high-pressure non-
equilibrium plasmas. The cleaning of surfaces, functionalization (such as
for better adhesion), etching, and deposition of films are discussed and prac-
tical examples are presented. Section 9.8 explores on the use of plasma
discharges for the decomposition of NOx and VOCs. All practical aspects
of the decomposition processes are discussed in detail. Sections 9.9 and
9.10 introduce the reader to the biological and medical applications of
'cold' plasmas. The emphasis of section 9.9 is on the use of air plasma to
--- Page 554 ---
Electrostatic Precipitation
539
inactivate bacteria efficiently and rapidly. The sterilization of heat-sensitive
medical tools and food packaging and the decontamination of biologically
contaminated surfaces are particularly attractive applications. The emphasis
of section 9.10 is the use of 'bio-compatible' plasmas for in vivo treatment
such as in electrosurgery. Cell detachment without damage using the
'plasma needle' is discussed. Wound healing is one example where 'bio-
compatible' plasma sources can be used.
Research on non-equilibrium air plasmas has been to a large extent
application-driven. Inter-disciplinary and cross-disciplinary efforts are
necessary to drive plasma-based technology forward and into new fields
and applications where air plasma has not been traditionally a component,
but its use can substantially improve the established conventional processes.
References
Blakely E A, Bjornstad K A, Galvin J E, Montero 0 R and Brown I G 2002 'Selective
neutron growth on ion implanted and plasma deposited surfaces' in Proc. IEEE
Int. Conf. Plasma Sci., Banff, Canada, p 253
Dorai R and Kushner M 2003 'A model for plasma modification of polypropylene using
atmospheric pressure discharges', J. Phys. D: Appl. Phys. 36 666
EI-Habachi A and Schoenbach K H 1998 'Emission of excimer radiation from direct
current, high pressure hollow cathode discharges' Appl. Phys. Lett. 72 22
Eliasson Band Kogelschatz U 1991 'Non-equilibrium volume plasma processing' IEEE
Trans. Plasma Sci. 19(6) 1063
Laroussi M 2002 'Non-thermal decontamination of biological media by atmospheric
pressure plasmas: Review, analysis and prospects', IEEE Trans. Plasma Sci. 30(4)
1409, 1415
Sanchez-Estrada F S, Qiu H and Timmons R B 2002 'Molecular tailoring of surfaces via rf
pulsed plasma polymerizations: Biochemical and other applications' in Proc. IEEE
Int. Conf Plasma Sci., Banff, Canada, p 254,
Smulders E H W M, Van Heesch B E J M and Van Paasen B S V B 1998 'Pulsed power
corona discharges for air pollution control' IEEE Trans. Plasma Sci. 26(5) 1476
Stadler K 2003 'Plasma characteristics of electro surgical discharges' in Proc. Gaseous Elec-
tronics Conf, San Fransisco, CA, p 16
Stoffels E, Kieft I E and Sladek R E J 2003 'Superficial treatment of mammalian cells using
plasma needle' J. Phys. D: Appl. Phys. 36 1908
9.2 Electrostatic Precipitation
9.2.1
Historical development and current applications
The influence of electric discharges on smoke, fumes and suspended particles
was described by William Gilbert as early as 1600. Gilbert acted as the
--- Page 555 ---
540
Current Applications of Atmospheric Pressure Air Plasmas
president of the British Royal College of Physicians and also as physician to
Queen Elizabeth I of England. His famous work De M agnete (on the magnet)
was a comprehensive review of what was then known about electrical and
magnetic phenomena. In 1824 Hohlfeld in Leipzig reported an experiment
of clearing smoke in a jar by applying a high voltage to a corona wire
electrode. Similar experiments were later repeated in Britain by Guitard in
1850 and by Lodge in 1884. Sir Oliver Lodge was the first to systematically
investigate this effect and to put it to test on large scale in lead smelters at
Bagillt in Flintshire, UK, to suppress the white lead fume escaping from
the chimney (Hutchings 1885, Lodge 1886). To supply the corona current
special electrostatic induction machines of the Wimshurst type were
designed, with rotating glass plates of 1.5 m diameter. This can be considered
the first, although not totally successful, commercial application of electro-
static precipitation for pollution control. The importance of this new
'electrical process of condensation for a possible purification of the atmos-
phere' was clearly recognized, and international patent coverage was
obtained (Walker 1884). Practically simultaneously and independently a
German patent was issued for a cylindrical precipitator (Moller 1884).
A number of important industrial applications followed the pioneering
work of Frederick Gardner Cottrell, a professor of physical chemistry at the
University of California-Berkeley. Starting in 1906 he conducted research on
air pollution control, responding to growing nuisance caused by factories in
his native San Francisco. The result was an improved precipitator, an elec-
trical device, which could collect dusts and fumes as well as acid mists and
fogs. Cottrell was the first to realize that for precipitation the negative
corona discharge was superior to the positive corona, and who took advan-
tage of the newly developed synchronous mechanical rectifier (Lemp 1904)
and better high voltage step-up transformers. Within a few years commercial
applications evolved for collecting sulfuric acid mists, for zinc and lead
fumes, for cement kiln dust, for gold and silver recovery from electrolytic
copper slimes, and for alkali salt recovery from waste liquors in paper-
pulp plants (Cottrell 1911). In 1923 the first use of electrostatic precipitators
(ESPs) collecting fly ash from a pulverized coal-fired power plant was
reported. This process became by far the largest single application of
ESPs. The fine wire corona discharge electrode, as it is used in many precipi-
tators today, one of the most important advances in precipitator technology,
was introduced and patented W A Schmidt (1920), a former student of
Cottrell. In the following years investigations by Deutsch (1922, 1925a,b)
and Seeliger (1926) brought new insight in the physical processes involved
in electrostatic precipitation and a first quantitative formulation of precipi-
tator performance. The Deutsch equation has been used ever since for
sizing precipitators. For further details the reader is referred to the classical
comprehensive treatment of industrial electrostatic precipitation by H J
White (1963), to some more recent books (Oglesby and Nicholls 1978,
--- Page 556 ---
Electrostatic Precipitation
541
Cross 1987, Parker 1997) and to well written review articles (White 1957,
1977/781984, McLean 1988, Lawless et a11995, Lawless and Altman 1999).
The main advantages of electrostatic precipitators are that various
types of dust, mist, droplets etc. can be collected under both dry and wet
conditions, and also that submicron size particles can be collected with
high efficiency. ESPs can handle very large air or flue gas streams, typically
at atmospheric pressure, with low power consumption and low pressure
drop.
These properties have led to a number of large-scale commercial appli-
cations in the following industries: steel mills, non-ferrous metal processing,
cement kilns, pulp/paper plants, power plants and waste incinerators,
sulfuric acid plants, and in petroleum refineries for powder catalyst recovery.
Much smaller ESPs of different design are used for indoor air cleaning in
homes and offices.
9.2.2
Main physical processes involved in electrostatic precipitation
Electrostatic precipitation is a physical process in which particles suspended
in a gas flow are charged electrically by ions produced in a corona discharge,
are separated from the gas stream under the influence of an electric field, and
are driven to collecting plates, from which they can be removed periodically
by mechanical rapping (dry ESP) or continuously by washing (wet ESP).
Typical configurations are corona wires centered in cylinders or wires
mounted at the center plane between parallel plates forming ducts (figure
9.2.1).
The discharge electrodes can be simple weighted wires, barbed wires,
helical wires, or rods, serrated strips and many other kinds. They all have
in common that they have parts with a small radius of curvature or sharp
edges to facilitate corona formation (see also chapters 2 and 6). The particle
laden gas flow is channeled to pass through many cylinders or ducts either in
___ Negative High Voltage
~~
~
Discharge
Electrodes
--- Weights----
~~jIff'JI¥,I'-
Collecting
Plates
at Ground
Potential
Figure 9.2.1. Cylindrical and planar precipitator configurations with weighted wire corona
discharge electrodes.
--- Page 557 ---
542
Current Applications of Atmospheric Pressure Air Plasmas
the vertical (cylinders) or horizontal direction (ducts). In large precipitators
negative coronas are used almost exclusively because they have a larger
stability range and can be operated at higher voltages. For these devices
electrode plate distances of O.2-O.4m and voltages in the range 50-110kV
are common. Small ESPs for indoor air cleaning normally use positive
coronas, because they produce less ozone, a matter of great concern for
indoor applications.
9.2.2.1
Generation of electrons and ions
The active corona region in which electrons as well as positive and negative
ions are generated is restricted to a very thin layer around the corona elec-
trodes. Typically ionization occurs only in a layer extending a fraction of
1 mm into the gas volume. Positive ions travel only a short distance to the
negative electrode, while electrons and negative ions start moving towards
the collecting surface at ground potential. In air or flue gas mixtures at
atmospheric pressure electrons rapidly attach to 02> CO2 or H20 molecules,
thus forming negative ions. As a consequence, most of the space in the duct is
filled with negative ions. They are utilized to charge dust particles so that
these can be subjected to electrical forces in order to separate the dust
from the gas stream. With modern computational tools it is possible to calcu-
late the ion charge density distribution for complicated electrode structures.
An example is given in figure 9.2.2 for one helical electrode (left part) and for
three helical electrodes in a duct formed by specially shaped collecting plates
(right part).
It is interesting to note that practically no ions are produced on the inner
side of the helical discharge electrode ( dark zone) because of shielding effects.
The shape and orientation of the ion clouds in the duct depends very much on
Figure 9.2.2. Ion charge density on a helical corona electrode and in three different hori-
zontal planes of an ESP duct formed by specially shaped collecting plates (maximum
charge density: 10-4 As m -3).
--- Page 558 ---
Electrostatic Precipitation
543
0.5
1
1.5
(mAIm:)
Figure 9.2.3. Current density on collecting plates and ion-induced secondary flow in an
ESP duct with helical corona electrodes and specially formed collecting plates.
where the horizontal plane used in the visualization cuts the helix as well as
on the location and shape of the closest collecting plane and on the distance
to the neighboring electrodes. The complicated ion flow leads to a very
inhomogeneous current density distribution on the collecting plates
including zones of zero current density (figure 9.2.3). Such inhomogeneous
current distributions were measured as well. They also show up in the
deposited dust patterns.
9.2.2.2 Space charge limitations and saturation current
For practical purposes the active corona layer where ionization takes place
can be regarded as very thin and as a copious source of charge carriers, in
this case negative ions. The amount of current that is drawn depends on
the characteristics of the ion drift region, which again depends on the applied
voltage. The maximum current scales linearly with the ion mobility p, and
with U2, when U is the applied voltage. The current is limited by the space
charge accumulated in the duct. A unipolar ion drift region can be described
by the following set of equations:
E = - V <I> = -grad <I>
V2<I> = divgrad<I> = -pleo
j = pp,E
V . j = div j = o.
(9.2.1 )
(9.2.2)
(9.2.3)
(9.2.4)
In these equations E stands for the electric field, <I> for the potential, p for the
ion space charge density, eo for the vacuum permittivity (8.85 x 10-12 As/
V m), and j for the current density. Poisson's equation (9.2.2) enforces a
strong coupling between the ion space charge and the electric field. Adequate
--- Page 559 ---
544
Current Applications of Atmospheric Pressure Air Plasmas
boundary conditions have to be formulated at the rim of the active corona
region and at the collecting plane.
Because of this strong dependence on the voltage, ESPs operate at the
maximum possible voltage stable corona discharge operation will allow.
Since the highest possible voltage is beneficial both for charging and precipi-
tation, ESPs are automatically controlled to run close to the sparking limit by
allowing a certain number of sparks per unit of time to occur (up to 60 sparks
per minute). Modern ESPs utilize all-solid-state high voltage rectifiers and
microcomputer controls.
9.2.2.3
Main gas flow and electric wind
Ions, traveling in the duct at a speed of the order 100 mis, move perpendicu-
larly to the gas stream flowing at a speed of about 1 m/s. Since they have
practically the same mass as the neutral components of the gas flow there
is an efficient collisional momentum transfer. As a result strong secondary
flows are induced. This phenomenon, referred to as the ion wind or electric
wind, has been known for a long time and has been reviewed by Robinson
(1962). At high applied voltages the magnitude of the ion-induced secondary
flow component in an ESP becomes comparable to the main flow velocity. In
a complicated electrode duct geometry like the helical discharge electrodes
discussed earlier, this leads to stationary or oscillating vortex structures
(Egli et al 1997), as demonstrated in the right-hand part of figure 9.2.3.
The computed cross flow velocity distribution is shown in a vertical plane
perpendicular to the main flow, located between the second and third helical
discharge electrode.
As already suspected by Ladenburg and Tietze (1930) the electric wind
can have a major adverse influence on particle collection. Recent 3D compu-
tations of corona charging, particle transport in the flow field and particle
collection show that this is indeed the dominating effect at certain operating
conditions (Egli et a11997, Lowke et aI1998).
9.2.2.4 Particle charging
The physical processes involved in corona charging of powders and droplets
have been studied in great detail. Apart from precipitators these phenomena
are utilized in electrophotography (Crowley 1998), copying machines,
printers, liquid spray guns, and in powder coating (Mazumder 1998). Solid
particles or droplets entering a precipitator pass many corona zones, undergo
collisions with ions resulting in charge accumulating, and are subjected to
Coulomb forces in the electric field and to drag forces in the viscous flow.
The charging process of solid particles or droplets has two main contri-
butions, the relative importance of which depends on particle size. Field
charging is the dominating process for particles of diameter of about 2 Ilm
--- Page 560 ---
Electrostatic Precipitation
545
or more. It is described by the following differential equation:
dqf = p7rr2 ILpE (1 _ qf)2
dt
P
qs
(9.2.5)
in which qf is the accumulated particle charge due to field charging,
p = 3cr/(2 + cr ), rp is the particle radius, and qs is the saturation charge.
The parameter p depends on the relative dielectric constant Cr of the particle
and varies only moderately between the value p = 1 for Cr = 1 and p = 3 for a
metallic particle (cr = (0). Charging stops when the saturation charge qs is
reached. At this point additional approaching ions will be deflected in the
electric field of the previously accumulated charges on the particle and will
no longer be able to impact.
(9.2.6)
At the ion densities and electric fields encountered in ESPs, field charging is a
fast process. Its rate is proportional to the ion density, the cross section of the
particle and to the electric field strength. Also the maximum attainable
charge is proportional to the particle cross section and the electric field.
Under typical precipitator conditions a 5)lm particle may accumulate several
thousand elementary charges.
For very small particles with r p :::; 1 )lm, field charging gets very slow and
another charging process depending on the Brownian motion of ions takes
over (Fuchs 1964). This process is referred to as diffusion charging and
follows a different law:
ILP
qd
co exp (
qd· e
) _ 1
47rcorpkT
(9.2.7)
where qd is the particle charge accumulated due to diffusion charging, e is the
elementary charge, k is the Boltzmann constant (1.38 x 10-23 J/K), and Tis
the gas temperature.
Diffusion charging is a much slower process than field charging. It
does not depend on the electric field and does not reach a saturation
charge. At the exit of a precipitator, after 10-15 s transit time, a 0.3)lm
particle has accumulated about 100 elementary charges. The theoretical
limit is reached (if ever) when the field at the particle surface has reached a
value where gas breakdown is initiated. In the intermediate particle size
rage O.I)lm < r p < lO)lm both charging mechanisms are of comparable
speed and occur simultaneously. The charging equations (9.2.5) and (9.2.7)
have to be integrated along the particle trajectories, simultaneously with
solving the coupled codes describing the corona discharge and the fluid
phenomena (Choi and Fletcher 1997, Egli et a11997, Meroth 1997, Gallim-
berti 1998, Medlin et aI1998). Instead of integrating (9.2.7) often a useful
--- Page 561 ---
546
Current Applications of Atmospheric Pressure Air Plasmas
approximate relation for the charge qd reached at time t is used:
3r kT
qd(t) = _P -
In(AIl,pt).
e
(9.2.8)
In this relation, suggested by Kirsch and Zagnit'ko (1990), A is a constant. It
shows that the charge obtained by diffusion charging is proportional to the
gas temperature and that it grows with the logarithm of the time t.
9.2.3 Large industrial electrostatic precipitators
Industrial precipitators can be very large installations. As an example the
precipitator at the exit of a pulverized-coal fired utility boiler of a 500 MW
power plant is described. Coal consumption is about 200 tons per hour
resulting in fly ash quantities of 20-80 tons per hour, depending on the
origin and quality of coal. Fly ash particles range from 0.1 to 10/lm size.
At the exit of the boiler they are dispersed in a flue gas stream of about 2.5
million m3 per hour with a mass concentration of about 20 g/m3. To meet
tolerable output concentrations of 20 mg/m3 the precipitator has to reach a
weight collection efficiency of 99.9%. With modern technology this can be
achieved. In extreme cases even 99.99% efficiency has been obtained. It is
one of the major achievements of modern precipitator technology that
these goals can be reached with an almost negligible power consumption
of 0.1 % of the generated power and a pressure drop of only 1 mbar.
9.2.3.1
Structural design
To handle such a large gas flow the flue gas is slowed down to about 1 m/s,
channeled into many parallel ducts of 15 m height, up to 15 m length, and
0.3-0.4 m width. Such large ESPs are subdivided into fields of about 5 m
length. About 11 0-150 such ducts add up to a total width of 45 m, being
typically sectionalized into 3 x 15 m. In total 60000 m2 of collecting area
are provided. At the center plane of each duct the discharge electrodes are
mounted. (See figure 9.2.4.) The helical electrodes shown in figures 9.2.2
and 9.2.3 have the advantage that, mounted under tension in metal frames
at the center plane of each duct, they are always self centered. In addition,
rapping of the metal frames induces vibration of the discharge electrodes,
thus efficiently cleaning them of deposited fly ash. The charged particles
impinging on the collecting plates, usually made of mild steel, and kept at
ground potential, form a dust cake, which is held in position by electric
forces. It is removed periodically by mechanical rapping using either side-
or top-mounted hammers. Upon rapping the collected material is dislodged
and slides down into hoppers at the bottom from where it is removed by
conveyor belts. The special shape of the collecting plates indicated in figures
9.2.2 and 9.2.3 is chosen to give them mechanical strength and to reduce
rapping-induced re-entrainment of already collected material.
--- Page 562 ---
Electrostatic Precipitation
547
High Voltage Supplies ~~:::::::~ .........
Screens for Gas Deceleration
and Distribution
Flue Gas with Fly Ash
coming from Boiler
Hoppeffif~ ~
Dust Collection
Figure 9.2.4. Structure of a large precipitator behind a coal-fired utility boiler (Flakt
design).
9.2.3.2 Numerical modeling
For many years ESPs have been sized according to the Deutsch equation
which was derived in 1922 and which, for the first time, established a quan-
titative relation between the collection efficiency TJ of a precipitator and some
operational and geometry parameters:
TJ= 1- (Cexit/CO) = 1-exp(-wA/Q).
(9.2.9)
The quantities Cexit and Co are the dust concentrations at the exit and entrance
of the precipitator, respectively, A is the total collection area and Q is
the volumetric gas flow. The parameter w has the dimension of a velocity
and is called the migration velocity. For ESP sizing this parameter was
determined empirically and contained all the pertinent information about
precipitator design, dust properties and corona operation.
With a better understanding of all the physical processes involved, and
taking advantage of fast computers and advanced computational tools,
individual particle paths can now be followed through a large industrial
precipitator. This approach requires that sufficiently accurate computational
models are available for the field distribution and ion production, the
charging process, the flow field and the particle motion. Since there is a
strong interaction between the different processes involved the differential
equations describing the different processes have to be solved simultaneously
with appropriate boundary conditions. As an example some results are given
of numerical studies in which individual particle paths where followed
through a 12 m long ESP duct in which they passed 45 helical corona
--- Page 563 ---
548
Current Applications of Atmospheric Pressure Air Plasmas
a i
0.1
~
0.1
0.1
l.
lIkII:1ricwlnd
)
~
0.01
0.01
~
(lOOl,._u.'
0.001
0.001
0.01
0.1
10
001
0.1
10
0.01
0.1
10
Particle Diameter (fJITl)
Figure 9.2.5. Fractional particle penetration curves demonstrating the influence of
different parameters.
electrodes (Kogelschatz et al 1999). For each size class 2000 particles with
different initial positions at the entrance were traced.
The plots, referred to as penetration curves, show the fraction of particles
that are able to pass the whole precipitator without getting collected, as a
function of particle size. The left-hand part of figure 9.2.5 demonstrates the
overwhelming influence of the electric wind. If it were not present, collection
would improve by more than 2 orders of magnitude. In the model computa-
tion this was simulated by switching off the electric volume forces on the
flow. These computations were performed for the specially formed collecting
plates (figures 9.2.2, 9.2.3), a O.4m duct, an initial flow velocity of 1 mls and
a corona voltage of 56kV. The middle graph of figure 9.2.5 shows results
for different flow velocities at a fixed voltage of 56kV in a O.4m duct with
planar walls. Clearly, slower transport velocity, and consequently longer resi-
dence time, results in better particle collection. The right-hand part shows the
influence of the applied voltage for a fixed initial flow velocity of 1 m/s. All
computations show that there is a particle size range between 0.1 and lllm
diameter that is difficult to collect. Larger particles are more efficiently
collected because they accumulate sufficient charge in the corona zones and
are subjected to strong electric forces. Very small particles are also easily
collected despite the reduced electric forces. The reason is that they experience
less flow resistance when particle diameters approach the mean free path of the
gas molecules (Cunningham slip). Measurements of particle size distributions
at the entrance and exit oflarge industrial precipitators yield the same form of
the penetration curves. Such numerical simulations, based on the fundamental
physical processes and validated in real situations, have become a powerful
tool for optimizing ESP performance.
9.2.3.4 Limitations by corona quenching and dust cake resistivity
The practical performance of electrostatic precipitators can be limited by
additional effects not mentioned so far. If large amounts of fine dust enter
--- Page 564 ---
Electrostatic Precipitation
549
the precipitator, the corona current in the entrance sections can drop to a
small fraction of what it had been without dust. This very pronounced
effect is called corona quenching. The reason is that the properties of the
corona discharge that were originally determined by ion mobility and ion
space charge are now determined by the much smaller dust mobility and
the dust space charge. Fortunately, after collecting most of this fine dust,
the corona recovers to its original current density, typically after a few
meters in the duct.
The collected material on the collecting plates can also pose limitations
on electrostatic precipitation. If particles have a very low electrical resistivity,
for example metal particles, they do not adhere to the collecting plates, thus
preventing collection. On the other hand, if dust resistivity is very high, one
might expect that the deposited dust layer would finally limit the current flow
and stop the corona. Normally a different phenomenon, called back corona,
occurs instead. Since the deposited dust forms a porous layer of growing
thickness and voltage drop, gas breakdown in interstices and on particle
surfaces can occur. When this happens, the corona current suddenly
increases and collection is severely effected. Now positive ions, generated
by back corona inside the dust cake, travel towards the center electrodes
and counteract the charging process with negative ions. This results in
what is called a bipolar corona. Obviously, for optimum charging conditions
we depend on a unipolar ion flow.
Back corona is observed in precipitators serving boilers using low sulfur
coal and also in powder coating, where high resistivity polymer particles and
pigments are deposited. It was first observed by Eschholz in 1919. The
described effects limit the useful range of electrostatic precipitators to
material with resistivity in the range of about 108 n·cm to less than
1013 n·cm. The resistivity range for optimum ESP performance is 108 to
1010 n·cm. In many cases high dust resistivity can be reduced by raising the
temperature or by conditioning, which means by using additives like H20
or S03. The cohesive properties of the dust cake can be influenced by
adding NH3 to the gas stream. It is also possible to detect malfunctioning
of a precipitator section as a consequence of corona quenching or back
corona and counteract by modifying the electrical feeding of the corona.
9.2.4 Intermittent and pulsed energization
In many cases pronounced improvement of ESP performance has been
obtained by abandoning the classical dc high voltage on the discharge elec-
trodes. Microprocessor control of the supply voltage allows simple variations
in the way the corona discharge in ESPs is fed. Intermittent energization can
be achieved by suppressing voltage half cycles or even several cycles in the
rectifier circuit. This way, peak voltages higher than those achievable with
dc energization, and lower average voltages and average currents are
--- Page 565 ---
550
Current Applications of Atmospheric Pressure Air Plasmas
obtained. In addition to energy savings this can result in improved perfor-
mance if back corona is a problem.
Even better results can be obtained if pulsed energization is used. This
technique originated about 1950 following pioneering research and develop-
ment by Hall and White (Hall 1990). We speak of a pulsed corona if the
duration of the applied voltage pulse is shorter than the ion transit time
from the discharge electrode to the collecting plate. In a large ESP this is
typically of the order 1 ms. Using this technique, periodic short high-voltage
pulses are superimposed on a dc high voltage. Typical pulse widths of < IllS
to about 300 IlS and repetition rates of about 30 to 300 per second are used.
Pulsed energization introduces a number of new parameters that can be
optimized: pulse duration, pulse repetition frequency, base dc voltage. It
increases the uniformity of the corona along the discharge electrodes and
on the collecting plates. It helps to suppress back corona in the collection
of high resistivity dust. Experience shows that application of short HV
pulses to high resistivity dusts of 1010_10 13 O'cm results in significant perfor-
mance improvement over that achievable with dc energization.
In conclusion it can be stated that electrostatic precipitation is the
leading and most versatile procedure for high-efficiency collection of solid
particles, fumes and mists escaping from industrial processes. It presents
by far the most important application of industrial air pollution control.
About one hundred years of practical experience with various kinds of
dust, a growing understanding of the physical processes involved, and
more recently, the use of advanced computational tools simulating the
whole particle charging, particle motion and collection process have led to
its present supremacy.
References
Choi B S and Fletcher C A J 1997 J. Electrost. 40/41 413--418
Cottrell F C 1911 J. Ind. Eng. Chern. 3 542-550
Cross J A 1987 Electrostatics: Principles, Problems and Applications (Bristol: Adam Hilger)
Crowley J M 1998 'Electrophotography' in Wiley Encyclopedia of Electrical and
Electronic Engineering Webster J G (ed) (New York: Wiley-Interscience) vol 6,
pp 719-734
Deutsch W 1922 Ann. Phys. 68335-344
Deutsch W 1925a Z. Techn. Phys. 6423--437
Deutsch W 1925b Ann. Phys. 76 729-736
EgJi W, Kogelschatz U, Gerteisen E A and Gruber R 1997 J. Electrostat. 40/41 425--439
Eschholz 0 H 1919 Trans. Am. Inst. Mining Metall. Eng. LX 243-279
Fuchs N A 1964 The Mechanics of Aerosols (Oxford: Pergamon)
Gallimberti I 1998 J. Electrostat. 43 219-247
Gilbert W 1600 Tractatus, sive Physiologia de Magnete, Magnetisque corporibus magno
Magnete tellure, sex libris comprehensus (London: Excudebat Petrus Short)
Guitard C F 1850 Mech. Mag. (London) 53346
--- Page 566 ---
Ozone Generation
551
Hall H J 1990 J. Electrostat. 25 1-22
Hohlfeld M 1824 Arch.f d. ges. Naturl. 2205-206
Hutchings W M 1885 Berg- u Hiittenmiinn Zeitschr. 44 253-254
Kirsch A A and Zagnit'ko A V 1990 Aerosol Sci. Technol. 12465--470
Kogelschatz U, Egli Wand Gerteisen E A 1999 ABB Rev. 4/1999 33--42
Ladenburg R and Tietze W 1930 Ann. Phys. 6 581-621
Lawless P A and Altman R F 1999 'Electrostatic precipitators' in Wiley Encyclopedia of
Electrical and Electronic Engineering, Webster J G (ed) (New York: Wiley-
Interscience) vol 7 pp 1-15
Lawless P A, Yamamoto T and Oshani 1995 'Modeling of electrostatic precipitators and
filters' in Handbook of Electrostatic Processes, Chang J S, Kelly A J and Crowley
J M (eds) (New York: Marcel Dekker) pp 481-507
Lemp H 1904 Alternating current selector, US Pat No. 774,090
Lodge 0 J 1886 J. Soc. Chem. Ind. 5 572-576
Lowke J J, Morrow R and Medlin A J 1998 Proc. 7th Int. Con! on Electrostatic Precipita-
tion (ICESP VII), Kyonju, Korea 1998, pp 69-75
Mazumder M K 1999 'Electrostatic processes' in Wiley Encyclopedia of Electrical and
Electronic Engineering, Webster J G (ed) (New York: Wiley-Interscience) vol 7
pp 15-39
McLean K J 1988 lEE Proc. 135347-361
Medlin A J, Fletcher C A J and Morrow R 1998 J. Electrostat. 43 39--60
Meroth A M 1997 Numerical Electrohydrodynamics in Electrostatic Precipitators (Berlin:
Logos-Verlag)
Moller K 1884 Rohrenformiges Gas und DampjJilter, German Pat. No. 31911
Oglesby S and Nichols G 1978 Electrostatic Precipitation (New York: Decker)
Parker K R (ed) 1997 Applied Electrostatic Precipitation (London: Blackie)
Robinson M 1962 Am. J. Phys. 30 366--372
Schmidt W A 1920 Means for separating suspended matter from gases, US Pat. No.
1,343,285
Seeliger R 1926 Z. Techn. Phys. 7 49-71
Walker A 0 1884 A process for separating and collecting particles of metals or metallic
compounds applicable for condensing fumes from smelting furnaces and for other
purposes, Brit Pat No. 11,120
White H J 1957 J. Air Poll. Contr. Ass. 7167-177
White H J 1963 Industrial Electrostatic Precipitation (Reading: Addison-Wesley)
White H J 1977/78 J. Electrostat. 4 1-34
White H J 1984 J. Air Poll. Contr. Ass. 34 1163-1167
9.3 Ozone Generation
9.3.1
Introduction: Historical development
In 1785 the natural scientist Martinus van Marum described a characteristic
odor forming close to an electrostatic machine, and in 1801 Cruikshank,
--- Page 567 ---
552
Current Applications of Atmospheric Pressure Air Plasmas
performing water electrolysis, noticed the same odor at the anode. Only in
1839 Schonbein, professor at the University of Basel, also working on elec-
trolysis, established that this very pronounced smell was due to a new
chemical compound which he named ozone after the Greek word OSElV for
to reek or smell. It took another 25 years of scientific vehement dispute
before J L Soret could establish in 1865 that this new compound was made
up of three oxygen atoms.
Industrial ozone generation is the classical application of non-equilibrium
air plasmas at atmospheric pressure. Low temperature is mandatory because
ozone molecules decay fast at elevated temperature. At the same time a
relatively high pressure is required because ozone formation is a three-
body reaction involving an oxygen atom, an O2 molecule and a third collision
partner, O2 or N2 • The dielectric barrier discharge (silent discharge) origin-
ally proposed by Siemens (1857) for 'ozonizing air' is ideally suited for this
purpose. Siemens' invention came at the right time. The foundations of
bacteriology had been laid through the work of the French microbiologist
Louis Pasteur and the German district surgeon Robert Koch. It had been
established that infectious diseases like cholera and typhoid fever were
caused by living micro-organisms, which were dispersed by contaminated
drinking water, food and clothing. Cholera epidemics like the ones reported
in Hamburg (1892) and in St Petersburg (1908) caused hundreds of casualties
per day. Occasional typhoid fever epidemics were common in many cities.
Ozone is an extremely effective oxidant, surpassed in its oxidizing power
only by fluorine or radicals like OH or 0 atoms. Siemens succeeded in
persuading Ohlmiiller, professor at the Imperial Prussian Department of
Health, to test the effect of ozone exposure on cholera, typhus and coli
bacteria. The result was complete sterility after ozone treatment. Soon after
the first official documentation of these bactericidal properties (Ohlmiiller
1891), industrial ozone production started for applications in small water
treatment plants in Oudshoorn, Holland (1893) and in Wiesbaden and Pader-
born, Germany (1901/2). Within the following years major drinking water
plants using ozone disinfection were built in Russia (St Petersburg 1905), in
France (Nice 1907, Chartres 1908, Paris 1909) and in Spain (Madrid 1910).
The water works at St Petersburg already treated 50000 m3 of drinking
water per day with ozone, those of Paris 90000 m3. Thus, historically speaking,
ozonation was the first successful attempt of disinfecting drinking water on a
large scale. Ever since, ozone generating technology has been closely linked to
the development of water purification processes. In many countries ozonation
in water treatment was later replaced by more cost-effective processes using
chlorine or chlorine compounds, which are not only cheaper but also more
soluble in water than ozone. Recent concerns about potentially harmful disin-
fection by-products have reversed this, tending towards the use of ozone again.
Many European cities and some Canadian cities have abandoned chlorination
in favor of ozone technology to disinfect water. Water works in the US as well
--- Page 568 ---
Ozone Generation
553
as in Japan are increasingly turning to ozone, in order to be able to meet more
stringent legislation about disinfection by-products like trihalomethanes
(THMs) and haloacetic acids. These compounds can be formed when chlorine
is added to the raw water containing organic water pollutants or humic
materials. Some THMs are suspected to cause cancer. For this reason many
experts consider ozone treatment the technology of choice for potable water
treatment. In the United States more than 250 operating plants use ozone.
For many years the Los Angeles Aqueduct Filtration Plant treating two
million m3 jday (600mgd) of drinking water with ozone generating capacity
of close to 10000kg per day, was the largest US plant. Very recently larger
ozone generating facilities have been installed at the Alfred Merrit Water
Treatment Plant in Las Vegas, the East Side Water Treatment Plant in
Dallas, Texas, and the Metropolitan Water District in Southern California.
In Europe, more than 3000 cities use ozone to disinfect their municipal
water supplies.
9.3.2 Ozone properties and ozone applications
0 3 is a triangle shaped molecule with a bond angle of 117° and equal bond
lengths of 0.128 nm. Ozone is a practically colorless gas with a characteristic
pungent odor (Horvath et a11985, Wojtowicz 1996). At -112°C it condenses
to an indigo blue liquid which is highly explosive. Below -193°C ozone
forms a deep blue-violet solid. Because of explosion hazards ozone is used
only in diluted form in gas or water streams. Its solubility is about 1 kg per
m3 of water. Due to its oxidizing power it finds applications as a potent
germicide and viricide as well as a bleaching agent. In many applications
ozone is increasingly used to replace other oxidants such as chlorine that
present more environmental problems and safety hazards. Strong oxidants
are chemically active species. Their storage, handling and transportation
involve substantial hazards. An important issue is also the question of
residues and side reactions. In all respects ozone represents a superior
choice due to its innocuous side product, oxygen. As a consequence of its
inherent instability ozone is neither stored nor shipped. It is always generated
on the site at a rate controlled by its consumption in the process.
The most important application of ozone is still for the treatment of
water. It is capable of oxidizing many organic and inorganic compounds in
water. Ozone chemistry in water involves the generation of hydroxyl free
radicals, very reactive species approaching diffusion controlled reaction
rates for many solutes such as aromatic hydrocarbons, unsaturated
compounds, aliphatic alcohols, and formic acid (Glaze and Kang 1988,
Hoigne 1998). Besides applications in drinking water, ultra-pure process
water, swimming pools, and cooling towers, ozone also finds applications
in municipal waste water treatment plants and in industrial processes. Very
large amounts of ozone are also used for pulp bleaching.
--- Page 569 ---
554
Current Applications of Atmospheric Pressure Air Plasmas
9.3.3 Ozone formation in electrical discharges
Ozone can be generated in different types of gas discharges in which the
electron energy is high enough to dissociate O2 molecules and in which the
gas temperature can be kept low enough for the 0 3 molecules to survive
without undergoing thermal decomposition. Mainly non-equilibrium
discharges can meet these requirements, above all corona discharges and
dielectric barrier discharges.
9.3.3.1
Ozone formation in corona discharges
Ozone formation in both positive and negative corona discharges has been
extensively investigated and is reasonably well understood. Ozone formation
is restricted to the thin active corona region where ionization takes place.
Since it is rarely used on an industrial scale it will not be treated in detail.
The reader is referred to the following references: Peyrous (1986, 1990),
Peyrous et al (1989), Boelter and Davidsen (1997), Held and Peyrous
(1999), Yehia et al (2000), Chen (2002), and Chen and Davidson (2002,
2003a,b).
9.3.3.2
Ozone formation in dielectric barrier discharges
The preferred discharge type for technical ozone generators has always been
the dielectric barrier discharge (silent discharge) as originally proposed by
Siemens. In recent years industrial ozone generation profited substantially
from a better understanding of the discharge properties and of the ozone
formation process (Filippov et a11987, Kogelschatz 1988, 1999, Samoilovich
et al 1989, Braun et al 1991, Kogelschatz and Eliasson 1995, Pietsch and
Gibalov 1998). Operating in air or oxygen at pressures between 1 and 3
bar, at frequencies between 0.5 kHz and 5 kHz, and using gap spacings in
the mm range the discharge is always of the filamentary type. Major improve-
ments were obtained by tailoring microdischarge properties in air or in
oxygen in such a way that recombination of oxygen atoms is mimimized
and ozone formation is optimized. This can be achieved by adjusting the
width of the discharge space, the operating pressure, the properties of the
dielectric barrier, and the temperature of the cooling medium. Changing
the operating frequency has little influence on individual microdischarge
properties. The power dissipated in the discharge is determined by the ampli-
tude and frequency of the operating voltage. In connection with the cooling
circuit, it determines the average temperature in the discharge gap. Cylind-
rical as well as planar electrode configurations have been used. The majority
of commercial ozone generators use cylindrical electrodes forming narrow
annular discharge spaces of 0.5-1 mm radial width. The outer electrode is
normally a stainless steel tube, which is at ground potential and which is
--- Page 570 ---
Ozone Generation
555
Discharge Gap
Outer Steel
Cooling Water Flow
Fuses
Wiring
Figure 9.3.1. Configuration of water-cooled discharge tubes in an ozone generator.
water-cooled. These tubes have a length of 1--4 m. The coaxial inner electrode
is a glass or ceramic tube, closed at one side, and having an inner metal
coating as a high voltage electrode (figure 9.3.1), or a closed steel cylinder
which is covered by a dielectric layer (ceramic, enamel). The feed gas is
streaming in the axial direction through the annular discharge region
between the inner and outer tube. Each volume element of the flowing gas
is subjected to the action of many microdischarges and leaves enriched
with ozone.
9.3.4 Kinetics of ozone and nitrogen oxide formation
Any electric discharge in air or oxygen causes chemical changes induced by
reactions electrons or ions with N2, O2 or trace elements like H20 and
CO2 and subsequent free radical reactions. Extensive lists of possible reac-
tions have been collected, and reliable sets of rate coefficients have been
established (Krivosonova et a11991, Kossyi et a11992, Herron 1999, 2001,
Herron and Green 2001, Sieck et al 2001). As far as ozone formation is
concerned, extensive reaction schemes also exist (Yagi and Tanaka 1979,
Samoilovich and Gibalov 1986, Eliasson and Kogelschatz 1986a,b, Eliasson
et a11987, Braun et a11988, Peyrous 1990, Kitayama and Kuzumoto 1997,
1999). It turns out that ion reactions play only a minor role and that the
main trends can be described by tracing the reactions of the atoms generated
by electron impact dissociation of O2 and N2 and those of a few excited
molecular states.
9.3.4.1
Ozone/ormation in oxygen
In pure oxygen, which is actually used in many large ozone generation
facilities, ozone formation is a fairly straightforward process. Ozone
always originates from a three body reaction of oxygen atoms reacting
--- Page 571 ---
556
Current Applications of Atmospheric Pressure Air Plasmas
with 202 molecules:
0+ O2 + O2 -
0 3 + O2 -
0 3 + O2
(9.3.1)
where 0 3 stands for a transient excited state in which the ozone molecule is
initially formed after the reaction of an 0 atom with an O2 molecule. The
time scale for ozone formation in atmospheric pressure oxygen is a few
microseconds.
o is formed in reaction of electrons with O2 after excitation to the A 3~~
state with an energy threshold of about 6 eV and via excitation of the B 3~~
state starting at 8.4eV.
Fast side reactions, also using 0 atoms or destroying 0 3 molecules,
compete with ozone formation.
0+0+02 -
202
o + 0 3 + O2 -
302
OeD) + 0 3 -
202
o + 0 3 + O2 -
302 .
(9.3.2)
(9.3.3)
(9.3.4)
(9.3.5)
The undesired side reactions (9.3.2)-(9.3.5) pose an upper limit on the atom
concentration, or the degree of dissociation, tolerable in the microdischarges.
Since equation (9.3.2) is quadratic in atom concentration while the ozone
formation equation (9.3.1) is linear one would expect that extremely low
atom concentrations are preferable. Computations with large reactions
schemes show that complete conversion of 0 to 0 3 can only be expected if
the relative atom concentration [0]/[02] stays below 10-4 . There are other
considerations, however, that exclude the use of extremely weak micro-
discharges. If the energy density in a micro discharge and consequently also
the degree of dissociation is too low, a considerable fraction of the deposited
energy is dissipated by ions (up to 50%). Since ions do not appreciably
contribute to ozone formation this situation has to be avoided. A reasonable
compromise between excessive energy losses due to ions and best use of 0
atoms for ozone formation is found when the relative oxygen atom concen-
tration in a microdischarge reaches about 2 x 10-3 in the micro discharge
channel. This concentration can be obtained at an energy density of about
20mJ/cm-3 (Eliasson and Kogelschatz 1987). In this case energy losses to
ions are negligible and 80% of the oxygen atoms are utilized for ozone
formation. At zero ozone background concentration this leads to a
maximum energy efficiency of ozone formation corresponding to roughly
25%. The efficiency of ozone formation is normally related to the enthalpy
of formation, which is 1.48 eV /03 molecule or 0.82 kWh/kg. Thus 100%
efficiency corresponds to the formation of 0.6803 molecules per eV or
1.22 kg ozone per kWh. The indicated reaction paths requiring dissociation
of O2 first (dissociation energy: 5.16eV) puts an upper limit at 0.7 kg/kWh.
--- Page 572 ---
Ozone Generation
557
,:) .. ~----..... ---------,
to"
10-'
T_lsl
Figure 9.3.2. Evolution of particle species after a short current pulse: with zero ozone
background concentration (left) and at the saturation limit (right) (p = 1 bar, T = 300 K).
If the electron energy distribution in oxygen is considered, and the combined
actual dissociation processes at 6 and 8.4eV, this value is further reduced to
0.4 kg/kWh. The best experimental laboratory values obtained at vanishing
0 3 background concentration are in the range 0.25-0.3 kg/kWh.
The ozone concentration in the gas stream passing through the ozone
generator is built up due to the accumulated action of a large number of
microdischarges. With increasing ozone concentration back reactions gain
importance. In addition to the already mentioned reactions equations
(9.3.2)-(9.3.5), 0 3 reactions with electrons and excited O2 molecules have
to be considered. This finally leads to a situation where each additional
microdischarge destroys as much ozone as it generates (figure 9.3.2, right-
hand section). The attainable saturation concentration defined by this
equilibrium depends strongly on pressure and on gas temperature.
9.3.4.2
Ozone formation in dry air
In air the situation is more complicated. The presence of nitrogen atoms and
excited atomic and molecular species as well as the nitrogen ions N+, Nt, Nt
add to the complexity of the reaction system. Again, ions are of minor
importance for ozone formation. Excitation and dissociation of nitrogen
molecules, however, lead to a number of additional reaction paths involving
nitrogen atoms and the excited molecular states N 2(A 3~~) and N 2(B 3IIg),
that can produce additional oxygen atoms for ozone generation.
N +02 -
NO+O
N+NO----N2+O
N +N02 -
N20+O
N 2(A,B) +02 ---- N2 +20
N2(A) + O2 -
N 20 + O.
(9.3.6)
(9.3.7)
(9.3.8)
(9.3.9)
(9.3.10)
--- Page 573 ---
558
Current Applications of Atmospheric Pressure Air Plasmas
lime (s)
Figure 9.3.3. Evolution of particle species after a short current pulse in a mixture of 80%
N2 and 20% O2 simulating dry air (p = I bar, T = 300 K).
These oxygen atoms, generated in addition to those obtained from direct
electron impact dissociation of 02, contribute about 50% of the ozone
formed in air, which now takes longer, roughly about 1001lS. The result is
that a substantial fraction of the electron energy initially lost in collisions
with nitrogen molecules can be recovered and utilized for ozone generation
through reactions (9.3.6)-(9.3.10). In addition to ozone a variety of nitrogen
oxide species are generated: NO, N 20, N02, N03, and N 20 5. All these
species have been measured at realistic ozone generating conditions (Elias son
and Kogelschatz 1987, Kogelschatz and Baessler 1987). In the presence of
ozone only the highest oxidation stage N20 5 is detected in addition to the
rather stable molecule N20 (nitrous oxide, laughing gas). Figure 9.3.3
shows results of a numerical simulation using a fairly extended reaction
scheme in dry air (20% 02, 80% N2). The formation of ozone and different
NOx species due to a single short discharge pulse is followed for a reasonably
long time.
A few results demonstrating special characteristics of ozone generation
in air are added. The maximum attainable energy efficiency is reduced to
about to 0.2 kg/kWh and it shifted to higher reduced electric field values
(200-300 Td). This has to be expected because dissociation of N2 requires
higher electron energies.
The maximum attainable ozone concentration is lower and, surprisingly
enough, no saturation concentration exists. When the power is increased or
the air flow is reduced, the ozone concentration passes through a maximum
--- Page 574 ---
Ozone Generation
559
and then decreases again until it drops to zero. This effect, referred to as
discharge poisoning, was reported by Andrews and Tait (1860), only a few
years after Siemens had presented his ozone discharge tube. The poisoning
effect was correctly associated with the presence of nitrogen oxides. Today
we know that catalytic processes involving the presence of NO and N02
can use up 0 atoms at a fast rate thus preventing 03 formation and can
also destroy already formed ozone. This is a phenomenon that involves
only fast chemical reactions between neutral particles and has little influence
on electrical discharge parameters. Addition of 0.1 % NO or N02 to the feed
gas of an ozone generator can completely suppress ozone formation. In the
absence of ozone only NO, N02 and N20 can be detected at the exit. In
dry air the catalytic reactions leading to enhanced removal of 0 and 03
are as follows:
0+ NO + M -
N02 + M
(9.3.11)
0+N02
-NO+02
(9.3.12)
0+0
-02
(9.3.13)
and
0+ N03 -
N02 + O2
(9.3.14)
0+N02 -
NO+02
(9.3.15)
0+03 -202
(9.3.16)
These NOy reactions also playa dominant role in atmospheric chemistry
(Crutzen 1970, Johnston 1992).
9.3.4.3 Ozone formation in humid oxygen and air
The situation is further complicated if water vapor is present in the feed gas.
Even traces of humidity drastically change the surface conductivity of the
dielectric. At the same electrical operating conditions fewer and more intense
microdischarges result. In addition, a strong influence on major reaction
paths results from the presence of OH and H02 • The hydroxyl radical OH
is formed by electron impact dissociation of H20 and, in most cases more
importantly, by fast reactions of electronically excited oxygen atoms and
nitrogen molecules:
e + H20 -
e + OH + H
OeD) + H20 -
20H
N2(A 3~~) + H20 -
N2 + OH + H.
H02 is then formed in a reaction of OH radicals with ozone:
OH+03 -
H02 +02·
(9.3.17)
(9.3.18)
(9.3.19)
(9.3.20)
--- Page 575 ---
560
Current Applications of Atmospheric Pressure Air Plasmas
The presence of OH and H02 can limit ozone production in oxygen by intro-
ducing a further catalytic ozone destruction cycle:
OH +03 -- H02 +02
H02 + 0 3 -- OH + 202
In air an additional fast NO oxidation reaction occurs:
NO + H02 -- N02 + OH.
(9.3.21)
(9.3.22)
(9.3.23)
(9.3.24)
The main paths for NO removal in wet air are oxidation to N02 and fast
conversion to HN02 and HN03.
NO + OH + M -- HN02 + M
N02 +OH+M -- HN03 +M.
9.3.5 Technical aspects of large ozone generators
(9.3.25)
(9.3.26)
Large ozone generators use several hundred discharge tubes and now
produce up to 100 kg ozone per hour. In most water works several ozone
generators are installed. Figure 9.3.4 shows a photograph of the entrance
section of a large ozone generator. One can see the glass tubes mounted in
slightly wider steel tubes, the high voltage fuses at the center of each tube
Figure 9.3.4. Large ozone generator at the Los Angeles Aqueduct Filtration Plant.
--- Page 576 ---
Ozone Generation
561
and the electric wires connecting them. Depending on the feed gas, ozone
concentration up 5wt% (from air) or up to 18wt% (from oxygen) can be
obtained. Advanced water treatment processes utilize ozone at concentra-
tions up to 12 wt%. Depending on the desired ozone concentration the
energy required to produce 1 kg of 03 ranges from 7.5 to 10 kWh in
oxygen and from about 15 to 20 kWh in air. Information on the technical
aspects of ozone generation and ozone applications can be found in Rice
and Netzer (1982, 1984) or in Wojtowicz (1996).
9.3.5.1
Design aspects and tolerances
To obtain such performance several design criteria and operating conditions
have to be met. The desired small width of the discharge gap in the range 0.5-
1 mm puts severe tolerance limits on the diameters and on the straightness of
the cylindrical dielectric and steel tubes. It is essential that the inner dielectric
tube is perfectly centered inside the outer steel tube. Even a small displace-
ment results in a drastic drop of performance. Microdischarge efficiency,
heat removal and axial flow velocity depend strongly on the width of the
discharge gap, which must be kept in tight tolerances. Also the pressure
has to be kept close to the design value, about 2 bar in O2 and closer to
3 bar in air. For a given dielectric tube its optimum value depends on the
desired ozone concentration, the gap width, the temperature of the cooling
fluid, and the power density the ozone generator is operated at.
9.3.5.2
Feed gas preparation
The feed gas for most ozone generators is air or oxygen. In large installations
operating at high ozone concentrations and power density also O2 with a
small admixture of N2 is used. It is essential that the feed gas contains
only a few ppm H20 (dew point below -60 QC). As mentioned above,
humidity has a strong influence on the surface conductivity of the dielectric
and on the properties of the microdischarges. In addition, we observe the
changes in the chemical reaction scheme as described in section 9.3.4.3.
Also traces of other impurities like Hb NOx and hydrocarbons have an
adverse influence on ozone formation. Some of them lead to a catalytically
enhanced recombination of 0 atoms, others to catalytic ozone destruction
cycles.
These requirements necessitate a feed gas preparation unit to remove
humidity even if air is used. For this reason many large ozone installations
use oxygen as a feed gas. If cryogenic oxygen is used one has to be aware
of the fact that in polluted areas hydrocarbons may accumulate in the
liquid oxygen. Oxygen prepared by pressure swing or vacuum swing
adsortion-desorption techniques, on the other hand, is practically free of
hydrocarbons « 1 ppm).
--- Page 577 ---
562
Current Applications of Atmospheric Pressure Air Plasmas
9.3.5.3
Heat balance and cooling circuit
The ozone formation efficiency and the stability of the 0 3 molecule deterio-
rate at elevated temperature. As a consequence only non-equilibrium
discharges are suited for ozone generation and efficient cooling of the
discharge gap is mandatory. This is the reason why ozone generators are
essentially built like heat exchangers. The average temperature increase
due to discharge heating in the narrow annular discharge gap can be approxi-
mated by a simple formula. After a few cm of entrance length stationary
radial profiles of velocity and temperature are established. The radial
temperature profile is a half parabola with its maximum at the inner
uncooled dielectric tube if a uniform power deposition in the discharge is
assumed. The average temperature increase in the gap /~.Tg is then deter-
mined by the power dissipated in the discharge and the heat removed through
the cooled steel electrode and kept at the wall temperature Tw. Unfor-
tunately, only a minor fraction of the energy is used for ozone formation
(efficiency: 'f)).
(9.3.26)
In this formula d is the gap width, ). is the heat conductivity of the feed gas
(discharge plasma) and P / F is the power density referred to the electrode
area F. For efficient ozone generation, especially at higher 0 3 concentrations,
the temperature has to kept as low as possible, definitely below 100 oe. If a
second cooling circuit is used to additionally cool the inner tube, the average
temperature increase t::..Tg is reduced by a factor of four. This allows for a
considerable increase of power density. However, it is rarely done in
commercial ozone generators, because it requires cooling of the high voltage
electrodes and introduces additional sealing problems.
9.3.5.4
Power supply units
Originally ozone generators were run at line frequency or were fed by motor
generators operating at rather low frequencies. Step-up transformers are
required to reach the desired voltage level. To achieve reasonable power
densities, high voltages (up to 50 kV) had to be used. Dielectric failure was
a common problem. Since all tubes are connected in parallel, high voltage
fuses were used to disconnect faulty elements. Modern high-power ozone
generators take advantage of solid state power semiconductors. They utilize
thyristor or transistor controlled frequency converters to impress square-
wave currents or special pulse trains in the frequency range 500 Hz to
5 kHz. Using this technology, applied voltages can be reduced to the range
of about 5 kV. Dielectric failure is no longer a problem. With large ozone
generators power factor compensation has become an important issue.
--- Page 578 ---
Ozone Generation
563
Typical power densities now reach 1-lOkW/m2 of electrode area. Using
semiconductors at higher frequencies brought several advantages: increased
power at lower voltage, fast shut off and improved process control.
9.3.6 Future prospects of industrial ozone generation
A better understanding of microdischarge properties in non-equilibrium
dielectric barrier discharges and advances in power semiconductors resulted
in improved performance and reliability of industrial ozone generation in
recent years. Raised ozone generating efficiency and drastically reduced
size of the ozone generators helped to lower the cost. Today, ozone can be
produced at a total cost of about 2 US$/kg. Further progress can be
expected. Engineering efforts for superior dielectric properties, better flow
control and improved thermal management will continue. Rapid advances
in power semiconductor design resulting in improved GTOs (gate turnoff
thyristors) and IGBTs (insulated gate bipolar transistors) will have a
major impact. Encapsulated IGBT modules now switch 1000 A at 5 kV. It
is foreseeable that soon bulky step-up transformers will be no longer required
and that almost arbitrary wave forms can be generated. Investigations into
homogeneous self-sustained volume discharges may even lead to more
favorable plasma condition for ozone formation (Zakharov et al 1988,
Kogoma and Okazaki 1994, Nilsson and Eninger 1997).
References
Andrews T and Tait P G 1860 Phi. Trans. Roy. Soc. (London) 150 113
Boelter K and Davidsen J H 1997 Aerosol Sci. Techno!. 27689-708
Braun D, Kuchler U and Pietsch G 1988 Pure Appl. Chem. 60741-746
Braun D, Kuchler U and Pietsch G 1991 J. Phys. D: Appl. Phys. 24 564-572
Chen J 2002 Direct current corona-enhanced chemical reactions PhD thesis, Minneapolis,
University of Minnesota
Chen J and Davidson J H 2002 Plasma Chem. Plasma Process 22 199-224
Chen J and Davidson J H 2003a Plasma Chem. Plasma Process 2383-102
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Crutzen P J 1970 Quart. J. Roy. Meteor. Soc. 96 320-325
Eliasson Band Kogelschatz U 1986a J. Chim. Phys. 83279-282
Eliasson Band Kogelschatz U 1986b J. Phys. B: At. Mol. Phys. 19 1241-1247
Eliasson Band Kogelschatz U 1987 Proc 8th Int Symp on Plasma Chemistry (ISPC-8),
Tokyo 1987, vol 2, pp 736-741
Eliasson B, Hirth M and Kogelschatz U 1987 J. Phys. D: Appl. Phys. 20 1421-1437
Filippov Yu V, Boblikova V A and Panteleev V I 1987 Electrosynthesis of Ozone (in
Russian), (Moscow: Moscow State University Press).
Glaze W Hand Kang J W 1988 J. A WWA 88 57-63
Held Band Peyrous R 1999 Eur. Phys. J AP 7 151-166
Herron J T 1999 J. Phys. Chem. Ref Data 281453-1483
--- Page 579 ---
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Herron J T 2001 Plasma Chern. Plasma Proc. 21 581-609
Herron J T and Green D S 2001 Plasma Chern. Plasma Process 21459-481
Hoigne J 1998 'Chemistry of aqueous ozone and transformation of pollutants by ozona-
tion and advanced oxidation processes' in Handbook of Environmental Chemistry,
Vol 5, Part C: Quality and Treatment of Drinking Water II, Hrubec J (ed)
(Berlin: Springer) pp 83-141
Horvath M, Bilitzky L and Huttner J 1985 Ozone (New York: Elsevier Science Publishing)
Johnston H S 1992 Ann. Rev. Phys. Chern. 43 1-32
Kitayama J and Kuzumoto M 1997 J. Phys. D: Appl. Phys. 302453-2461
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Kogelschatz U 1988 'Advanced ozone generation' in Process Technologiesfor Water Treat-
ment Stucki S ed (New York: Plenum Press) pp 87-120
Kogelschatz U and Baessler P 1987 Ozone Sc. Eng. 9 195-206
Kogelschatz U 1999 Proc. Int. Ozone Symp., Basel, pp 253-265
Kogelschatz U 2000 'Ozone generation and dust collection' in Electrical Discharges for
Environmental Purposes: Fundamentals and Applications van Veldhuizen E M (ed)
(Huntington, NY: Nova Science Publishers) pp 315-344
Kogelschatz U and Eliasson B 1995 'Ozone generation and applications' in Handbook of
Electrostatic Processes, Chang J S, Kelly A J and Crowley J M (eds) (New York:
Marcel Dekker) pp 581-605
Kogoma M and Okazaki S 1994 J. Phys. D: Appl. Phys. 27 1985-1987
Kossyi I A, Kostinsky A Yu, Matveyev A A and Silakov V P 1992 Plasma Sources Sci.
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Krivosonova 0 E, Losev S A, Nalivaiko V P, Mukoseev Yu K and Shatolov 0 P 1991
'Recommended data on the rate constants of chemical reactions among molecules
consisting of Nand 0 atoms' in Reviews of Plasma Chemistry, Smirnov B M Ed
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Nilsson J 0 and Eninger J E 1997 IEEE Trans. Plasma Sci. 25 73-82
Ohlmuller W 1891 Ueber die Einwirkung des Ozons auf Bakterien (Berlin: Springer)
Peyrous R 1986 Simulation de ['evolution temporelle de diverses especes gazeuses creees par
['impact d'une impulsion etectronique dans ['oxygene ou de ['air, sec ou humide PhD
Thesis, Universite de Pau
Peyrous R 1990 Ozone Sci. Eng. 12 19-64
Peyrous R, Pignolet P and Held B 1989 J. Phys. D: Appl. Phys. 22 1658-1667
Pietsch G and Gibalov V 11998 Pure Appl. Chern. 70 1169-1174.
Rice R G and Netzer A 1982 and 1984 (eds) Handbook of Ozone Technology and Applica-
tions volland 2 (Ann Arbor: Ann Arbor Science Publishers)
Samoilovich V G and Gibalov V I 1986 Russ. J. Phys. Chern. 60 1107-1116
Samoilovich V G, Gibalov V I and Kozlov K V 1989 Physical Chemistry of the Barrier
Discharge (in Russian) (Moscow: Moscow State University Press) (English transla-
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Sch6nbein C F 1840 Compt. Rend. Hebd. Seances Acad. Sci. 10706-710
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Siemens W 1857 Poggendorfs Ann. Phys. Chern. 10266-122
Soret J L 1865 Ann. Chim. Phys. (Paris) 7 113-118
Wojtowicz J A 1996 'Ozone' in Kirk-Othmer Encyclopedia of Chemical Technology, (John
Wiley) 4th edition, vol 17, pp 953-994
Yagi S and Tanaka M 1979 J. Phys. D: Appl. Phys. 12 1509-1520
--- Page 580 ---
Electromagnetic Reflection, Absorption, and Phase Shift
565
Yehia A, Abdel-Salam M and Mizuno A 2000 1. Phys. D: Appl. Phys. 33 831-835
Zakharov A I, Klopovskii K S, Opsipov A P, Popov A M, Popovicheva 0 B, Rakhimova
TV, Samarodov V A and Sokolov A P 1988 Sov. J. Plasma Phy.\'. 14 191-195
9.4 Electromagnetic Reflection, Absorption, and Phase Shift
9.4.1
Introduction
The effect of plasma on electromagnetic (EM), wave propagation in the
ionosphere is well known and documented by Budden (1985) and Gurevich
(1978). A particularly striking example of plasma in air is the EM black out
and fluctuation of radar cross section (ReS), associated with re-entry
vehicles reported by Gunar and Mennella (1965) and discussed by Ruck
et al (1970, pp 874--875). A shock wave and resulting plasma develop
around a vehicle because of the increasing gas pressure and friction as it
descends from space. At an altitude of 200000 ft (60.9 km) and higher, a
5 GHz radar frequency is greater than the plasma frequency and the
momentum-transfer collision rate between electrons and the bulk gas, the
ReS corresponds to the bare skin value. At ",180000ft (55km), however,
the plasma frequency increases to approximately the radar frequency and
the ReS decreases up to 10 dB because of refraction from the plasma
enclosing the re-entry vehicle. At 150000ft (45.7km) the plasma frequency
is significantly greater than the radar frequency and an enhanced reflection
produces a net increase in ReS of 5-10 dB. At 60000 ft (18.3 km) the
atmosphere is significantly thicker, and the momentum-transfer collision
rate is ",9 x 109 s-1, which is roughly equal to the plasma frequency with
both exceeding the radar frequency. In this collision dominated plasma,
absorption dominates and the Res decreases approximately 15 dB. At
lower altitudes the re-entry vehicle slows, the plasma dissipates, and the
ReS returns to its bare skin value.
Another example is an artificial ionospheric mirror. Borisov and Gure-
vich (1980) and Gurevich (1980) suggest that a reflective plasma layer below
the D-layer could be generated at the intersection of two high-power EM
pulses. The utility of such a mirror is the ability to reflect radio waves at
frequencies above those supported by the ionosphere to great distances.
This would permit long range high-frequency point-to-point communication
and may even permit some radar to extend their range by bouncing their
signals off such mirrors.
In this section, EM effects based on a cold collisional plasma with a
spatially varying plasma density are discussed. The dispersion relation and
density profile theory is quantified, summary formulas for reflection, trans-
mission, absorption, and phase shift provided, air-plasma characteristics
--- Page 581 ---
566
Current Applications of Atmospheric Pressure Air Plasmas
quantified, electron-beam produced plasmas discussed, and typical applica-
tions described.
9.4.2 Electromagnetic theory
The theory of an EM wave propagating in air plasma is that of a wave propa-
gation in a cold collisional plasma. In this approximation ions are assumed to
be at rest compared to electrons. In the presence of a strong electric field it is
possible for a non-equilibrium system to develop with an electron, ion, and
bulk gas temperatures that are all different. The following material describes
a cold system where the contribution to electrical conductivity by ions is
small and has been neglected.
9.4.2.1
Cold collisional dispersion relationship
For wave propagation in an air plasma the effect of collisions between
electrons and the bulk gas is important. The Langevin equation of motion
for electrons includes the damping of electron motion due to momentum-
transfer collisions (Tanenbaum 1967),
du
me dt = -e(E + u X B) - mevu
(9.4.1)
where me is electron mass, u is electron velocity, e is electron charge, E is
electric field strength, B is magnetic field density, v is momentum-transfer
collision rate, and MKS units are used throughout. For propagation of
a transverse EM wave at frequency f through a collisional plasma, the
dispersion relation provides a succinct relation between angular frequency
w = 21Tf and a complex wavenumber k,
w
k(w) =-c
w2
1 -
p
w(w - iv)
(9.4.2)
where c is the speed of light, wp = (nei /come)1/2 is the plasma frequency,
i = +(_1)1/2, ne is electron density, e is electron charge, and co is the free-
space permittivity. Wave propagation is proportional to exp[+i(wt - kz)]'
where t is time and z is distance. For v = 0 in (9.4.2) the dispersion relation
reduces to a cold lossless dispersion relation with a cutoff frequency at w = wp.
For a lightly ionized collisional plasma with
Iw~/w(w - iv)1 « 1
equation (9.4.2) can be expanded and factored into real and complex parts,
W
wp
[
2]
kr(w) = C 1 - 2(J + v 2) ,
(9.4.3)
The value of kr is directly proportional to frequency. The leading term of kr
can be interpreted as ko = w/ c, which is the free-space wavenumber, but the
--- Page 582 ---
Electromagnetic Reflection, Absorption, and Phase Shift
567
first-order plasma term is proportional to both wand ne. Consequently, an
EM wave will encounter an impedance that depends on ne. If ne exhibits a
step-like change in number density there will be a coherent reflection. If
the change in ne is smooth and extends over several free-space wavelengths,
reflections along the smooth profile add incoherently and can be quite small.
The value of ki for w < v is effectively independent of frequency and so
implies that a collisional plasma is a broadband EM wave absorber. These
two processes of reflection and absorption are present in collisional plasmas
with the dominant effect depending on the profile for ne and the frequency of
observation.
9.4.2.3
Electron density profiles
The exact profile for ne depends on the plasma source and the intended
application. Large changes in ne over a distance of less than one free-space
wavelength generally result in a strong coherent reflection (often modeled
as a slab discontinuity), whereas the same change in ne over several wave-
lengths produces an incoherent reflection. Ruck et al (1970, pp 473--484)
describe a layered-media matrix approach that takes internal reflections
into account and can be applied to an arbitrary plasma distribution. The
values of ne and the momentum-transfer collision rate can change for each
layer and equation (9.4.2) is used to generate a complex wavenumber for
each frequency of interest. A few distribution functions for ne yield analytic
results. Budden (1985) provides analytic expressions for the reflection and
transmission coefficients for linear, piecewise linear, parabolic, Epstein,
and sech2 electron distributions. The Epstein distribution is used to model
a variety of plasma sources that generates a high electron density near the
source, which diminishes with distance from the source. The Epstein distribu-
tion is particularly useful in modeling the plasmas generated by a high-energy
electron beam or beta rays and photo processes that adhere to the Beer-
Lambert law such as photo-ionization.
10.3.2.3 Epstein distributions
Epstein (1930) discussed a general electron density distribution with three
arbitrary constants and wave propagation in absorbing media. Specific
wave solutions are discussed by Budden (1985). Vidmar (1990) adapt the
Epstein distribution to one suitable for modeling ionization sources. The
electron number density utilized is
no
n (z) - ----'------:--:-
- 1 + exp( -z/zo)
(9.4.4)
where Zo is a dimensional scale factor and no is the maximum electron
concentration for z ----* +00. Equation (9.4.4) varies from n(z = -(0) = no
--- Page 583 ---
568
Current Applications of Atmospheric Pressure Air Plasmas
to n(z = +00) = O. For a source that deposits energy over a finite distance,
it is possible to match n(z) at the 95% (z/zo = +2.944), 50% (z/zo = 0),
and 5% (z/zo = -2.944) values and so determine an approximate value
for zoo
9.4.2.3
Epstein's power reflection and transmission coefficients
Using the Epstein distribution in (9.4.4) for a wave incident at an angle e,
where e = 0 implies backscatter and e = 90° implies grazing incidence. The
power reflection, R, and transmission, T, coefficients are
R = IC - q121r[1 + ikozo(q + C)]1 4
C + q r[l + ikozo(q - C)]
4C2 I
r2[1 + ikozo(q + C)]
12
T = IC + ql2 r[l + 2ikozoq]r[1 + 2ikozoCJ exp[+2Im(koq)z]
2
2
2
wp
q = C -
---,----.!:.----:-
w(w - iv)
(9.4.5)
(9.4.6)
(9.4.7)
where C = cos e and q is a solution of the Booker quartic. For some atmos-
pheric plasma the arguments of the gamma functions become large, complex,
and produce an overflow condition. Lanczos (1964) provides an asymptotic
expansion for r and evaluation of In r avoids overflow.
9.4.2.4
Attenuation and phase-shift coefficients for an Epstein profile
In some applications, such as those relating to radar, the effects on signal
attenuation and phase path-length for round trip propagation through
plasma with reflection from a good conductor are of interest. Analytic
expressions are evaluated using the approximate values for k in (9.4.3) and
evaluating exp( +2i f kdz), where the integral is from z = -00 to the
reflective surface. For reference the integration of w~ is proportional to ne,
(9.4.4), and the integral of ne from z = -x to z = +x is nox. By noting
that the ionization source plasma was modeled by (9.4.4) from the 95-5%
values, the integration of f kdz is from free space for z = -2.944zo to
the conductive body and ionization source at z = +2.944zo. For
Iw~/w(w - iv) « 11 the round trip attenuation, A in dB, and the net phase
change, ~<p in radians, compared to free space propagation for a lightly
ionized collisional plasma simplify to
A(dB) = 4.343 (~) ( 2nov 2)
(9.4.8)
EomeC
w + v
(9.4.9)
--- Page 584 ---
Electromagnetic Reflection, Absorption, and Phase Shift
569
where h = 5.888zo is the thickness of the plasma distribution from its 5-95%
values. These analytic formulas are useful in generating estimates of absorp-
tion and phase shifts and provides insight on the functional dependencies of
A and ~<I> on no, h,f, and //.
9.4.3 Air plasma characteristics
The air chemistry for a plasma depends on many factors such as air density
determined from altitude, moisture content, electron density, present
populations of excited states, electron temperature, bulk gas temperature,
magnitude of electric field, and method of ionization. For production of
plasma without any external wire electrodes, a high-energy electron-beam
source is proposed. A 250 kV electron beam source, for example, is capable
of producing a plasma cloud that extends 1.5 m from its source at 30000 ft
(",9.l4km) altitude. Macheret et al (2001) investigated electron beam
produced air plasmas and quantified a return current from free space to
the source, due to charge transport by fast electrons. Their electric field
varies spatially, being most intense near the source. Consequently, the
plasma generated by an electron beam varies spatially in electron concentra-
tion, electric field, and electron temperature. The air chemistry production-
deionization solution must also treat these variations. Analytic air-chemistry
approaches are tedious due to the complexity and nonlinear aspects of the air
chemistry. Numerical approaches can easily involve hundreds of reactions to
model the air chemistry but provide useful estimates of plasma lifetime for
pulsed systems and estimates of power expenditure with curves of species
as a function of time for a variety of excitation waveforms.
9.4.3.1
Momentum-transfer collision rate
For an electron beam source an electric field may be present with sufficient
magnitude to elevate the electron temperature above thermal. Lowke
(1992) has investigated free electrons in air as a function of water-vapor
content and the reduced electric field E/N, where N is the bulk gas density.
The curves Lowke generated explicitly treat the effects of N2, O2, CO2, and
H20 as a gas mixture on the electron energy as a function of E / N. The
momentum-transfer collision rates in table 9.4.1 were deduced from Lowke
and appear as a function of altitude from sea level to 300000 ft
(",91.4 km). Atmospheric parameters of pressure, bulk gas density, and
temperature appear below each altitude.
9.4.3.2 Major attachment mechanisms
Electrons attach primarily to oxygen molecules in a three-body process,
Bortner and Baurer (1979) and Vidmar and Stalder (2003) for E/N
--- Page 585 ---
Table 9.4.1. Momentum transfer collision rate and atmospheric parameters.t
E/N
Momentum transfer collision rate (S-l)
Sea level
30 000 ft
60 000 ft
(9.14km)
(18.3 km)
764 torr
228 torr
54.8 torr
2.55 x 1019cm-3
9.58 x 1018
2.43 X 1018
V -cm-2
288.1 K
228.8K
216.6K
0.0
9.53 X IO lD S-l
3.58 X IO lD
9.09 X 109
1.0 X 10-19
9.53
3.58
9.09
5.0 x 10-19
1.31 X lOll
4.92
1.25 x IO lD
1.0 X 10-18
1.75
6.60
1.67
1.5 X 10-18
6.75
1.91 x 1011
4.90
1.0 X 10-17
7.25
2.63
6.72
1.5 X 10-17
1.11 X 1012
5.60
1.42 x 1011
1.0 X 10-16
1.94
8.41
2.13
1.5 X 10-16
3.31
1.24 x 1012
3.16
1.0 x 10-15
3.92
1.47
3.74
t 1962 US standard atmosphere
100 000 ft
200 000 ft
(30.5km)
(60.9km)
8.45 torr
149 x 10-3 torr
3.58 X 1017
5.86 X 1015
226.9K
244.6K
1.34 X 109
2.19x107
1.34
2.19
1.84
3.01
2.47
4.04
7.18
1.11 X 108
9.86
1.54
2.09 X IO lD
3.41
3.14
5.14
4.66
7.62
5.52
9.03
300000 ft
(91.4 km)
1.31 x 10-3 torr
5.91 X 1013
214.2K
2.21 X lOS
2.21
3.03
4.07
1.19 x 106
1.63
3.45
5.18
7.68
9.10 x 107
VI
-.l
o
()
;:::
....
....
~
;:: -
:.t..
~
:::-:
'"'
!:)
5·
;::
c.,
~
:.t..
§'
<::>
~
;::..
~
....
;::;.
"tI
....
~
c.,
c.,
;:::
....
~
:.t..
::;;.
"tI
is"'
~
!:)
c.,
--- Page 586 ---
Electromagnetic Reflection, Absorption, and Phase Shift
571
dependencies. The resulting O2 ion undergoes numerous charge-transfer
reactions, hydration, and eventually becomes N03 and N03·H20 prior to
negative-ion/positive-ion recombination. The rate for three-body attachment
of electrons to O2 depends on the altitude-dependent O2 concentration and
the E/N-dependent electron temperature. The extent to which O2 or N03
is the dominant ion depends on how long the plasma is generated. A typical
time scale for generation and deionization for an aircraft flying near the
speed of sound that generates then flies through a plasma cloud"", 1.5 m in
extent is "",5 ms. A time scale of several hundred microseconds to several
milliseconds typifies many plasma applications for aircraft.
9.4.3.3
lie plasma lifetime
The 1/ e plasma lifetime is the time for plasma that has been suddenly ionized
to an electron density of no to deionize to a value of no/ e. A set of curves that
quantifies plasma lifetime as a function of altitude and electron density
appears in Vidmar (1990) and quantifies electron densities, where the
dominant process for electron loss is three-body attachment to O2 with an
electron as the third body, three-body attachment with O2 as the third
body, and electron-positive ion recombination. These curves have been
extended to include an E / N dependency in Vidmar and Stalder (2003).
Plasma lifetime is shown to increase by approximately an order of magnitude
for 10-17 V cm -2 < E / N < 10-16 V cm -2. The increase in lifetime corresponds
to a decrease in the rate of three-body attachment for E / N > 10-17 V cm-2
predicted by Aleksandrov (1993). This trend towards longer lifetime reverses
for E / N ~ 10-16 V cm -2, when the reaction rate for dissociative attachment
to oxygen increases significantly and dominates the attachment process.
9.4.4 Plasma power
The energy deposited by an electron beam to generate an electron-ion pair in
dry air, Ej , is 33.7 eV. For a pulsed source a lower estimate of the power per
unit volume, P / V, is approximated by using Ej , the electron number density,
and the plasma lifetime:
P
nOEj
V
T
(9.4.10)
where no is the peak electron concentration and T is plasma lifetime. The
value of T as a function of altitude is quantified in Vidmar (1990) and
Vidmar and Stalder (2003). For example, an electron density of 1010 cm-3
at 30000ft (9.l4km) with E/N = 0 has a plasma lifetime of l57ns with
P / V = 343 m W Icm3 or 343 kW 1m3• Plasma lifetime is effectively indepen-
dent of electron number density below 1010 cm -3, because the dominant
electron loss mechanism is three-body attachment to O2, which is linear
--- Page 587 ---
572
Current Applications of Atmospheric Pressure Air Plasmas
with respect to electron concentration. Consequently, power is proportional to
no, and the total power is the integral of P / V over the electron distribution.
For plasma generated by an electron beam and sustained by an electric
field, the expression for power includes a term to account for louIe heating,
P = noEj +J.E
V
T
(9.4.11)
where J = aE is current density and (J is the plasma conductivity. Vidmar
and Stalder (2003) calculated plasma lifetime as a function of E / N for a
continuous electric field and quantified total power at 30000 ft (9.14 km).
Although louIe heating increases as the square of electric field strength,
the increase in plasma lifetime for 1O-17 Vcm-2 < E/N < 1O-l6 Vcm-2
results in a net decrease in total power from 343 to 230 m W jcm3 for a
plasma density of 1010 cm -3. This decrease in net power is also accompanied
by an increase in excited states with Oil ~g) reaching 8 x 109 cm-3 .
Additional research on power in air plasma involves continuous and
pulsed ionization to quantify the concentrations and effect of excited states
as a function of time. Because the energy deposited in plasma eventually
heats the bulk gas, the concentration of all species will decrease due to volu-
metric expansion. Over short intervals such as those for an aircraft in flight,
the generation of excited states under some conditions can significantly
reduce the concentration of ground state species. These two effects slow
the attachment process. The reaction rates for all the excited states on the
major attachment, detachment, and deionization processes are not well
known. Consequently, additional research, both theoretical and experi-
mental, is necessary to quantify total power deposition in air plasma as a
function of electron concentration, E / N, and altitude.
9.4.5 Applications
The application of collisional plasma for reflection, absorption, and phase
shift has been motivated by early investigations of the ionosphere (Epstein
1930). Reflection from plasma slabs with sharp discontinuities is well
understood and application to a surface radar for beam steering has been
investigated (Manheimer 1991). Reflections from an ionospheric mirror
have been advanced by Borisov and Gurevich (1980) and Gurevich (1980).
A set of curves that apply to an ionospheric mirror at 230000 ft (70.1 km)
appears in Vidmar (1990) based on the Epstein distribution and the profile
for n(z) in equation (9.4.4). These curves quantify the power reflection
coefficient at a shallow angle of 75° off broadside for an electron density of
107 cm-3 and v = 7.4 X 107 s-l. It was found that the power reflection
coefficient was 0.80 or greater for frequencies below 100 MHz and
Zo < 10 m. At higher frequencies or for Zo > 10 m the power reflection
coefficient decreased substantially. In terms of the profile in (9.4.4) the
--- Page 588 ---
Electromagnetic Reflection, Absorption, and Phase Shift
573
value of Zo = 10m implies the means of ionization must transition the air at
230000ft (70.1 km) from 5-95% of the maximum electron concentration
over a distance of h = 5.888zo = 58.88 m.
The use of microwave absorption as a diagnostic technique to determine
electron concentration is well known. Spencer et al (1987) experimentally
measured the amplitude and phase in a microwave cavity to quantify the
plasma lifetime, complex conductivity, and momentum-transfer collision
rate of an electron-beam generated plasma.
The application of the Epstein distribution to model collisional plasma
as a broadband absorber by Vidmar (1990) has curves of absorption versus
frequency and zoo These curves quantify total reduction, which refers to the
sum of the reflected power, R in equation (9.4.5), the round-trip absorption,
A in equation (9.4.9), and points out the power advantage of generating
plasma in a noble gas rather than air. The total reduction curves that
appear in Vidmar (1990) imply 10-40 dB signal reduction at frequencies
that extend from how> c/(4zo) and extends to fhigh < v/5. Physically, the
broadband reduction requires approximately five collisions per cycle and
the 5-95% gradient of the Epstein distribution, h = 5.888zo must be one to
two wavelengths at the lowest frequency. The total reduction noted transfers
of EM energy from a wave to heat via momentum-transfer collisions with the
bulk gas. This reduction in reflected power reduces the RCS for the surface
directly behind the plasma. The results of Santoru and Gregoire (1993)
provide an experimental link between the Epstein theory for reflection and
absorption with laboratory measurements.
Some radar systems utilize coherent integration over many cycles to
improve their signal-to-noise ratio. For such radars a sudden change in
phase interferes with the coherent integration and so degrades radar perfor-
mance. The phase change ~<I> in (9.4.9) can be used to quantify such effects in
terms of radar frequency, electron number density, collision rate, and Epstein
gradient.
For all of these applications the EM effects of plasma on reflectivity and
RCS are approximated by the Epstein distribution and the derived expressions
for reflectivity, transmission, absorption, and phase shift. The means to
achieve a man-made Epstein distribution in air all require power. The
means of plasma generation for a particular application that minimizes net
power required is not known at this time. Electron-beam generated air
plasma is a candidate system for some applications because it has a unique
excited-state air chemistry, the advantage that no wires are necessary in
the plasma, and that the beam energy controls the Epstein gradient. A
detractor on the use of electron beams is the problem of window heating
that limits beam current and duty cycle. This problem is addressed by
liquid cooling around the window or within the window (Vidmar and
Barker 1998), or by propagation from vacuum to air through a small
opening. Additional research on power required as a function of a
--- Page 589 ---
574
Current Applications of Atmospheric Pressure Air Plasmas
continuous or pulsed source, altitude, and electron concentration is neces-
sary to prove the utility of the electron beam approach.
References
Aleksandrov N L 1993 Chern. Phys. Lett. 212 409--412
Borisov N D and Gurevich A V 1980 Geomagn. Aeronomy 20587-591
Bortner M Hand Baurer T 1979 Defense Nuclear Agency Reaction Rate Handbook, 2nd
edition, NTIS AD-763699 ch 22
Budden K G 1985 The Propagation of Radio Waves, The Theory of Radio Waves of Low
Power in the Ionosphere and Magnetosphere (New York: Cambridge University
Press) 438--479
Epstein P S 1930 Proc. Nat. A cad. Sci. 16627-637
Gunar M and Mennella R 1965 Proceedings of the 2nd Space Congress-New Dimensions
in Space Technology, Canaveral Council of Technical Societies 515-548
Gurevich A V 1978 Nonlinear Phenomena in the Ionosphere, Physics and Chemistry in Space
vol 10 (New York: Springer) p 370
Gurevich A V 1980 Sov. Phy. Usp. 23862-865
Lanczos C 1964 J. SIAM Numer. Anal. Ser. B 1 86-96
Lowke J J 1992 J. Phys D: Appl. Phys. 25202-210
Macheret S 0, Shneider M N and Miles R B 2001 Physics of Plasmas 81518-1528
Manheimer W M 1991 IEEE Trans. Plasma Sci. PS-19 1228-1234
Ruck G T, Barrick D E, Stuart W D and Krichbaum C K 1970 Radar Cross Section Hand-
book vol 2 (New York: Plenum) 473--484 and 874-875
Santoru J and Gregoire D J 1993 J. Appl. Phys. 74 3736-3743
Spencer M N, Dickinson J S and Eckstrom D J 1987 J. Phys D: Appl. Phys. 20923-932
Tanenbaum B S 1967 Plasma Physics (New York: McGraw-Hill) 62-86
Vidmar R J 1990 IEEE Trans. Plasma Sci. PS-18 733-741
Vidmar R J and Barker R J 1998 IEEE Trans. Plasma Sci. PS-26 1031-1043
Vidmar R J and Stalder K R 2003 AIAA 2003-1189
9.5
Plasma Torch for Enhancing Hydrocarbon-Air Combustion
in the Scramjet Engine
9.5.1 Introduction
The development of the scramjet propulsion system [1-3] is an essential part
of the development of hypersonic aircraft and long-range (greater than 750
miles (1207 km)) scram jet-powered air-to-surface missiles with Mach-8
cruise capability [4]. This propulsion system has a simple structure as
required by the hypersonic aerodynamics. Basically, the combustor has the
shape of a flat rectangular box with both sides open. Air taken in through
the frontal opening mixes with fuel for combustion and the heated exhaust
--- Page 590 ---
Plasma Torchfor Enhancing Hydrocarbon-Air Combustion
575
gas at the open end is ejected through a MGD accelerator and a nozzle to
produce the engine thrust.
For the hydrocarbon-fueled scramjet in a typical startup scenario, cold
liquid JP-7 is injected into a Mach-2 air crossflow (having a static tem-
perature of ",500 K); under these conditions, the fuel-air mixture will not
auto-ignite. Instead, some ignition aid-for example a cavity flameholder
in conjunction with some mechanism to achieve a downstream pressure
rise--is necessary to initiate main-duct combustion. With sufficient down-
stream pressure rise, a shock front will propagate upstream of the region
for heat release. The heat release from combustion will maintain the pre-
combustion shock front, while subsonic conditions in the mixing and
combustion region favor stable combustion and flameholding.
Of course, even though the device operates as a ramjet under startup
conditions (i.e. subsonic flow downstream of the pre-combustion shock)
the residence time through the combustion region is short, of order 1 ms.
Within scramjet test facilities, the typical mechanisms for achieving the
required downstream pressure rise (and stable combustion) are the so-
called aero-throttle, where a 'slug' of gas is injected in the downstream
region, and the heat is released from the pyrophoric gas silane (SiH4).
Indeed, silane injection into the combustor is the current mechanism by
which the X43A scramjet vehicle is started. Both of these approaches,
however, have their disadvantages: for example, the aero-throttle approach
may not allow re-lighting attempts and silane poses obvious safety risks.
Thus, an alternative approach is desired.
For the purpose of developing techniques to reduce the ignition delay
time and increase the rate of combustion of hydrocarbon fuels, Williams
et al [5] have carried out kinetics computations to study the effect of
ionization on hydrocarbon-air combustion chemistry. The models being
developed-which include both the normal neutral-neutral reactions and
ion-neutral reactions-focus primarily on the development of plasma-
based ignition and combustion enhancement techniques for scramjet
combustors. The results computed over the 900-1500 K temperature range
show that the ignition delay time can be reduced significantly (three order
of magnitude over the 900-1500 K temperature range) by increasing the
initial temperature of fuel-air mixture.
Moreover, detailed kinetics modeling also shows a significant decrease
in ignition delay in the presence of initial ionization-in the form of a
H30+ INO+ Ie ~ plasma-at levels of ionization mole fractions greater than
1O~6. The ignition delay time is decreased most significantly at low tempera-
tures. Indeed, the computational results suggest that even larger effects may
be observed at the low temperatures encountered under engine startup.
Plasma torches can deliver enough heat to replace silane for ignition
purpose. Moreover, use of a torch as a fuel injector also introduces an initial
ionization in the fuel. The significant decrease in the ignition delay time and
--- Page 591 ---
576
Current Applications of Atmospheric Pressure Air Plasmas
Figure 9.5.1. A photo of the plasma torch module. (Copyright 2004 by IEEE.)
the initial energy carried by plasma may elevate the heat release from
combustion to exceed a threshold level for flameholding. These are the
primary reasons that plasma torches [6-8] are being developed for the appli-
cation.
Nevertheless, to make use of the high-temperature torch effluent, which
may include quantities of radicals, ions, and electrons, it is necessary to
project this gas into the engine in such a way that it readily mixes with a
fuel-air stream. Poor penetration of the torch plume into the combustor,
and/or improper placement of each torch-that is, more than one torch
may be required-will limit its effectiveness. Shown in figure 9.5.1 is a
photo of a plasma torch module, which is developed [9-10] in the present
effort for the generation of torch plasma. The unique features of this
plasma torch make it well suited for the purpose of ignition in a scramjet
engine. These features include the following.
1. The compact size. It can be easily mounted to the combustor wall and
requires no water cooling.
2. Flexible design. It can deliver high peak powers (and pulse/cycle energy)
in 60 Hz or pulsed modes. Furthermore, it can deliver high mass flow rates
due to the large annular flow area.
3. High mass flow operation. It can be configured to deliver 10 g offeedstock
(which can be the fuel) per second.
4. Durability. It can be run for long periods with an air feedstock.
5. High-voltage operation. Rather than running at high current, the torch
runs at high voltage, which allows greater penetration of the arc into
the combustor and reduces the power loss to the electrodes (leading to
--- Page 592 ---
Plasma Torch for Enhancing Hydrocarbon-Air Combustion
577
longer electrode life); higher E / N also enhances dissociations in fuel and
air by direct electron impact.
9.5.2
Plasma for combustion enhancement
In the combustion, fuel-air mixing is critical. Without oxygen, fuel will not
burn by itself. The hydrocarbon fuel provides hydrogen and carbon to
react with oxygen in the combustion process. The reaction rate increases
with the temperature of the mixture, which changes the ratios of the compo-
nents in the composition of the mixture. In low temperature, the gas mixture
contains mainly neutral molecules, and neutral-neutral reactions are often
immeasurably slow. For example, the rate coefficient for the reaction
between H2 and O2 is 6 X 10-23 cm3 S-I. As temperature increases, some radi-
cals such as atomic species are produced. Neutral-radical reactions have
rates in the range of 10-16_10- 11 cm3 S-I. For example, the reaction between
Hand O2 has a rate coefficient equal to 1 x 10-13 cm3 S-I. Reactions also
occur between radicals, which in fact have higher rates in the range 10-13_
10-10 cm3 S-I. Hence, the combustion rate is increased as the percentage of
radicals in the mixture becomes significant by the temperature increase. If
the temperature of the mixture is high enough to cause significant ioniza-
tions, the combustion rate is further enhanced. This is because ion-neutral
and ion-electron reactions have rates larger than 10-9 and 10-7 cm3 S-I,
respectively. For instance, the reaction Hi + O2 has a rate coefficient of
8 x 10-9 cm3 S-I. It turns out only long-range ion-electron and ion-dipole
reactions are fast enough to react on hypersonic flow time scales in the micro-
second range. Therefore, it is desirable to use energy to heat the mixture and
also to introduce ionized species to the mixture. Usually, thermal plasma is
not very energy efficient to introduce ionized species to the mixture. Non-
equilibrium plasmas produced by corona, streamer, pulsed glow and micro-
wave discharges have been suggested, as alternatives to the torch plasma, for
aiding the ignition. These discharges run at high E / N can potentially
enhance dissociations in fuel and air by direct electron impact [11], where
E is the electric field and N is the gas density. However, the practical issue
of the research efforts is the combustion efficiency, rather than the energy
efficiency of the igniter. The combustion efficiency depends not only on the
chemical processes but also on the spatial distribution of the plasma
energy, in particular, in a supersonic combustor. If the igniter can only
start the ignition locally, for instance, near the wall, a considerable percen-
tage of injected fuel will not be ignited before exiting the combustor. The
plasma torch presented in the following demonstrates that it can produce
high enthalpy supersonic plasma jet to penetrate the supersonic cross flow,
as required to be a practical igniter of a supersonic combustor.
Two types of power supply are applied to operate the torch module
shown in figure 9.5.1. One is a 60 Hz source, which sustains the discharge
--- Page 593 ---
578
Current Applications of Atmospheric Pressure Air Plasmas
periodically. Such produced plasma will be termed '60 Hz torch plasma' in
the following. This power source [12] includes (1) a power transformer
with a turn ratio of 1: 25 to step up the line voltage of 120 V from a wall
outlet to 3 kV, (2) capacitors of C = 3 IlF in series with the electrodes, and
(3) a serially connected diode (made of four diodes, connected in parallel
and each having 15kV and 750 rnA rating) and resistor (R = 4kO) placed
in parallel to the electrodes to further step up the peak voltage. The series
resistor is used to protect the diode by preventing the charging current of
the capacitor from exceeding the specification (750 rnA) of each diode and
to regulate the time constant of discharge. In one half cycle when the
diode is forward biased, the capacitor is charging, which reduces the avail-
able voltage for the discharge in the torch module. However, since the time
constant RC = 12 ms is longer than the half period 8.5 ms of the ac input,
the discharge can still be initiated during this half cycle (even though the
discharge has lower current and voltage than the corresponding ones in
the other half cycle). During this other half period, the diode is reversed
biased and the charged capacitor increases considerably the available voltage
and current for the discharge in the torch module. The torch energy (i.e. the
thermal energy carried by torch plasma) in each cycle varies with the gas
supply pressure Po. The dependence measured in the pressure range from
1.36 to 7.82 atm is presented in figure 9.5.2(a).
As shown, the dependence has a maximum at the gas supply pressure
Po = 6.12 atm, where the plasma energy is 25.6J. The increasing dependence
of the plasma energy on the flow rate in the region of low gas supply pressure
(i.e. Po < 6.12 atm) is realizable because the supplied gas flow works to
increase the transit time of charge particles by keeping the discharge away
from the shortest (direct) path between two electrodes. As the flow rate
increases, the transit time loss of charge particles is reduced and thus the
plasma energy increases. However, when the flow rate becomes too high
(i.e. Po > 6.12 atm), the mobilities of charge particles crossing the flow
becomes significantly affected by the flow. In such a way that the torch
energy decreases with increasing pressure. It is noted in figure 9.5.2(a) that
there is a significant plasma energy drop at Po = 4.08 atm. This unexpected
result may be explained as follows. Schlieren images indicate that a transition
from subsonic to supersonic flow at the exit of the module occurs near
Po = 3.4 atm, which was identified by the sudden appearance of the shock
structure at the exit of the torch nozzle in the schlieren image of the flowfield.
After the transition, the flow becomes underexpanded. At Po = 4.08 atm, the
low pressure region in the flow that favors gas breakdown is narrow in the
flow direction and close to the exit of the module. Thus the discharge channel
is narrow and the transit times of charge particles are small. Consequently,
the plasma energy is reduced. As the pressure is further increased, this low-
pressure region extends rapidly outward from the exit of the module so
that the discharge can again appear in a larger region.
--- Page 594 ---
Plasma Torchfor Enhancing Hydrocarbon-Air Combustion
579
30
f-O-i
.......
20
.......
~
.....
>+l
W
10
0
(a)
pO(atrr$
20
E
E
15
10
5
5
(b)
mm
Figure 9.5.2. (a) Dependence of the plasma energy in one cycle on the gas supply pressure
and (b) a planar image of torch plasma taken by an ultra-fast CCD camera with lOns
exposure to laser-induced fluorescence from NO molecules. (Copyright 2004 by IEEE.)
As a consequence of the high-voltage nature of the discharge, the arc
loop can be many times the distance between the anode and cathode. The
arc loop structure is illustrated in the image (typical of those recorded)
shown in figure 9.5.2(b), which was recorded through a 239nm interference
filter, 10 nm FWHM, with an intensified CCD camera (Roper Scientific
PIMAX) set for an 80 ns exposure time. The current loop is coincident
with the thin, intense emission loop shown in the figure. For this measure-
ment, pure nitrogen with a pressure of 1.7 atm was supplied to the torch
module. The horizontal extent of the arc loop is ca. 3.2 mm, whereas the
vertical extent is about 2.5 cm. Such an extended arc loop increases the
path length of the charged particles in the discharge by more than 15 times
the direct path length from the cathode to the anode. Also shown in figure
--- Page 595 ---
580
Current Applications of Atmospheric Pressure Air Plasmas
9.5.2(b) is laser-induced fluorescence (LIF) from nitric oxide, NO, obtained
using a Nd:YAG-pumped dye laser system to generate laser radiation at
226 nm probing the overlapped QI (12.5) and Q2(l9.5) transitions in the
8(0,0) band of NO. The LIF image appears as the diffuse, less intense
background and is best seen on the left-hand side of the figure towards the
outer portion of the arc loop. NO is produced within the torch plume in
the region where the hot torch gas (pure N2), i.e. the gas near the arc,
mixes with quiescent laboratory air. Thus, NO is formed primarily near
the outer portion of the arc loop.
The extended arc loop structure produced with this torch module has
several distinct advantages. For instance, such images indicate that high
temperature, dissociated, and ionized air extends well above the surface of
the torch module, which is important for ignition applications. The long
electrode lifetime may in part be due to extended arc length since the charged
particles' kinetic energy is reduced before hitting electrodes. Furthermore,
the conversion of electrical energy to plasma energy may be enhanced due
to the longer interaction region. Images such as that shown in figure 9.5.2(b)
indicate that the length of the arc loop is not strongly sensitive to the flow
rate, but the width of the loop becomes narrower as the flow rate increases,
which is consistent with the change in the flowfield structure as the jet becomes
underexpanded and supersonic with increased supply pressure.
The other power supply applied is a dc pulsed discharge source, which
uses a RC circuit for charging and discharging, where a 281lF capacitor is
used. A very energetic torch plasma, albeit one with a low repetition rate,
can be generated. In the circuit, a ballasting resistor R2 is connected in
series with the torch to regulate the discharging current and adjust the
pulse duration. Shown in figure 9.5.3(a) is a power function obtained by
connecting a resistor of R2 = 26 n in series with the torch. This power func-
tion has a peak of about 300 kW and a pulse length of about 800 IlS, which is
very close to the time constant R2C = 728Ils. The difference is accountable
from the effective resistance of the discharge. As R2 is increased to 250 n,
now the power function shown in figure 9.5.3(b) consists of two parts: an
initial part with a large peak of about 20 kW for the ignition of the discharge
and a subsequent near-constant low-power part keeping at about 2.5 kW for
10 ms, which maintains the discharge. The energy contained in the pulse is
about 50J.
Because torch plasma delivers adequate energy, it can be an ignition aid
and combustion enhancer within a scramjet engine.
9.5.3 Plasma torch for the application
The performances of plasmas produced by the torch module in a Mach-2.5
supersonic crossflow are discussed in the following. Measurements consist
of video images of the torch emission and of the flowfield schlieren. We
--- Page 596 ---
Plasma Torch/or Enhancing Hydrocarbon-Air Combustion
581
400
! 200
~
Go
01-_"""",1 '---__________ _
(a)
25
20
_ 15
1,0
5
-0.5
o
0.5
1
t(ms)
1.5
2
o
~-~5--~~~0~~~~5~~~~~,0~~~~,5
(b)
t(ms)
2.5
Figure 9.5.3. Power functions of pulsed dc discharges with no flow in the background; gas
supply pressure of the torch module is 2.72 atm. (a) R2 = 26 r! and (b) R2 = 250 r!.
note that due to the limited framing rate, 30 frames per second, these images
represent a temporal average during the frame time. Thus, one does not
freeze the arc-loop structure as was done with the intensified CCD (figure
9.5.2(b)). This is true regardless of whether one is viewing the 60 Hz or
pulsed discharge.
Experiments [13, 14] were conducted in the test section, measuring
38 cm x 38 cm, of a supersonic blow-down wind tunnel. The upstream flow
had a flow speed of 570 mis, a static temperature TI = 135 K, and a pressure
PI = 1.8 X 104 N/m2 (about 0.20 atm). These conditions approximate the
scramjet startup conditions listed earlier, though the temperature and
pressure are somewhat low (e.g. the static temperature for engine startup is
about 500 K). The torch plume is injected normally into the supersonic
flow, and the performance of torch plasma in terms of its height and shape
in the supersonic flow is studied. In experiments, the air supply pressure is
varied from 1.7 to 9.2 atm.
We first investigate the 60 Hz torch plasma in the wind tunnel. Presented
in figure 9.5.4(a) is an airglow image of the plasma torch produced in the
Mach-2.5 crossflow with 4.1 atm of air pressure supplied to the gas
chamber of the torch module. This image shows the typical shape of the
plasma torch in each half cycle; clearly, the supersonic flow causes significant
deformation in the shape of the plasma torch. The penetration height of
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Current Applications of Atmospheric Pressure Air Plasmas
E
E
o
20
90
(a)
mm
(b)
Figure 9.5.4. (a) Sideview of the airglow image of ac torch plasma in each half cycle in the
Mach-2.5 crossflow. The gas supply pressure of the torch module is 4.1 atm. In the insert,
d, = d)' = 11.4 mm define the horizontal and vertical scales of the image. (b) Shadow image
of the flow; an oblique shock wave is generated in front of the torch. (c) Airglow image of
pulsed dc torch plasma in a supersonic crossflow (about 10° off the sideview line); the field
of view is estimated to be 9.5 cm x 6 cm; the gas supply pressure of the torch module is
2.72 atm. (d) Schlieren image of pulsed dc torch plasma; the backpressure of the torch is
9.2 atm. (Copyright 2004 by IEEE.)
--- Page 598 ---
Plasma Torch lor Enhancing Hydrocarbon-Air Combustion
583
e e
o
10
20
30
Figure 9.5.4. (Continued)
(c)
(d)
the torch is reduced significantly as the plume is swept downstream by the
high-speed flow; nevertheless, the torch plume can still penetrate into the
supersonic crossflow by more than I cm and also extends downstream
about 1 cm, based on these emission images. A bow shock wave is also
generated in front of the torch (since the torch acts as an obstruction to
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Current Applications of Atmospheric Pressure Air Plasmas
the oncoming flow), as observed by the image presented in figure 9.5.4(b).
This, of course, is typical behavior for a jet injected normally in a supersonic
crossflow.
We next study the torch operation in the supersonic flow using the high-
power pulsed power supply. Shown in figure 9.5.4(c) is an airglow image of
the torch plasma in the supersonic crossflow; the supply pressure was 2.7 atm.
As shown in the figure, the (penetration) height of the torch is again reduced
considerably by the wind tunnel crossflow. Comparing with that shown in
figure 9.5.4(a), obtained in the case of higher gas supply pressure but lower
power, the one shown in figure 9.5.4(c) extends about five times as far in
the downstream direction and has a slightly larger penetration depth into
the crossflow.
Clearly, the increased discharge power produces larger volume plasma,
which is evident in comparing figures 9.5.4(a) and 9.5.4(c). To increase torch
penetration height in the wind tunnel, the air supply pressure was increased
to 9.2 atm. The resulting schlieren image is shown in figure 9.5.4(d). An
oblique shock wave is also generated in front of the torch as shown in this
schlieren image. The voltage and current of the discharge as well as the
shape and dimension of torch plasma vary with the torch flow rate and
the crossflow condition. The results show that in addition to increasing the
flow rate, one can increase the torch power to improve the penetration of
the plasma into the crossflow.
Initial evaluation of plasma-assisted ignition of hydrocarbon fuel was
conducted in a supersonic, Mach-2 flow facility, at Wright-Patterson Air
Force Research Laboratory, with heated air at a total temperature and
pressure of 590 K and 5.4 atm, respectively. The resulting static temperature
was thus ",330 K, still a relatively low value insofar as ignition is concerned.
This facility allows testing of an individual concept with both gaseous and
liquid hydrocarbon fuels without a cavity based flame-holder. In the tested
configuration, a 15.2 cm x 30.5 cm test section floor plate fits into a simulated
scram jet combustor duct with an initial duct height of 5.1 cm. At the
upstream edge of the test section insert, the simulated combustor section
diverges on the injector side by 2S. This particular hardware was intention-
ally designed not to study main-duct combustion (ignition of the entire duct),
but to reduce the chance of causing main-duct combustion by limiting the
equivalence ratio of the tunnel below 0.1. In particular, this was accom-
plished by placing the fuel injector at the centerline of the tunnel and not
adding any flame-holding mechanisms such as a cavity or backwards-
facing step. This approach allows the interactions of the fuel plume with
the plasma torch to be studied by itself, and any flame produced is strictly
created by this interaction, hence decoupling the ignition and flameholding
problems as much as possible from the combustor geometry. Tests have
been conducted using gaseous ethylene fuel, with the 15° downstream-
angled single hole.
--- Page 600 ---
Plasma Torchfor Enhancing Hydrocarbon-Air Combustion
585
Figure 9.5.5. Flame plume ignited by 60 Hz torch plasma with fuel injected by a single-hole
injector. (Copyright 2004 by IEEE.)
The 60 Hz plasma torch module was evaluated and was found to
produce a substantial flame plume as observed both from flame chemi-
luminescence and OH planar laser-induced fluorescence [14]. The flame
chemiluminescence (blue emission in the tail of the plume) is illustrated in
figure 9.5.5, which shows a single frame taken from video recordings of a
flame plume ignited by the 60 Hz plasma torch in operation 5 cm downstream
of the ethylene-fueled single-hole injector. Several feedstock flowrates
were tried over the torch module operational range and a flowrate of
",500 SLPM was determined to produce the largest visible flame for the
current electrode configuration. Air produced a larger flame when compared
to nitrogen as the torch feedstock. This difference in flame size indicates that
this type of flame is very sensitive to the local equivalence ratio and coupling
of the ignition source with the mixture.
Shown in figure 9.5.6 is a schematic of a conceptual Ajax vehicle and its
engine. The engine is located at the bottom of the vehicle. Plasma torch
modules are installed on the top wall of the box-shaped combustor right
Power Demanding ...... Excess energy
Payload
-
Power Conditioning
Plasma Generation and...----
Systems
Control Systems
Aerodynamic heat
Masnetoplasmochemlcal engine
~
Thrust
Figure 9.5.6. Schematic of a conceptual Ajax vehicle and the engine.
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Current Applications of Atmospheric Pressure Air Plasmas
behind the fuel injectors to work as igniters. The torch modules can also be
used as injectors to directly introduce ionizations and heat in the fuel for
reducing ignition delay. It is worth pointing out that shock waves generated
in front of torch plasma can help for holding flame and increasing its spread
to achieve thorough combustion.
References
[I] Gruber M, Jackson, K Mathur T, Jackson T and Billig F 1998 'A cavity-based fuel
injector/flameholder for scramjet applications' 35th JANNAF Airbreathing
Propulsion Subcommittee and Combustion Subcommittee Meeting, Tucson, AZ,
p 383
[2] Mathur T, Streby G, Gruber M, Jackson K, Donbar J, Donaldson W, Jackson T,
Smith C and Billig F 1999 'Supersonic combustion experiments with a cavity-
based fuel injector' AIAA Paper 99-2102, American Institute of Aeronautics and
Astronautics, Washington, DC, June 1999
[3] Gruber M, Jackson K, Mathur T and Billig F 1999 'Experiments with a cavity-based
fuel injector for scramjet application' ISABE Paper IS-7154
[4] Mercier R A and Weber J W 1998 'Status of the US Air Force Hypersonic
Technology Program' 35th JANNAF Airbreathing Propulsion subcommittee and
Combustion Subcommittee Meeting, Tucson, AZ, p 17
[5] Williams S, Bench P M, Midey A J, Arnold S T, Viggiano A A, Morris R A, Maurice
L Q and Carter C D 2000 Detailed Ion Kinetic Mechanisms For Hydrocarbon/Air
Combustion Chemistry, AFRL report 2000, Hanscom AFB, MA 01731-3010, pi
[6] Wagner T, O'Brien W, Northam G and Eggers J 1989 'Plasma torch igniter for
scramjets' J. Propulsion and Power 5(5)
[7] Masuya G, Kudou K, Komuro T, Tani K, Kanda T, Wakamatsu Y, Chinzei N,
Sayama M, Ohwaki K and Kimura I 1993 'Some governing parameters of
plasma torch igniter/flameholder in a scramjet combustor' J. Propulsion and
Power 9(2) 176-181
[8] Jacobsen L S, Carter C D and Jackson T A 2003 'Toward plasma-assisted ignition in
scramjets' AIAA Paper 2003--0871, American Institute of Aeronautics and
Astronautics, Washington, DC
[9] Kuo S P, Koretzky E and Orlick L 1999 'Design and electrical characteristics of a
modular plasma torch' IEEE Trans. Plasma Sci. 27(3) 752
[10] Kuo S P, Koretzky E and Orlick L 2001 Methods and Apparatus for Generating a
Plasma Torch (United States Patent No. US 6329628 BI)
[II] Parish J and Ganguly B 2004 'Absolute H atom density measurement in short pulse
methane discharge' AIAA Paper 2004--0182, American Institute of Aeronautics and
Astronautics, Washington, DC
[12] Koretzky E and Kuo S P 1998 'Characterization of an atmospheric pressure plasma
generated by a plasma torch array' Phys. Plasmas 5(10) 3774
[13] Kuo S P, Bivolaru D, Carter C D, Jacobsen L S and Williams S 2003 'Operational
Characteristics of a Plasma Torch in a Supersonic Cross Flow', AIAA Paper
2003-1190, American Institute of Aeronautics and Astronautics, Washington, DC
[14] Kuo S P, Bivolaru D, Carter C D, Jacobsen L S and Williams S 2004 'Operational
characteristics of a periodic plasma torch', IEEE Trans. Plasma Sci., February issue
--- Page 602 ---
Plasma Mitigation of the Shock Waves
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9.6 The Plasma Mitigation of the Shock Waves in
Supersonic /Hypersonic Flights
9.6.1
Introduction
A flying object agitates the background air; the produced disturbances
propagate, through molecule collisions, at the speed of sound. When the
object flight approaches the speed of sound (roughly 760mph in level
flight), those disturbances deflected forward from the object move too
slowly to get away from the object and form a sound barrier in front of
the flying object. Ever since Chuck Yeager and his Bell X-I first broke the
sound barrier in 1947, aircraft designers have dreamed of building a
passenger airplane that is supersonic, fuel efficient and economical. However,
the agitated flow disturbances by the flying object at supersonic/hypersonic
speed coalesce into a shock appearing in front of the object. The shock
wave appears in the form of a steep pressure gradient. It introduces a
discontinuity in the flow properties at the shock front location, at the
reachable edge of the flow perturbations made by the object. The back-
ground pressure behind the shock front increases considerably, leading to
significant enhancement of the flow drag and friction on the object.
Shock waves have been a detriment to the development of supersonic/
hypersonic aircraft, which have to overcome high wave drag and surface
heating from the additional friction. The design of high-speed aircraft
tends to choose slender shapes to reduce the drag and cooling requirements.
While that profile is fine for fighter planes and missiles, it has long dampened
dreams to build a wide-bodied airplane capable of carrying hundreds of
people at speeds exceeding 760 mph. This is an engineering tradeoff between
volumetric and fuel consumption efficiencies and this tradeoff significantly
increases the operating cost of commercial supersonic aircraft. Moreover,
shock wave produces a sonic boom on the ground. This occurs when flight
conditions change, making the shock wave unstable. The faster the aircraft
flies, the louder the boom. The noise issue raises environmental concerns,
which have precluded for, example, the Concorde supersonic jetliner from
flying overland at supersonic speeds.
A physical spike [1] is currently used in the supersonic/hypersonic object
to move the original bow shock upstream from the blunt-body nose location
to its tip location in the new form of a conical oblique shock. It improves the
body aspect ratio of a blunt-body and significantly reduces the wave drag.
However, the additional frictional drag occurring on the spike structure
and related cooling requirements limit the performance of a physical spike.
Also another drawback of a physical spike is its sensitivity to off-design
operation of the vehicle, i.e. flight Mach number and vehicle angle of
attack. A failure regime at aspect ratios less than one also prohibits the
practical uses of these physical spikes alone for shock wave modification.
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Current Applications of Atmospheric Pressure Air Plasmas
Therefore, the development of new technologies for the attenuation or
ideal elimination of shock wave formation around a supersonic/hypersonic
vehicle has attracted considerable attention. The anticipated results of
reduced fuel consumption and having smaller propulsion system require-
ments, for the same cruise speed, will lead to the obvious commercial gains
that include larger payloads at smaller take-off gross weights and broadband
shock noise suppression during supersonic/hypersonic flight. These gains can
make commercial supersonic flight a reality for the average traveler.
9.6.2 Methods for flow control
Considerable theoretical and experimental efforts have been devoted to the
understanding of shock waves in supersonic/hypersonic flows. Various
approaches to develop wave drag-reduction technologies have been explored
since the beginning of high-speed aerodynamics. In the following, a few of
these are discussed.
Buseman [2] suggested that geometrical destructive interference of shock
waves and expansion waves from two different bodies could work to reduce
the wave drag. However, the interference approach is effective only for one
Mach number and one angle of attack, which makes the design for practical
implementation difficult.
Using electromagnetic forces for the boundary layer flow control have
been suggested as possible means to ease the negative effect of shock wave
formation upon flight [3]. However, an ionized component in the flow has
to be generated so that the fluid motion can be controlled by, for instance,
an introduced j x B force density, where j and B are the applied current
density and magnetic field in the flow.
Thermal energy deposition in front of the flying body to perturb the
incoming flow and shock wave formation has been studied numerically [4, 5].
Heating of the supersonic incoming flow results in a local reduction of the
Mach number. This in turn causes the shock front to move upstream and
thus in this process the stronger bow shock is modified to a weaker oblique
shock with significantly lower wave drag to the object and much less shock
noise. Although this heating effect is an effectual means of reducing the
wave drag and shock noise in supersonic and hypersonic flows, it requires a
large power density to significantly elevate the gas temperature [5]. It is
known that using the thermal effect to achieve drag reduction in supersonic
and hypersonic flight does not, in general, lead to energy gain in the overall
process. Thus this is not an efficient approach for drag reduction purposes,
but it can be a relatively easy approach for sonic boom attenuation.
Direct energy approaches have also been applied to explore the non-
thermal/non-local effect on shock waves. Katzen and Kaattari [6] investi-
gated aerodynamic effects arising from gas injection from the subsonic
region of the shock layer around a blunt body in a hypersonic flow. In one
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Plasma Mitigation of the Shock Waves
589
particular case, when helium was injected at supersonic speed, the injected
flow penetrated the central area of the bow shock front, modifying the
shock front in that area to a conical shape with the vertex much farther
from the body (at about one body diameter). Laser pulses [7, 8] could
easily deposit energy in front of a flying object. However, plasma generated
at a focal point in front of the model had a bow radius much smaller than the
size of the shock layer around the model, and its non-local effect on the flow
was found to be insignificant.
Plasma can effectively convert electrical energy to thermal energy for gas
heating. Moreover, it has the potential to possibly offer a non-thermal
modification effect on the structure of shock waves. The results from early
and recent experiments conducted in shock tubes exhibited an increased
velocity and dispersion on shock waves propagating in the glow discharge
region [9, 10]. Measurements using laser beam photo deflection concluded
that the dispersion and velocity increase of shock wave were attributed to
the inhomogeneous plasma heating by the local electric field [11]. Plasma
experiments were also conducted in wind tunnels. When plasma was gener-
ated ahead of a model either by the off-board or on-board electrical discharge
[12-15] or microwave pulses [16, 17] the experimental results showed that the
shock front had increased dispersion in its structure as well as increased
standoff distance from the model. One of the non-thermal plasma effects
was evidenced by an experiment [18] investigating the relaxation time of
the shock structure modification in decaying discharge plasma. The observed
long-lasting effect on the shock structure was attributed to the existence of
long-lived excited states of atoms and molecules in the gas.
The study of the plasma effect on shock waves was further inspired by a
wind tunnel experiment conducted by Gordeev et al [19]. High-pressure
metal vapor (high Z) plasma, produced inside the chamber of a cone-
cylinder model by exploding wire by electrical short circuit, is injected into
the supersonic flow through a nozzle. A significant drag reduction was
measured [19]. A brief history of the development in this subject area was
reported in an article published in lane's Defence Weekly [20].
The research in plasma mitigation of the shock waves has two primary
goals:
1. to improve the effective aerodynamic shape of an aircraft, but without the
cooling requirements of a physical spike, and
2. to reduce the shock noise and possibly make net energy savings.
9.6.3 Plasma spikes for the mitigation of shock waves: experiments
and results
To further study plasma effects on shock waves, Kuo et al [21] have carried
out experiments in a Mach-2.5 wind tunnel. A cone-shaped model having a
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Current Applications of Atmospheric Pressure Air Plasmas
Figure 9.6.1. Plasma produced in front of the model, which is moving around the tip in
spray-like forms. (Copyright 2000 by AlP.)
60° cone angle was placed in the test section of the wind tunnel. The tip and
the body of the model were designed as two electrodes with the tip of the
model designated as the cathode for gaseous discharge. A 60 Hz power
supply was used in the discharge for plasma generation. The peak and
average powers of the discharge during the wind tunnel runs were measured
to be about 1.2kW and lOOW, respectively. Shown in figure 9.6.1 is the
airglow image of a spray-like plasma generated by the 60 Hz self-sustained
diffused arc discharge, at the nose region of the model, where the usual
attached conical shock is formed in the supersonic flow. The plasma density
and temperature of the discharge were not measured. However, the electrode
arrangement and the power supply were similar to those used in producing a
60 Hz torch plasma, which was measured [22] to have peak electron density
and temperature exceeding 1013 electrons/cm3 and 5000 K (time averaged
temperature [23] is less than 2000 K), respectively. During the run, the back-
ground pressure drops, thus the plasma density is expected to increase
slightly. On the other hand, the electron plasma is cooled considerably by
the supersonic flow. The produced spray-like plasma acted as a spatially
distributed spike, which could deflect the incoming flow before the flow
reached the original shock front location. The effect of this plasma spike
on the shock wave formation was explored by examining a sequence of
shadowgraphs taken during typical wind tunnel runs.
The shadowgraph technique is briefly described as follows. A uniform
collimated light beam is introduced to illuminate the flow. The second deriva-
tive of the flow density deflects the light rays to a direction perpendicular to
the light beam, which results in light intensity variation on a projection
--- Page 606 ---
Plasma Mitigation of the Shock Waves
591
(a)
(c)
(b)
(d)
Figure 9.6.2. A sequence of shadowgraphs taken during a wind tunnel run at Mach-2.S in
the presence of plasma. (a) At the instant close to initiating plasma, (b) at a later time
during the run, (c) at a later time during the same run, and (d) at the time when the
discharge is around the peak and the shock wave is eliminated. (Copyright 2000 by AlP.)
screen showing the shadow image of the flow field. Thus the location of a
stationary shock front in the flow, where the second derivative of the
density distribution is very large, is revealed in the shadowgraph as a dark
curve because the light transmitted through that region is reduced to a
mInImum.
In the shadowgraphs shown in figure 9.6.2 the flow is from left to right.
The upstream flow has a flow speed v = 570m/s, temperature T J = 135K,
and a pressure PI = 0.175 atm. Figure 9.6.2(a) is a snapshot of the flow at
the instant close to initiating the plasma. As shown, an undisturbed conical
shock is formed in front of the plasma-producing model. To further examine
the flow structure, a Pitot tube was installed in the tunnel, which can be seen
on the top portion of the shadowgraph with its usual detached shock front.
Figure 9 .6.2(b) taken at a later time during the run, on the other hand, clearly
demonstrates the pronounced influence of plasma on the shock structure.
Comparison of figures 9.6.2(a) and (b) clearly indicates an upstream
displacement of the shock front along with a larger shock angle, indicating
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Current Applications of Atmospheric Pressure Air Plasmas
a transformation of the shock from a well defined attached shock into a
classic highly curved bow shock structure. It is also interesting to note that
the shock in front of the Pitot probe, which is placed at a distance above
the plasma-producing model, has been noticeably altered as is evident
from the larger shock angle. A highly diffused detached shock front is
observed in figure 9.6.2(c) taken at a later time during the same run. The
diffused form of the shock front could be the result of less spatial coherency
in the flow perturbations introduced by the spatially distributed plasma; it
could also be ascribed to a visual effect from an asymmetric shock front
caused by the non-uniformity of the generated plasma, a well-known
integration effect inherent in the shadowgraph technique when visualizing
a three-dimensional flow field. This phenomenon is commonly observed
when the spatial extent of the region leading to the shock is small compared
to the test section dimensions.
Closer examination of figure 9.6.2(c) demonstrates a further upstream
propagation of the bow shock, having an even more dispersed shape and a
larger shock angle. It is also interesting to note that the shock wave in
front of the Pitot probe has also moved upstream and some evidence of
flow expansion may be seen near the tip of the probe. This is an interesting
result indicating that the effect of plasma is not confined to the vicinity of
the plasma-generating model but rather influences a large region of the
flow field. As a final example, figure 9.6.2(d) demonstrates the effectiveness
of the plasma in eliminating the shock near the model, an encouraging
result, which may have significant consequences in the effectiveness of this
scheme in minimizing wave drag and shock noise at supersonic speeds.
In summary, the experimental results represented by the shadowgraphs
(figures 9.6.2(b)-(d)) of the flowfield show that the spray-like plasma has
strong effect on the structure of the shock wave. It causes the shock front
to move upstream toward the plasma front and to become more and more
dispersed in the process (figures 9.6.2(b) and (c)). A shock-free state (figure
9.6.2(d)) is observed as the discharge is intensified.
A follow up experiment by Bivolaru and Kuo [24] further demonstrated
the plasma effect on shock wave mitigation. The experiment used a similar
truncated cone model except that the nose of the model has a 9 mm
protruding central spike, which also served as the discharge cathode. More-
over, the power supply was a dc pulse discharge source using RC circuits for
charging (Re = 10 kO) and discharging (Rd = 1500 to ballast the dischar-
ging current) and a 5 kV/400mA dc power supply to charge the capacitor
(C = 150IlF). It produced very energetic plasma with a low repetition rate.
The peak power exceeded 40 kW and the energy in each discharge pulse
was about 150J. Again, the plasma density and temperature were not
measured during the runs. However, from the current measurement, the
peak electron density is estimated to exceed 1014 electrons/cm3 . Without
the spike, a detached curved shock would be generated in front of the
--- Page 608 ---
Plasma Mitigation of the Shock Waves
593
(a)
Figure 9.6.3. (a) A baseline schlieren image of a Mach-2.5 flow over 60° truncated cone
(pin hole knife-edge of 0.2mm in diameter); the aspect ratio of the spike length I to the
spike diameter d, lid = 6, (b) video graph of the plasma airglow showing a cone-shaped
plasma around the spike of the model; and (c) schlieren image of the flowfield modified
by the cone-shaped plasma shown in (b). (Copyright 2002 by AlP.)
truncated cone model. The added spike with the selected length modified the
structure of the curved shock (which is the one intended to be modified by the
plasma) only in the central region around the spike, where the shock front
becomes conical and attached to the tip. This is seen in figure 9.6.3(a), a base-
line schlieren image of the flow field around the spike and the nose of the
cone; the flow is from left to right. The use of this design facilitates the
discharge (starting at the base of the truncated cone model) to move
upstream through the subsonic region of the boundary layer, along the
spike/electrode surface, so that plasma can always be generated in the
region upstream of the curved shock front (but it will appear behind the
oblique part of the shock front as shown later).
In the schlieren method, again, a uniform collimated light beam is
introduced to illuminate the flow. In addition, an obstruction (i.e. a light
ray selecting device) is introduced in the light path (e.g. a knife-edge placed
at the focal point of the image-forming lens). It uniformly decreases the
image illumination in the absence of any disturbance; however, when a
density gradient exists in the flow, only some rays will pass the obstruction
with a specific variation in the image illumination. The contrast of the
image will be proportional to the density gradient in the flow. When rays
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Current Applications of Atmospheric Pressure Air Plasmas
are deflected toward the knife-edge, the image field becomes darker (negative
contrast) and vice-versa. The images can be recorded directly by a CCD
camera, without going through an image projection screen. It is noted that
if too many rays are stopped, the image quality will deteriorate. Therefore,
the knife-edge must be adjusted with a compromise between image quality
and contrast.
Much more energetic plasma was generated by this pulsed dc discharge
than that generated by 60 Hz discharge in the other experiment. This spike
also guided the pulsed electrical discharge to move upstream such that
plasma was easily generated in the region upstream of the curved shock
front. As plasma was generated, it was found that the schlieren image of
the flowfield became quite different from that shown in figure 9.6.3(a). The
discharge was symmetric; it produced a cone-shaped plasma around the
spike of the model, as shown by the video graph in figure 9.6.3(b).
Comparing the corresponding schlieren image of the flowfield presented in
figure 9.6.3(c), again the flow is from left to right, with the baseline schlieren
image shown in figure 9.6.3(a), it is found that the original curved shock
structure in front of the truncated cone is not there any more. The
complicated shock structure in figure 9.6.3(a) is now modified to a simple
one displaying a single attached conical (oblique) shock similar to the one
generated by a perfect cone in the absence of plasma. In other words, it
seems that plasma has reinstated the model to a perfect cone configuration.
The wave drag to the model caused by oblique shock is much smaller than
that caused by the original bow shock.
This experiment has demonstrated that the performance of a small
physical spike on the body aerodynamics can be greatly improved by
generating plasma around it to form a plasma aero-spike, without increasing
the cooling requirement to that for a large physical spike. A change of the
shock wave pattern from bow shock dominated structure to oblique shock
structure is equivalent to an effective increase in the body aspect ratio
(fineness), from L/ D = 0.5 (blunt conical body) to L/ D = 0.85 (conical
body), by 1.7 times (70%). Although the modification on the shock wave
structure by this plasma aero-spike is characteristically different from that
by a spread-shaped plasma that causes the shock front to have increased
dispersion in its structure as well as standoff distance from the model, both
are effective in the mitigation of shock waves. Moreover, it was found, in
both experiments, that significant plasma effect on the shock wave was
observed only when two criteria were met: (1) plasma is generated in the
region upstream of the baseline shock front and (2) plasma has a symmetrical
spatial distribution with respect to the axis of the model.
Although experiments have clearly demonstrated that plasmas can
significantly modify the shock structure and reduce the wave drag to the
object, neither the physical mechanism nor a net energy saving from the
drag reduction were confirmed. More experiments are needed to resolve
--- Page 610 ---
Plasma Mitigation of the Shock Waves
595
these issues. Some of the facts deduced from the experimental results,
however, suggest that deflection of the incoming flow by a symmetrically
distributed plasma spike in front of the shock may prove to be a useful
process against shock formation.
The effect of plasma aerodynamics on the shock wave observed in
experiments may be understood physically. A shock wave is formed by
coherent aggregation of flow perturbations from an object. In the steady
state, a sharp shock front signified by a step pressure jump is formed to
separate the flow into regions of distinct entropies. The shock wave angle
(3 depends on the Mach number M and the deflection angle () of the flow
through a ()-~M relation, where (3 increases with (). Since the shock front
is at the far reachable edge of the flow perturbations deflected forward
from an object, flow is unperturbed before reaching the shock front. In
order to move the shock wave upstream, the flow perturbations have to
move upstream beyond the original shock front. An easy way is to start
the flow perturbation in front of the location of the original one by, for
instance, introducing a longer physical spike. The added plasma spike
serves the same purpose; it encounters the flow in the region upstream of
the location of the original shock front. It increases the deflection angle ()
of the incoming flow as well as the oblique angle (3 of the tip-attached
shock. As the discharge is intensified, the induced flow perturbations from
the plasma spike can be large enough to coalesce into a new shock front,
which replaces the original one located behind it. This is also realized by
the ()-(3-M relation. When the deflection angle of the flow exceeds the
maximum deflection angle in the ()-(3-M relation, then the oblique shock
in this region does not exist any more. Instead, the shock structure in this
region becomes curved and detached (figure 9.6.2(c)). The deflection
mechanism is also applicable for explaining the plasma effect shown in
figure 9.6.3(c). As shown in figure 9.6.3(b), on-board generated plasma
filled the truncated part of the model. It deflected the incoming flow as
effectively as a perfect cone. Because much less flow could reach and be
deflected by the frontal surface of the truncated cone, the original bow
shock was replaced by an oblique shock attached to the tip of this 'virtually
perfect cone'.
The shock front is also expected to appear in a dispersed form because
the effective plasma spike is distributed spatially and is not as rigid as the
tip of the model or a physical spike. In other words, the flow perturbations
by the plasma spike are less coherent as they coalesce into a shock and
consequently form a weaker new shock.
References
[I] Chang P K 1970 Separation of Flow (Pergamon Press)
[2] Buseman A 1935 'Atti del V Convegna "Volta'" Reale Accademia d'italia, Rome
--- Page 611 ---
596
Current Applications of Atmospheric Pressure Air Plasmas
[3] Kantrowitz A 1960 Flight Magnetohydrodynamics (Addison-Wesley) pp 221-232
[4] Levin V A and Taranteva LV 1993 'Supersonic flow over cone with heat release in the
neighborhood of the apex' Fluid Dynamics 28(2) 244-247
[5] Riggins D, Nelson H F and Johnson E 1999 'Blunt-body wave drag reduction using
focused energy deposition' AIAA J. 37(4)
[6] Katzen E D and Kaattari G E 1965 'Inviscid hypersonic flow around blunt bodies'
AIAA J. 3(7) 1230-1237
[7] Myrabo L Nand Raizer Yu P 1994 'Laser induced air-spike for advanced trans-
atmospheric vehicles' AIAA Paper 94-2451, 25th AIAA Plasmadynamics and
Laser Conference, Colorado Springs, CO, June
[8] Manucci MAS, Toro P G P, Chanes Jr J B, Ramos A G, Pereira A L, Nagamatsu
H T and Myrabo L N 2000 'Experimental investigation of a laser-supported
directed-energy air spike in hypersonic flow' 7th International Workshop on
Shock Tube Technology, hosted by GASL, Inc., Port Jefferson, New York,
September
[9] Klimov A N, Koblov A N, Mishin G I, Serov Yu L, Khodataev K V and Yavov I P
1982 'Shock wave propagation in a decaying plasma' Sov. Tech. Phys. Lett. 8
240
[10] Voinovich P A, Ershov A P, Ponomareva S E and Shibkov V M 1990 'Propagation of
weak shock waves in plasma oflongitudinal flow discharge in air' High Temp. 29(3)
468-475
[11] Bletzinger P, Ganguly B Nand Garscadden A 2000 'Electric field and plasma
emission responses in a low pressure positive column discharge exposed to a low
Mach number shock wave' Phys. Plasmas 7(7) 4341-4346
[12] Mishin G I, Serov Yu. Land Yavor I P 1991 Sov. Tech. Phys. Lett. 17413
[13] Bedin A P and Mishin,G I 1995 Sov. Tech. Phys. Lett. 21 14
[14] Serov Yu Land Yavor I P 1995 Sov. Tech. Phys. 40248
[15] Kuo S P and Bivolaru D 2001 'Plasma effect on shock waves in a supersonic flow'
Phys. Plasmas 8(7) 3258-3264
[16] Beaulieu W, Brovkin V, Goldberg I et al 1998 'Microwave plasma influence on
aerodynamic characteristics of body in airflow' in Proceedings of the 2nd
Workshop on Weakly Ionized Gases, American Institute of Aeronautics and
Astronautics, Washington, DC, p 193
[17] Exton R J 1997 'On-board generation of a "precursor" microwave plasma at Mach 6:
experiment design' in Proceedings of the 1st Workshop on Weakly Ionized Gases, vol
2, pp EE3-12, Wright Lab. Aero Propulsion and Power Directorate, Wright-
Patterson AFB, OH
[18] Baryshnikov A S, Basargin I V, Dubinina E V and Fedotov D A 1997
'Rearrangement of the shock wave structure in a decaying discharge plasma'
Tech. Phys. Lett. 23(4) 259-260
[19] Gordeev V P, Krasilnikov A V, Lagutin V I and Otmennikov V N 1996 'Plasma
technology for reduction of flying vehicle drag' Fluid Dynamics 31(2) 313
[20] 'Drag Factor' 1998 Jane's Defence Weekly (ISSN 0265-3818) 29(24) 23-26
[21] Kuo S P, Kalkhoran I M, Bivolaru D and Orlick L 2000 'Observation of shock wave
elimination by a plasma in a Mach 2.5 flow' Phys. Plasmas 7(5) 1345
[22] Kuo S P, Bivolaru D and Orlick L 2003 'A magnetized torch module for plasma
generation and plasma diagnostic with microwave', AIAA Paper 2003-135,
American Institute of Aeronautics and Astronautics, Washington, DC
--- Page 612 ---
Surface Treatment
597
[23] Kuo S P, Koretzky E and Vidmar R J 1999 'Temperature measurement of an
atmospheric-pressure plasma torch' Rev. Sci. Instruments 70(7) 3032-3034
[24] Bivolaru D and Kuo S P 2002 'Observation of supersonic shock wave mitigation by a
plasma aero-spike' Phys. Plasmas 9(2) 721-723
9.7 Surface Treatment
9.7.1
Introduction
Low-temperature non-equilibrium plasmas are effective tools for the surface
treatment of various materials in micro-electronics, manufacturing and other
industrial applications. The application of atmospheric pressure discharges
presents advantages such as plasma treatment with cheap gas mixtures,
low specific energy consumption and short processing time. Plasma pro-
cedures in chemically reactive gases are easy to control and, as dry processes
with low material insert, they are environmentally friendly.
The interaction of plasmas with surfaces can be systematized according
to the following definitions:
1. Etching means the removal of bulk material. The process includes
chemical reactions which produce volatile compounds containing atoms
of the bulk material. Sputtering is a physical process which removes
bulk atoms by collisions of energetic ions with the surface. Applications
are, for example, structuring in micro-electronics and micro-mechanics.
These processes are connected with a loss of a weighable amount of the
bulk substance.
2. Cleaning is the removal of material located on the surface which is not
necessarily connected with the removal of bulk material. This process is
applied, for example, in assembly lines as a preparation step for sub-
sequent procedures.
3. Functionalization leads to the formation of functional groups and/or of
cross links on the surface by chemical reactions between gas-phase species
and surface species/reactive sites and/or surface species (Chan 1994).
Grafting is a surface reaction between gas phase and polymer material.
The mass yield or loss in these processes is very small. Functionalization
changes, but mostly improves the wettability, the adhesion, lamination to
other films, the printability, and other coating applications. Biological
properties may be influenced too, for example, the probability of settle-
ments of cells or bacteria.
4. Interstitial modifications occur, for example, by ion implantation for the
hardening of metal surfaces.
5. Deposition of films of non-substrate material change the mechanical
(tribology), chemical (corrosion protection), and optical (reflecting and
--- Page 613 ---
598
Current Applications of Atmospheric Pressure Air Plasmas
Table 9.7.1. Plasma components and their efficiency in surface treatment (Meichsner
2001).
Plasma
Kinetic
component
energy
Ions, neutrals
~lOeV
Electrons
5-10eV
Reactive neutrals
Thermal
O.OSeV
Photons
>SeV (VUV)
<5eV (UV)
Processes and effects in the
material
Adsorbate sputtering, chemical
reactions
Inelastic collisions, surface
dissociation, surface ionization
Adsorption, chemical surface
reactions, formation of functional
groups, low molecular (volatile)
products
Diffusion and chemical reactions
Photochemical processes
Secondary processes
Depth of
interaction
Monolayer
~lnm
Monolayer
Bulk
100SOnm
11m range
decorative) properties of materials. For films that are not too thin the
mass yield is weighable. Systems of thin films with different electrical
properties are the basic essentials of micro electronics.
6. The depth scale of the different processes are as follows: etching 10-
100nm, functionalization 1 nm, coating 1O-1000nm (Behnisch 1994).
In reality these different processes are not strongly separated, e.g. cleaning may
include sputtering or functionalization. The efficiency of the various plasma
components in surface treatment is presented in table 9.7.1 (Meichsner 2001).
The dielectric barrier discharge (DBD) seems to be the most promising
plasma source for a plasma-assisted treatment of both large-area metallic
and polymer surfaces at atmospheric pressure. Investigations of the homoge-
neous DBD commonly known as 'atmospheric pressure glow discharge'
(APGD) (Kogoma et al 1998), and of the filamentary or disperse DBD
(Behnke 1996, Schmidt-Szalowski et a12000, Massines et a12000, Sonnenfeld
2001b) proved the applicability ofDBD for surface treatment techniques.
Special applications of DBD under atmospheric pressure exist in the
modification of large-area surfaces for the purpose of the corrosion
protection of metals and of an improvement of e.g. the wetting behavior of
polymers.
This modification of surfaces usually consists of three steps:
1. the cleaning of the bulk material of hydrocarbon containing lubricants
and other fatty contaminants,
2. especially for metals, the deposition of a stable oxide layer of a thickness
of some 10 nm as a diffusion barrier of the metallic bulk material, and
--- Page 614 ---
Surface Treatment
599
3. the deposition of a surface protecting thin layer (thickness of some
hundreds of nm) with a good adhesive characteristics of a primer coating.
The surface functionalization of polymers takes place after the cleaning
procedure.
The advantage of the surface treatment of metals by means of the DBD
plasma consists in the fact that all three sub-processes can run off successively
in the same plasma equipment (Behnke et al 2002).
The effect of plasma treatment depends on the energy input into the
process. For the energy flow on the mostly moving substrate, the dosage D
is used (Softal Report 151 E Part 2/3)
D = :v [~2]
where P is the power introduced into the discharge [W], s is the electrode
width [m], and v is the substrate velocity [m/s].
The power density L in the discharge volume is given by
P
L=Ej=-
[W/m3]
Aa
where E is the averaged voltage gradient inside the plasma [VIm], j is the
current density [A/m2], A is the electrode surface [m2] , and a is the gap
distance of the discharge [m].
The power density 0 on the electrode surface is defined by
O=~
[W/m2].
A
D is an important parameter to achieve desired surface properties, L charac-
terizes the plasma properties, 0 is a measure of the electrode strain. For a
resting substrate the dosage is given by the product of 0 and the treatment
time.
This section is organized as follows: it first deals with experimental
questions mainly oriented to the dielectric barrier discharge. The next part
is devoted to cleaning by atmospheric pressure discharges. Then oxidation
and functionalization are discussed, followed by plasma etching. The final
topic deals with coating of substrates by deposition of a thin film. Closing
remarks outline the advantages and limits of surface treatment by atmos-
pheric pressure discharges in air.
9.7.2 Experimental
Here are presented special investigations with typical parameters which are
used for surface cleaning, oxidation and thin film deposition (Behnke
2002). The DBD apparatus consists of two dielectric high-voltage electrodes
of rectangular cross section. The ceramic shell (AI20 3) of this hollow block is
--- Page 615 ---
600
Current Applications of Atmospheric Pressure Air Plasmas
gas flow
:
:
U {O ... 20kV)'
b
PTFEblock
.~.p .
(gas flow and electrode support)
banier profile
substrate
1,111'1 II :UI! .rrl;I}llllllllltI mill III [Ill II :Iilll !111, 11111; Ill: II r:IIIIIHIIIIIlIIllllldll] III 1:1
movable substrate electrode
c
Figure 9.7.1. Scheme of the DBD equipment for surface treatment with a dynamic
electrode arrangement.
about 0.1 cm thick, 2cm wide and l5-50cm long, and coated inside with a
silver layer for the electrical contacts.
The DBD operates within the region between the electrodes and the
substrate (grounded electrode) with a gap of 0.05-0.1 cm. The electrodes
are moved periodically along the substrate by a step motor. The effective
treatment time tp depends on the relative speed between the substrate and
dielectric electrodes vs, the length b and the number n of the electrodes and
the number of the moving periods p during the plasma process
tp = pnb/vs• The slit between the rectangular profiles is used to introduce a
laminar flow of the process gas mixture (air, vapors of silicon organic
compounds as hexamethyldisiloxane (HMDSO, (CH3hSiOSi(CH3h) and
tetraethoxysilane (TEOS, (CH3CH20)4Si)) into the discharge zone. To
reduce excess heating the electrode system as well as the substrate holder
are cooled by a flowing liquid. The DBD is driven by a sinusoidal voltage
of some 10 kV in a continuous or pulsed mode of frequencies between 5
and 50 kHz. For characterization of the experimental conditions the elec-
trical power absorbed in the discharge is measured.
A schematic view of the experimental set-up is given in figure 9.7.1. The
typical operating conditions during plasma treatment are represented in table
9.7.2. The cleaning and coating experiments are carried out with aluminum
plates (80 mm x 150 mm) and Si wafers for ellipsometric measurements of
the layer properties.
For the investigation of the cleaning process the substrates were covered
with defined quantities of oil (80-300 nm). For the deposition experiments
the substrates are chemically pre-cleaned and cleaned in the DBD in air
under atmospheric pressure with effective treatment times of about 100 s.
--- Page 616 ---
Surface Treatment
601
Table 9.7.2. Typical operation conditions during DBD-plasma treatment.
Cleaning
Oxidation
Deposition
Functionalization
Frequency (kHz)
10-25
10-25
6.6
0.050-125
Voltage (kV)
<15
<15
<15
3-50
Power (yV)
60-80
80
45
Power density (W cm-2)
2.2-3.0
3
1-1.6
Volume power density
20-60
30-60
10-30
(yVcm-3)
Dosage (Jjcm2)
5-10
5-10
50-80
1-300
Discharge gap (mm)
0.5-1.0
0.5-1.0
0.5-1.0
1-5
Process gas
dry air
dry air
N2 or dry air
Air
Reactive gas
0 220%
0 220%
TEOS 0.1 %
HMDSOO.l%
Gasfiow (slm)
1.6
1.6
1
1-10
Effect. treatment time (s)
<120
<600
<90
10-100
Mean residence time (s)
0.06
0.06
0.1
The time dependence of the oil removal and of the mass increase during the
oxidation phase as well as the deposition of SiOxCyHz coatings are measured
gravimetrically by weighing the samples with a micro-scale. The contami-
nated and cleaned substrates are quasi in-situ characterized ellipsometrically
by a spectroscopic polarization modulation ellipsometer (633 nm). The
thickness of the deposited Si organic layer is also measured gravimetrically.
The chemical composition of the substrate surface before and after
plasma treatment is studied by x-ray photoelectron spectroscopy (XPS)
and Fourier transform infrared (FTIR) spectroscopy. The surface morpho-
logical properties are investigated by scanning electron microscopy (SEM)
and contact angle measurements.
9.7.3 Cleaning
Metal surfaces are frequently covered with fats and oils in order to protect
them temporarily against corrosion and to improve their manufacturing
properties. For the following surface treatments this contamination must
be removed by wet-chemical cleaning procedures or by vapor cleaning tech-
niques using chlorinated and chloro-fluoro compounds. These processes are
critically estimated to be environmentally undesirable. A plasma-assisted
treatment operating at atmospheric pressure without greenhouse gases
represents an environmentally friendly economical alternative. Since for
such procedures no vacuum equipment is needed, they can be easily
integrated in process lines (Klages 2002).
Non-thermal atmospheric pressure air plasmas generate reactive oxygen
atoms and ozone, which easily react with organic compounds and produce
--- Page 617 ---
602
Current Applications of Atmospheric Pressure Air Plasmas
40 ~~
____ r-__ ~
____ ~
____ ~
____ r-__ ~
____ -r __
~1BO
D
35
30
25
2D
15
10
.oaOD--.o~
P /
----0---...0
/
o;;;;owing
-0- A
,
cilln Ilmple
\ I
y~""m;" ... "
-A-Y
~.A6A
____ AA-__ ~6~ ___ 6a----6----A
t[s]
160
140
120
100
BD
flO
I>
Figure 9.7.2. \IT and Ll during a whole cleaning process (633nm, PDBD = 80W) in
dependence on the effective treatment time in seconds.
volatile reaction products like CO, CO2 and H20. Air plasmas have been
tested for surface cleaning, especially of contaminated metal.
In order to understand the cleaning procedure in a DBD in air, the
erosion of oil contamination on silicon surfaces was investigated by ellipso-
metry and fluorescence microscopy (Behnke et aI1996a,b, Thyen et a12000,
Behnke et al 2002).
Figure 9.7.2 shows a typical plot of the ellipsometric angles \II and Do
versus treatment time, which was monitored during the whole cleaning
procedure (A = 633nm, DBD power 80W) of a contaminated Si wafer.
The ellipsometric angles were measured before and after the oil contamina-
tion (Wisura Akamin) (Behnke et al 2002).
The angles \II (decreases) and Do (increases) change considerably during
the surface treatment. In a short time they approach the values of pure
silicon. That means the purification process runs very fast « 10 s). However,
the initial values before the contamination are not reached, because the Si
surface properties were changed by oxidation.
More information about cleaning and the following oxidation process
is elucidated by spectroscopic ellipsometrical investigations. The layer
thickness d(t) and therefore the etching rate ret) are also evaluated from
the ellipsometrical data of the wavelengths between 1.5 and 4.5 eV by
means of the dispersion formula of Cauchy using model approximations.
The contamination thickness and etching rate decrease nearly exponentially.
--- Page 618 ---
100
80
~
60
&:: tj
:2 -
40
'0
20
0
o
Surface Treatment
603
•
oil thickness
0
etching rate
--model
d(t) = do *exp(-tlt)
r(t) = d d(t)/d t .. dJ't*exp(-tlt)
do = 105 nm
T = 2.64 5
5
treatment time [s]
•
10
40
30
CD g:
:j"
20 CQ
ii1 it
'S'
10~
o
Figure 9.7.3. Contamination thickness d and etching rate r versus treatment time for the
discharge power of SOW. Substrate: Si wafer.
The etching rate reaches values up to 40 nm s ~ 1• It decreases linearly with the
contamination thickness. An example for the exponential decay of thickness
and etching rate is given in figure 9.7.3. The following relations are valid:
d(t) = doe~t/T
r(t) = ladtl = dt
at
T
d(t) =! = const
r(t)
T
where T is a time constant which characterizes the cleaning process in
dependence on the discharge power and of the initial contamination do.
The same functional correlation is described by (Thyen et al 2000) for the
cleaning of contaminated Si wafers. A similar exponential temporal behavior
of the erosion of the contamination was determined from gravimetric
measurements on aluminum substrates (Behnke et al 2002) as well as from
fluorescence microscopic measurements on steel substrates (Thyen et al
2000).
In contrast to these results, cleaning investigations in rf oxygen low-
pressure discharges show a linear reduction of the contamination thickness
--- Page 619 ---
604
Current Applications of Atmospheric Pressure Air Plasmas
and thus a constant etching rate during the entire plasma process. Hence it
follows that in low-pressure discharges each sub-layer of the contamination
is removed with a constant rate.
One reason for the exponential behavior may be the statistical character
of the cleaning process. A single filament removes nearly all the contami-
nation from the sample within the relevant area. The temporal sequence of
the filaments is statistically distributed on the substrate. That means that
removed mass dm in the time interval dt is proportional to the mass m of
the contamination.
dt
dm=-m-.
T
The second reason is the polymerization of the lubricant for higher initial
thickness. That is clearly seen from the increase of the optical constants n
and k of the layer which is related to higher layer density. Also Thyen et al
(2000) explained the exponential decline of d(t) by initiation of polymeriza-
tion reactions of the oil.
An improved understanding will be achieved by studying the etching
process in the remote plasma outside the DBD. There the contaminated
metallic plate is not touched by filaments. Etching takes place only due to
active species which are produced by the discharge. Under these conditions
the etching rates are much lower and the process stops if the contamination
reaches about 20% of the initial thickness. That means the filaments are
essential for the cleaning process. Without filaments the polymerization of
the lubricant becomes the most preferred mechanism. In case of small
contamination thickness (l00-150nm) substrates can be completely cleaned
using any tested values of power. The time constants for the removal of the
contamination decrease approximately linearly with discharge power.
Contamination above 6 g m -2 could not be removed by a barrier discharge.
The cleaning rate r depends strongly on the oxygen content in the
process gas. Thyen et al (2000) found that in pure nitrogen the rate is over
ten times lower than in the air mixture. An admixture of 0.5% oxygen to
the process gas raises the rate in relation to that in pure nitrogen by a
factor around 3, but in pure oxygen this factor again decreases to 1.3. On
the other hand the removal rate increases in dependence on the gas flow. A
saturation is reached at a gas throughput of around 5 slm (Thyen et al
2000). With increasing flow rate more dismantling products of the hydro-
carbons in the exhaust gas stream are removed, because a higher flow
counteracts a reassembly of these products on the surface. The saturation
of the rate is achieved if the flux of broken hydrocarbon chains equals the
products removed by the gas flow (Behnke 1996b). Concerning the chemical
reactions of an air plasma with hydrocarbons the reader will be referred to
the discussion of the plasma-functionalization of polypropylene as an
example of hydrocarbons in section 9.7.5.
--- Page 620 ---
Surface Treatment
605
Becker and coworkers (Korfiatis et a12002, Moskwinski et a12002) have
been using a non-thermal atmospheric-pressure plasma generated in a
capillary plasma electrode configuration (Kunhardt 2000; see also chapter
2 of this book) to clean Al surfaces contaminated with hydrocarbons.
Efficient hydrocarbon removal of essentially 100% of the contaminants in
this discharge type was reported for plasma exposure times of only a few
seconds and contaminant films of up to 300 nm. Specifically, these
researchers have studied the utility of a plasma-based cleaning process in
removing oils and grease from Al surfaces both during manufacturing and
prior to the use of the Al in a specific application.
All these experimental investigations show that hydrocarbons can be
removed completely from metallic substrates by using an atmospheric
plasma in air. From the ellipsometric measurements on a silicon wafer it
was found that the residual contamination is in the order of one atomic
layer.
One important parameter for the characterization of the surface
cleanness is the specific surface energy, which is determined by means of
contact angle measurements of several liquids (Owen plot). After the
plasma cleaning procedure the total surface tension (67 mN/m) is very
high. For further treatment procedures the time behavior of the surface
tension is important. While the dispersive fraction does not change
(27 mN/m) the polar fraction decreases exponentially in time (time constant:
166 h). A high wettability of the cleaned surface remains stable for 24 h if the
energy dosage of the DBD plasma process is between 50 and 100Jcm-2 •
9.7.4 Oxidation
Metallic substrates (e.g. AI, Si, eu) are usually covered with a native, mostly
fragile oxide coating with a thickness of some nm during long storage in air.
This layer must be conventionally chemically eliminated in order to treat the
surface for corrosion protection. Afterwards the deposition of a stable
thicker oxide coating follows (e.g. Al20 3 on aluminum surfaces) which is
produced conventionally by a galvanic anodization. The plasma-supported
treatment will also win extra relevance in the future because of the polluting
disposal of galvanic baths.
In the example given in figure 9.7.2 the values of the initial ellipsometric
angles IT! and ~ of a silicon wafer without contamination cannot be reached
completely after the air plasma cleaning in a DBD. Moreover ~ decreases
again after reaching a maximum. The main reason for this is the oxide
growth on the substrate. This result is also confirmed by the XPS measure-
ments. The XPS spectra of an Al layer were measured before and after the
plasma treatment. Before treatment the intensity of the Al 2p peak reaches
20% of the oxide peak. After the treatment the oxide peak remarkably increases
and the Al 2p peak almost disappears (figure 9.7.4). An increase of the oxide
--- Page 621 ---
606
Current Applications of Atmospheric Pressure Air Plasmas
1170
1175
1180
1185
1500
before plasma
treatment
!'~\
aluminium
'3'
/ \l·
1000
\/
.!. 500
aluminium --... lr
... :
lit
oxyde
..
.
F
/
......
h-
~ 0 f-.L."'_"'f,,-~_
•• 1,,-J;4_· 'oIM
........ "..-'-~ ....... I._
......... _
......... ---1---'
.. _ ............
~-'-fr_
... L-t
1500
1000
500
o
after plasma
treatment
1170
1175
1180
~n(eV)
1185
Figure 9.7.4. XPS spectra of an aluminum layer deposited on a silicon wafer before and
after the air plasma treatment.
thickness from 3.2 to 8.6 nm is shown by angle resolved measurements. Figure
9.7.5 shows the increase of the weight of an AI-substrate in dependence on the
plasma treatment time (Behnke et aI2002). In both cases the thickness of the
oxide increases approximately proportional to 0.
Therefore oxide growth of the oxide is diffusion determined. Diffusion
coefficients of about 2-7 x 10-16 cm2 S-1 are estimated. These are typical
0.8
~mox' •• t. = mo(t - to)o .•
plasma treatment time t.,.,
C>
E 0.6
-
~
I/)
I/)
m
0.4
E 0.2
0.0
2
4
6
8
10
12
time I min
0
t •• ,:84s
• t.,., : 42 s
6
t.,., : 10 s
14
16
18
20
Figure 9.7.5. Increase of the weight after treatment of an aluminum surface with a DBD
(P = 80 W), parameter: plasma treatment time.
--- Page 622 ---
Surface Treatment
607
values for grain boundary diffusion (Wulff and Steffen 2001). The quality of
this oxide depends on the treatment time. If the samples are treated con-
tinuously for some minutes the oxide layer is rough. If the samples are treated
intermittently only for some seconds with breaks, no roughness can be
observed. For aluminum samples the thickness of the oxide reaches about
10 nm after some minutes.
The formation of an oxide layer (AI20 3, Si02) starts if the DBD is
filamented. The high local energy input by the individual filaments leads to
a restructuring of the natural oxide coating and to a local evaporation of
the bulk material (AI, Si).
The evaporated aluminum or silicon atoms are oxidized by the oxygen
atoms inside the DBD plasma and deposited as oxide on the surface. The
high current densities between 102 and 103 Acm-2 of an individual micro-
discharge causes a compaction of the deposited oxide coating. The local
evaporation of the bulk atoms is prevented by increasing oxide thickness
and the layer growth is finished. The oxide coating in filamentary air
discharge reaches a layer thickness of up to 10-20 nm. This process was
monitored by the time-dependent measurement of the aluminum resonance
line in a ferro-electrical barrier discharge. The relative line intensity
decreased exponentially with the treatment time (Behnke et at 1996b). In
summary it can be asserted that the DBD supported oxide coating is of a
high quality. It has a high density with small roughness.
9.7.5 Functionalization
One important task of functionalization is the improvement of adhesion
properties, e.g. for better printing and easier coating. Plastic foils, fibers
and other polymer materials are mostly characterized by non-polar
chemically inert surfaces with surface energies in the 20-40 mN/m range
(polyamide 43.0 mN/m, polyethylene 31.0 mN/m, polytetrafluorethylene
18.5mN/m). In general polymers are wetted by liquids when the surface
energy of the polymer exceeds the surface energy of the liquid. The surface
energy of common organic solvents is lower (toluene 28.4mN/m, carbon
tetrachloride 27mN/m, ethanol 22.1 mN/m) than that of the polymers,
therefore paint and inks based on organic solvents are successfully applied
to polymers. Environmental requirements call for a replacement by water-
based paints, inks, or bonding agents. Because of the high surface strength
of water (72.1 mN/m) a treatment of polymer surfaces is necessary to
improve their surface energy (Softal Report 102 E).
On the one hand low surface energy impedes surface contamination and
allows easy cleaning, but on the other hand it complicates printing, coating,
sticking, etc. The surface properties are determined by a thin layer of
molecular dimensions and can be changed without influencing the bulk
properties of the polymer. Various processes have been developed for surface
--- Page 623 ---
608
Current Applications of Atmospheric Pressure Air Plasmas
treatment to enhance adhesion, such as mechanical treatment, wet-chemical
treatments, exposure to flames, and plasma treatments in corona and glow
discharge plasmas. What is meant by corona discharge is explained in
chapter 6. In most cases the corona discharge for the polymer treatment is
a dielectric barrier discharge because the non-conductive, dielectric plastic
film inside the discharge gap is the barrier. Corona treatment is a well estab-
lished method. High-capacity systems have been developed and offered by
various manufacturers, and are applied to various synthetics. The principles
of the action of an air plasma on a polymeric material will be exemplified by
the case of polypropylene (PP). After this some characteristic examples for
recent activities in surface functionalization will be presented.
Dorai and Kushner (2002a,b, 2003) investigated in detail the processes
associated with surface functionalization of an isotactic polypropylene film
(0.05 mm thick) in an atmospheric pressure discharge in humid air. Industrial
equipment (Pillar Technologies, Hartland, WI) was used for the corona
treatment. The discharge is operated at a frequency of 9.6 kHz between a
ceramic coated steel ground roll and stainless steel 'shoes' as the powered
electrode, separated by a gap of 1.5 mm. The corona energy varied from
0.1 to 17 W s/cm2 . The relative humidity of the air flow in the discharge
region was either 2-5% or 95-100% at 25°C. The treated surface was
analyzed to determine its chemical composition by ESCA, its surface
energy by contact-angle measurements and its topology by AFM. Addition-
ally the molecular weight of water-soluble low-molecular-weight oxidized
material (LMWOM) was investigated. These materials can be separated by
washing of the surface in polar solvents like water and alcohols.
The untreated polypropylene surface is free of oxygen. The oxygen
content grows with increasing discharge energy. A significant decrease of
oxygen is observed after washing. A careful investigation of the LMWOM
shows an averaged molecular weight of 400 amu. These oligomers originate
from cleavage of the PP chain and contain oxidized groups such as COOH,
CHO, or CH20H. The molecular weight is independent on the discharge
energy and the humidity of air. Agglomerates of LMWOM are visible by
AFM.
The increase of the discharge energy is associated with a decrease as well
as of the advancing and receding water contact angle, that means increasing
wettability. The decrease of the advanced contact angle is much smaller for
washed samples than for unwashed.
For the treatment of PP in humid air plasma a model was developed
(Dorai and Kushner 2003). It includes gas phase chemistry with the forma-
tion of 0, H, OH radicals and 0 3 as important active species. Excited O2
molecules, N atoms and H02 need not to be taken into account because of
their lower reactivity towards PP. The reactivity of radicals with the PP is
different for the position of the C atom where the reaction occurs. Primary
C atoms are bound with only one C atom, secondary with two and tertiary
--- Page 624 ---
Surface Treatment
609
with three C atoms inside the polymer. The reaction probability is maximum
for the primary C atoms, decreases for secondary and is minimum for tertiary
C atoms. The surface reactions can be classified in analogy to polymerization
processes in initiation, propagation, and termination.
The initiation reaction is the abstraction of an H atom from the
polypropylene surface by an 0 radical
O(g) +
H
I
- CH2 C-CH2 -
I
CH3
or by an OH radical
H
I
OH(g) + - CH2- y-CH2 -
CH3
-
-CH-C-CH -
2
I
2
+
OH(g)
CH3
-CH-C-CH -
2
I
2
CH3
associated with the generation of an alkyl radical.
The propagation leads to peroxy radicals on the PP surface in a reaction
of the alkyl radical with O2:
O2 + -CH-C-CH -
2
I
2
CH3
Alkoxy radicals are formed by the reaction of 0 atoms with the PP alkyl
radicals:
Also reaction with ozone results in alkoxy radical formation:
o·
I
-CH-C-CH -
2
I
2
- CH2y-CH2 -
+
02(g)
CH3
CH3
The abstraction of a neighboring H atom of the PP surface by a peroxy
radical produces hydroperoxide:
O·
0'
I
-CH-C-CH -
2
I
2
CH3
H
I
+ -CH-C-CH-
2
I
2
CH3
O-H
0'
I
-CH-C-CH - +
2
I
2
CH3
The reaction of the alkyl radical with O2 may generate, as shown, new peroxy
radicals.
--- Page 625 ---
610
Current Applications of Atmospheric Pressure Air Plasmas
A scission of the carbon chain occurs via alkoxy radicals and leads to the
formation of ketones
-{
O·
I
- CH:zC-CH2-
I
CH3
or aldehydes:
H
o· H
I
I
I
-CH-C-C-C-CH -
-
2
I
I
I
2
CH3 H CH3
-CH-C-CH -
2 II
2
0
/CH3
-CH-C
2
~
0
H
I
-CH-C·
+
2
I
CH3
+
+
CH3
• CH2-
o H
II
I
C-C-CH -
I
I
2
H CH3
Alcohol groups are formed m reactions of alkoxy radicals with the
polypropylene:
O·
I
-CH-C-CH -
2
I
2
CH3
H
I
+ -CH-C-CH-
2
I
2
CH3
OH
I
-CH-C-CH -
2
I
2
CH3
+ -CH2"y-CH2-
CH3
Alkoxy radicals are generated by reactions of 0 and OH radicals:
OH
I
o{g) + - CH:zy-CH2-
CH3
OH
I
OH{g) + - CH:zy-CH2-
CH3
Termination reactions are
H{g) +
- CH:zC-CH2-
I
CH3
OH{g) + - CH:zC-CH2-
I
CH3
H I
OH{g) +
-CH-C-C=O
2 I
CH3
0-
I
- CH:zy-CH2-
+ OH{g)
CH3
O·
I
- CH:zC-CH2-
I
CH3
H I
-CH2-C-CH2-
I
CH3
OH
I
- CH:zC-CH2-
I
CH3
H OH
I
I
-
-CH-C-C=O
2 I
CH3
--- Page 626 ---
Surface Treatment
611
The reactions with OH result in the formation of alcohols and acids,
respectively.
These reactions illustrate some possibilities of radical production by
plasma reactions with a polypropylene surface. Reactions leading to cross
linking of the polypropylene matrix must also be taken into account in a
detailed description of the plasma-polymer interaction. The probabilities
of surface reactions of ultraviolet radiation and ions are supposed to be
small.
The surface reaction processes together with the reaction probabilities
or reaction rate coefficients are listed in table 9.7.3 (Dorai and Kushner
2003). The calculated values for the percentage coverage of the polypropy-
lene surface by alcohol (-C-OH), peroxy (-C-OO) and acid (-COOH)
groups accord well with experimental results (O'Hare et at 2002). This
successful approach indicates that in spite of the complexity the essential
processes of this plasma-surface interaction were comprehensible.
Table 9.7.3. Surface reaction mechanism for polypropylene (Dorai and Kushner 2003).
Reaction"
Probabilities or reaction rate
coefficientsb
Initiation
Og + PP-H -
PP* + OHg
10-3, 10-4, 10-5
OHg + PP-H -
PP* + H20 g
0.25, 0.05, 0.0025
Propagation
PP* + Og -
PP-O*
10-1, 10-2, 10-2
pp* + 02,g -
PP-OO*
1.0 X 10-3, 2.3 X 10-4, 5.0 X 10-4
PP* + 03.g -
PP-O* + 02,g
1.0, 0.5, 0.5
PP-OO* + PP-H -
PP-OOH + PP* 5.5 X 10- 16 cm2 S-1
PP-O* -
aldehydes + PP*
10 S-1
PP-O* -
ketones + PP*
500 S-1
Og + PP=O -
OHg + * PP=O
0.04
OHg + PP=O -
H20 g +* PP=O
0.4
Og +* PP=O -
CO2,g + PP-H
0.4
OHg +* PP=O -
(OH)PP=O
0.12
PP-O* + PP-H -
PP-OH + PP*
8.0 X 10-14 cm2 S-1
Og + PP-OH -
PP-O + OHg
7.5 x 10-4
OHg + PP-OH -
PP-O + H20 g
9.2 X 10-3
Termination
Hg + pp* -
PP-H
0.2, 0.2, 0.2
OHg + PP* -
PP-OH
0.2, 0.2, 0.2
"Subscript g denotes gas phase species, PP-H denotes PP.
b Those coefficients without units are reaction probabilities.
CommentC
C
C
C
C
C
C
C
c C = reaction probabilities for tertiary, secondary, and primary radicals, respectively.
--- Page 627 ---
612
Current Applications of Atmospheric Pressure Air Plasmas
The atmospheric plasma surface treatment of polypropylene was a
subject of various studies.
A comparison of the action of a homogenous N 2 barrier discharge and a
filamentary air discharge (Guimond et al 2002) shows that the maximum
surface energy 'Y is higher in the first than in the second one (N2:
'Y = 57 mN/m, E: 2.8 W s/cm2, air: 'Y = 39 mN/m, E: 0.6 W s/cm2), but
requires a higher specific energy input E. A rapid decrease of the surface
energy is observed during the first week of storage, but then the surface
energy is fairly stable for more than three months (N2: 'Y = 49 mN/m,
untreated film: 'Y = 27 mN/m).
The action of homogenous and filamentary DBD in various gases,
including air, on polypropylene was studied by (Mas sines et al 2001). Cui
and Brown (2002) studied the chemical composition of a polypropylene
surface during the air plasma treatment. Changes appear to terminate after
about 25% of the surface carbon is oxidized. Oxidation produces polar
groups like acetals, ketones and carboxyl groups which enhance the surface
energy.
A comparison of the treatment of several hydrocarbon polymers (poly-
ethylene PE, polypropylene PP, polystyrene PS and polyisobutylene PIB)
by air plasmas at atmospheric pressure of a silent or dielectric barrier
discharge and at low pressure (0.2 torr) of an inductively coupled
13.56 MHz discharge was presented by Greenwood et al (1995). The dielec-
tric barrier discharge between two plane Al electrodes with a gap of 3 mm
was driven by an operating voltage of 11 kV at 3 kHz. The samples on the
lower grounded electrode were treated for 30 s and investigated by x-ray
photoelectron spectroscopy and atomic force microscopy. Carbon singly
bonded to oxygen was found to be the predominant oxidized carbon func-
tionality for all polymers and discharges. The maximum amount of oxygen
is incorporated into polystyrene with its 7r bonds. DBD modification
increases the surface roughness of PP, PIB, and PS more than the low
pressure discharge. For PE a smoothing is observed. Atmospheric pressure
plasma treatment of polyethylene was studied also by Lynch et al (1998)
and Akishev et al (2002). The latter compare the results with polypropylene
and polyethylene terephthalate. The surface properties of polypropylene and
tetrafluoroethylene perfluorovinyl ether copolymer were investigated after
treatment in an atmospheric plasma pretreatment system with a discharge
distance of up to 40 cm, which is suitable for a large plastic molding, e.g.
an automobile bumper (Tsuchiya et al 1998). The increase of the water
contact angle with storage time after plasma treatment is explained by a
migration of oxygen from a very thin surface area into the inner layer.
Polyimide is an interesting material in the electronics industry for
flexible chip carriers. It is characterized by low costs, outstanding properties
such as flame resistance, high upper working temperature (250-320 0q, high
tensile strength (70-150 MPa), and high dielectric strength (22 kV /cm). The
--- Page 628 ---
Surface Treatment
613
application as a chip carrier demands a metallization with copper. The low
surface energy must be enhanced to improve the adhesion of copper. The
modification of po1yimide surface in a DBD in air is studied by Seeb6ck
et al (2000, 2001) and Charbonnier et al (2001). The DBD operates at
125 kHz between two plane copper or stainless steel electrodes which have
diameters between 0.6 and 2 cm and are separated by a gap of 0.1 mm.
There, the dielectric barrier is the polyimide film (thickness 50 or 38/lm).
The dielectric barrier discharge with a specific energy input of 3 x 103 W sf
cm2 leads to an increase of the surface roughness. For a polyimide foil
filled with small alumina grains (to improve thermal conductivity) a rough-
ness between 50 and 100 nm is measured. Microscopic inspection shows an
increasing number of alumina grains visible at the surface as a consequence
of the etching of the polymer. On the surface of the plasma-treated pure poly-
imide foil, crater-like structures are observed. The DBD in air at atmospheric
pressure is filamentary with ignition of the filaments at random spatial pos-
itions. The crater formation is assumed as a consequence of repeated ignition
of a filament at the same site. This surface roughness enables a metallization
with good adhesion (SeebOck et al 2001). An obvious enhancement of the
surface energy is observed after air plasma treatment. This is caused by the
formation of oxygen containing polar groups at the polyimide surface
(Seeb6ck et al 2000). XPS investigations demonstrate the increase of
oxygen concentration at the surface and show the opening of the aromatic
ring under the action of the plasma (Charbonnier et al 2001). This bond
scission in the imide rings is an important step in the plasma surface reaction
with aromatic polymers. For aliphatic polymers H atom abstraction is an
essential reaction step, as has been discussed for polypropylene above.
An example for air plasma treatment of a natural material refers to the
felt-resistant finishing of wool. By means of an atmospheric pressure barrier
discharge in air the content of carboxyl-, hydroxyl- and primary amino-
groups on the wool surface is increased. The resulting improved adhesion
to special resins enables a uniform and complete coating that leads to a
felt-resistance comparable with the results of the environmentally polluting
traditional procedures (VDI-TZ 2001, Rott et al 1999, Jansen et al 1999,
Softal Report 152 E).
Non-woven fabrics of synthetic material were successfully treated to
increase the surface energy by an air plasma at atmospheric pressure (Roth
et al 2001a). The treatment of metals was also reported. The removal of
mono-layers of contaminants is supposed to be the dominant process of
surface energy improvement (Roth et al2001 b).
9.7.6 Etching
Concerning the chemical processes, etching is closely related to cleaning,
especially if the removal of hydrocarbons or similar materials is studied.
--- Page 629 ---
614
Current Applications of Atmospheric Pressure Air Plasmas
Here examples will be presented of the plasma etching of photo-resists
supplemented by one example of plasma etching of Si-based materials and
the decomposition of soot in the diesel engine exhaust.
The etch rate of photo-resist on a silicon wafer in a He/02 mixture
placed on the powered electrode is investigated in an atmospheric pressure
dielectric barrier discharge (20-100 kHz, air gap 5-l5mm) (Lee et aI2001).
Both electrodes are coated with 50 11m polyimide. The grounded electrode
is additionally covered with a dielectric plate (thickness 8 mm) furnished
with capillaries to induce glow discharges. For a He/02 mixture (2.5 or
0.2 slm) 20.7 kHz, 10 mm air gap, and an aspect ratio of 10 average etch
rates up to 200 nm/min were obtained. In front of the capillaries an etch
rate >3 11m/min was observed.
The photo-resist etching in a dielectric barrier discharge in pure oxygen
is studied in dependence on the specific energy input (J/cm2 and J/cm3) with
the result that the DBD at atmospheric pressure is an alternative to low-
pressure plasma processing (Falkenstein and Coogan 1997).
To overcome the difficulties in surface treatment of thick samples or
samples with a complicated shape, spray-type reactors were developed
(Tanaka et aI1999). In a reaction gas Ar/02 (100: 1) ashing rates of organic
photo-resist of up to 111m/min were achieved.
The application of a barrier discharge in air (5-7 kHz, 8.5-11 kV, gap
width up to 1.5 cm) leads to etching rates of 270 nm/min (Roth et al
2001b). The appearance of vertical etching structures under such conditions
is observed.
The remote and active plasma generated in a pulsed corona (400 Hz
20 ns rise time, 30 kV) is tested for etching of a photo-resist coating on a
silicon wafer (air plasma, remote, 9 nm/min) and the removal of organic
films. Etching of the latter is more effective in the active plasma than
under remote conditions (Yamamoto et aI1995).
An increase of the etch rate of Si-based materials (Si02: 111m/min;
SiN: 211m/min; poly Si: 211m/min) by more than one order of magnitude
in relation to low-pressure plasma etching is observed in an atmospheric
pressure of 40.68 MHz discharge in an 02/CF4 (up to 1: 1) mixture (Kataoka
et aI2000).
An interesting application of plasma etching in an air discharge
concerns the soot decomposition in diesel engine exhaust (Muller et al
2000). The reactor operates with a dielectric barrier discharge (lOkVpp ,
'" 10 kHz, power on/power off: 3: 7, 1: 1, 3: 7) with an outer tube like
porous SiC ceramics electrode (width of the honeycomb channel 5.6 mm)
and an inner dielectric barrier electrode (4.2 mm diameter). The flue gas
from the diesel engine flows across the discharge gap and is afterwards
filtered by the porous outer electrode, leaving the soot particles on its surface.
They were decomposed either in the continuous mode or by a regeneration
procedure from time to time. More than 95% of the soot particles are
--- Page 630 ---
Surface Treatment
615
removed by the reactor and due to the soot decomposition on the surface a
continuous gas flow is achieved across the reactor.
9.7.7
Deposition
Investigations about plasma deposition with DBD have been performed on a
broad variety of films in the past ten years. The spectrum ranges from coat-
ings on plastic materials (e.g. polypropylene) for the improvement of the
long-term behavior of the wetting ability (Meiners et at 1998, Massines et at
2000) and hard carbon-based films (Klages et at 2003) up to layer systems for
the corrosion protection on metal surfaces (Behnke et at 2002, 2003, 2004,
Foest et at 2003, 2004). The kind of precursor used determines the function-
ality of the deposited layer. The precursors hexamethyldisiloxane (HMDSO,
(CH3)3SiOSi(CH3h) and tetraethoxysilane (TEOS, (CH3CH20)4Si) are
frequently studied in atmospheric plasmas concerning their applicability
for plasma-supported chemical vapor deposition of silicon-organic thin
films (Sonnenfeld et at 2001 b, Schmidt-Szalowski et at 2000, Behnke et at
2002, Klages et at 2003).
The decomposition of HMDSO and TEOS in the plasma of DBD is
controlled by electron impacts (Sonnenfeld et at 2001a,b, Basner et at
2000). The electron impact induced scission of Si-CH3 and/or the Si-O
bond of the HMDSO monomer is important for the layer deposition via
this precursor. The cleavage of the Si-O bond is the main reaction path of
the plasma chemical conversion of TEOS with the separation of
CH3-CH2-O- radicals. In further reaction sequences ethanol and water
are produced.
The silicon-organic polymer film is mostly deposited from nitrogen or
air DBD with an admixture of the silicon-organic precursor in the order
of 0.1% (see table 9.7.2).
The deposition occurs on the basis of small fragments of the silicon-
organic precursor. These radicals are adsorbed on the substrate surface.
For high energy dosage the gas phase reactions of the precursor and the inter-
action of the plasma with the surface leads to highly cross-linked films. The
films have good adhesion to the substrate surface, they are visually uniform,
and transparent. The films are chemically resistant and protect the substrate
against corrosive liquids (e.g. NaOH, NaCl, water). SEM images show that
damages of the substrate surface «350 m) are uniformly covered by the
films.
The thickness of the deposited silicon-organic polymer films are esti-
mated by gravimetric measurements under the assumption of a film mass
density of 1 g cm -3, also by XPS, SEM and interferometric measurements.
The average deposition rate strongly depends on the discharge power density
and on the structure of the DBD plasma. One example is presented in
figure 9.7.6. Up to the maximum of the deposition rate the DBD appears
--- Page 631 ---
616
Current Applications of Atmospheric Pressure Air Plasmas
Power density, W/cm2
340
1.0
1.2
1.4
1.6
1.8
3.6
320 L~
• i3.4 ~
300
13.2 ~
~ 280
iii
•
3.0 ~
:II 260
7~'
1""
c:
~ 240
film strudure
2.6~
:E
0
I- 220
2.4 5r
200
-.- deposition for 92 sec.
'2.2°
•
at speed of O.037cmlsec
~2.0
180
25
30
35
40
45
50
Power, W
Figure 9.7.6. Thickness and deposition rate ofSiO, polymer films versus discharge power,
effective deposition time 92 s, N2 DBD with admixture of 0.1 % TEOS.
quasi-homogeneous: in this discharge range the deposition is quasi-
homogeneously dispersed across the substrate. As long as the discharge
changes to the mode of stronger filamentation with higher power densities
the deposition rate describes a minimum. The film morphology alters to a
stripe-shaped structure on the substrate, possibly due to some turbulent
convection processes connected with the non-homogeneity of the discharge.
FTIR measurements were carried out on the substrate after plasma
treatment. Figure 9.7.7 shows spectra of films produced by an air plasma,
S
I::
~
'E
II)
I:: g
!E
C
1,1
1,0
0,9
0.8
0,7
0,6
----.. --.-.. --............. ---•...... -..... ~-----............ -.... .
.... .. _.' ........... _4 ... --_ ...... -....... - ........... -....... ... _...
.
.. ~ .... , : ..........
...... 0.1 % TEeS air
---'0.1 %TEeSAr
--0.1 % TEeS N2
,
I
~~¢
G"
Q ii5 .-
0,5 .h--~..;~~;;;:;:::::::::;::==~~cn~-~cnu
3500
3000
2500
2000
1500
1000
wave number I cm'1
Figure 9.7.7. FTIR spectra of SiO, polymer films deposited in air, N2 and Ar DBD with
precursor admixture of 0.1 % TEOS (P = 50 W).
--- Page 632 ---
Surface Treatment
617
a N2 plasma and an Ar plasma with 0.1 % TEOS admixture. The spectra are
dominated by a broad peak in the region of 1000-1250cm-1 which denotes a
macromolecular structure of the form (Si-Ox)n- The feature is more
broadened for the films produced with air- and Nz-containing plasmas,
indicating a slightly enhanced cross linking as compared to the Ar-based
film. The specific energy per precursor molecule is comparable in all three
cases, hence the effect is presumably caused by increased oxidation of the
film.
The (Si-OJn structure is overlapped by the prominent SiOx peak at
l240cm- l . Both features along with the very low carbon content (e.g. CH3
at 2950 cm -I) reveal the pronounced inorganic chemical nature of the film
indicative for rather high specific energies per precursor molecule. With
increasing specific energy the inorganic character of the film increases-a
common effect proven for several silicon-organic precursors, such as
HMDSO (Behnke et at 2002).
Different technical test procedures for the estimation of the adhesion of
a primer on the polymer layer and the determination of the corrosion protec-
tion properties of the coating show a sufficient effect only for substrate
temperatures above 40°C. With the dissociation of TEOS in the DBD,
ethanol and water are formed, which are linked into the layer without a
chemical bonding. The stoichiometric relationship of SiOx (x >::;j 2) thereby
is never reached and the layer does not become leak-proof. The water
stored in the layer withdraws with time and the residual hole-like laminated
structure decreases both the adhesion and the anti-corrosion properties of
the coating. The water entering the layer is avoided if the coating process
is performed at higher substrate temperatures. Layers, which are deposited
in a filamentary air DBD plasma, show a better adhesion and corrosion
protection effect in contrast to those which are coated by quasi-homogeneous
nitrogen DBDs. There will be also an improvement of these layer character-
istics, if the layer is deposited only by a one-cycle procedure as a 'mono' layer
in relation to a deposition in a multi-cycles procedure (Behnke et at 2003).
9.7.8 Conclusions
Atmospheric pressure plasmas are successfully implemented for various
surface treatment tasks. When comparing atmospheric-pressure plasma
processing with the well established low-pressure plasma processes, one
has to consider that the latter methods have been continuously developed
for more than 50 years. In contrast, the study of plasma processing at
atmospheric pressure on a broader scale has just begun.
The main advantage of atmospheric pressure plasma processing is that it
requires much lower investment costs, because no vacuum devices are
needed-in the case of ambient air, not even a housing. Hence, the implemen-
tation of devices into assembly lines with renouncement of batch procedures
--- Page 633 ---
618
Current Applications of Atmospheric Pressure Air Plasmas
is greatly facilitated. The majority of atmospheric plasmas such as DBD and
corona discharges are easily scaled up.
The low level of maturity is one of the disadvantages of atmospheric
pressure plasma processing in our day. Tailored plasma diagnostic tech-
niques have to be developed for an effective process control.
The state of the art atmospheric pressure plasma technology is holding
promising prospects from the economical and environmental point of view.
Therefore it is encouraging further research and development activities.
Acknowledgments
The financial support of our activities in the field of atmospheric pressure
discharges by the BMBF of Germany Project no. 13N7350/0 and
l3N7351/0 is gratefully acknowledged.
References
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Behnke J F, Steffen H, Sonnenfeld A, Foest R, Lebedev V and Hippler R 2002 'Surface
modification of aluminium by dielectric barrier discharges under atmospheric pres-
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Surface Treatment
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Chan C-M 1994 Polymer Surface Modification and Characterization (Munich: Carl
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Charbonnier M, Romand M, Esrom Hand Seebock R 2001 'Functionalization of polymer
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Cui N-Y and Brown N M D 2002 'Modification of the surface properties of a propylene
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Dorai R and Kushner M 2002a 'Atmospheric pressure plasma processing of polypropy-
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Dorai R and Kushner M 2002b 'Plasma surface modification of polymers using atmos-
pheric pressure discharges' 29th ICOPS Banff, Canada
Dorai R and Kushner M 2003 'A model for plasma modification of polypropylene using
atmospheric pressure discharges' J. Phys. D: Appl. Phys. 36 666-685
Falkenstein Z and Coogan J J 1997 'Photoresist etching with dielectric barrier discharges in
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Foest R, Adler F, Sigeneger F and Schmidt M 2003 'Study of an atmospheric pressure
glow discharge (APG) for thin film deposition' Surf Coat. Technol. 163/164 323-
330
Foest R, Schmidt M and Behnke J 2004 'Plasma polymerization in an atmospheric
pressure dielectric barrier discharge in a flowing gas' in Gaseous Dielectrics vol X,
ed. Christophorou L G (New York: Kluwer Academic/Plenum Publisher) in print
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polyisobutylene, and polystyrene' J. Adhesion Sci. Technol. 9 311-326
Guimond S, Radu I, Czeremuszkin G, Carlsson D J and Wertheimer M R 2002 'Biaxially
orientated polypropylene (BOPP) surface modification by nitrogen atmospheric
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Jansen B, Kummeler F, Muller H B and Thomas H 1999 'EinfluB der Plasma- und
Harzbehandlung auf die Eigenschaften der Wolle' Proc. Workshop Plasmaanwen-
dungen in der Textilindustrie Stuttgart, Germany, 17-23
Kataoka Y, Kanoh M, Makino N, Suzuki K, Saitoh S, Miyajima Hand Mori Y 2000 'Dry
etching characteristics of Si-based materials used CF4/02 atmospheric-pressure
glow discharge plasmas' Jpn. J. Appl. Phys. 39 294-298
Kersten H, Behnke J F and Eggs C 1994 'Investigations on plasma-assisted surface
cleaning of aluminium in an oxygen glow-discharge' Contr. Plasma Phys. 34 563
Klages C P and Eichler M 2002 'Coating and cleaning of surfaces with atmospheric
pressure plasmas' (in German) Vakuum in Forschung und Praxis 14149-155
Klages C P, Eichler M and Thyen R 2003 'Atmospheric pressure PA-CVD of silicon- and
carbon-based coatings using dielectric barrier discharges' New Diamond Front C
Tee 13175-189
Kogoma M, Okazaki S, Tanaka K and Inomata T 1998 'Surface treatment of powder in
atmospheric pressure glow plasma using ultra-sonic dispersal technique' Proc. 6th
Int. Symp. on High Pressure Low Temperature Plasma Chemistry (HAKONE VI),
Cork, Ireland, 83-87
Korfiatis G, Moskwinski L, Abramzon N, Becker K, Christodoulatos C, Kunhardt E,
Crowe Rand Wieserman L 2002 'Investigation of Al surface cleaning using a
novel capillary non-thermal ambient-pressure plasma' in Atomic and Surface
Processes eds Scheier P and Mark T D, University of Innsbruck Press (2002)
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Current Applications of Atmospheric Pressure Air Plasmas
Kunhardt E E 2000 'Generation of large-volume atmospheric-pressure, non-equilibrium
plasmas' IEEE Trans. Plasma Sci. 28 189-200
Lee Y-H, Yi C-H, Chung M-J and Yeom G-Y 2001 'Characteristics of He/02 atmospheric
pressure glow discharge and its dry etching properties of organic materials' Surface
and Coatings Technology 146/147 474-479
Lynch J B, Spence P D, Baker D E and Postlethwaite T A 1999 'Atmospheric pressure
plasma treatment of polyethylene via a pulse dielectric barrier discharge: Com-
parison using various gas composition versus corona discharge in air' J. Appl.
Polym. Sci. 71319-331
Massines F, Gherardi N and Sommer F 2000 'Silane based coatings on propylene. Depos-
ited by atmospheric pressure glow discharge' Plasmas and Polymers 5151-172
Massines F, Gouda G, Gherardi N, Duran M and Croquesel E 2001 'The role of dielectric
barrier discharge atmosphere and physics on polypropylene surface treatment'
Plasma and Polymers 6 35-49
Meichsner J 2001 'Low-temperature plasmas for polymer surface modification' in Low
Temperature Plasma Physics Hippler R, Pfau S, Schmidt M and Schonbach K
(eds) (Berlin: Wiley-VCH) 453-472
Meiners S, Salge J G H, Prinz E and Foerster F 1998 'Surface modifications of polymer
materials by transient gas discharges at atmospheric pressure' Surf Coat. Technol.
98 1112-1127
Moskwinski L, Ricatto P J, Babko-Malyi S, Crowe R, Abramzon N, Christodoulatos C
and Becker K 2002 'AI surface cleaning using a novel capillary plasma electrode
discharge' GEC 2002, Minneapolis, MN (USA), Bull. APS 47(7) 67
Muller S, Conrads J and Best W 2000 'Reactor for decomposing soot and other harmful
substances contained in flue gas' International Symposium on High Pressure
Low Temperature Plasma Chemistry, (Hakone VII), Greifswald, Germany,
Contr. Papers 2 340-344
O'Hare L A, Leadley Sand Parbhoo B 2002 'Surface physicochemistry of corona-
discharge-treated polypropylene film' Surface and Interface Analysis 33335-342
Roth J R, Chen Z, Sherman D M, Karakaya F, Tsai P P-Y, Kelly-Wintenberg K and Montie
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Roth J R, Chen Z Y and Tsai P P-Y 200 I b 'Treatment of metals, polymer films, and fabrics
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14391-407
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Schmidt-Szalowski K, Rzanek-Boroch Z, Sentek J, Rymuza Z, Kusznierewicz Z and
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Seebock R, Esrom H, Char bonnier M and Romand M 2000 'Modification of polyimide in
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Chemical Decontamination
621
Seebi:ick R, Esrom H, Charbonnier M, Romand M and Kogelschatz U 2001 'Modification
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9.8 Chemical Decontamination
9.8.1 Introduction
NOx gases are emitted from coal burning electric power plant, boilers in
factories, co-generation system and diesel vehicles. Some liquids and gases
such as trichloroethylene, acetone and fluorocarbon are useful for clean-up
of materials used in the semiconductor industry, for refrigerants, and so
--- Page 637 ---
622
Current Applications of Atmospheric Pressure Air Plasmas
on. However, recently, it has been noticed that these are harmful to human
health. These must be processed for global environmental problems.
Concerning NOx processing, selective catalytic reductions (SCRs)
have been used. Soot and S02 exhausted from diesel engines prevent the
conventional SCR from removing NOr Non-thermal plasmas (NTP) are
attractive for decomposing these gases because the majority of the electrical
energy goes into the production of energetic electrons with kinetic energies
much higher than those of the ions or molecules. Energetic electron impact
brings about the decomposition of the harmful gases or induced radicals
facilitate the decompositions.
In this section, removal of the harmful gases by NTPs is discussed. In
sections 9.8.2-9.8.4, mainly de-NOx processes and kinetics, instrumentation
and influencing parameters for de-NOy will be treated. In section 9.8.5,
processing of environmentally harmful gases such as halogen gases, hydro-
carbons, and chlorofluorocarbon removed by NTPs will be presented.
9.8.2 de-NO x process
Decomposition of NOx to their molecular elements (N2 and O2) is the most
attractive method. However, it is seen that the major mechanism of NOx
removal is oxidation to convert NO into N02 as shown in figure 9.8.1 for
NO/N2/02 without water vapor. First, N2 and O2 collide with energetic
electrons in the NTP to generate ions, excited species and radicals, in
which oxygen related species such as 0, O2 and 0 3 mainly contribute to
convert NO into N02. In the case of exhaust gases, including air with
water vapor, not only oxygen related radicals but also hydroxyl radicals
(OH radicals) are produced and contribute to oxidize NO to N02. However,
in these systems, NO is only oxidized to N02, directly or indirectly, by these
radicals. As a result, the net reduction of NOx (NO + N02) remains
unchanged. Gases such as ammonia, H20 2, hydrocarbon, N2H4, hydrogen
and catalyst as additives are used to dissolve N02. The case that ammonia
is added into the NO stream field is shown in figure 9.8.2. NO is converted
into N02 by hydroxyl and peroxy radicals as well as oxygen radicals. N02
Figure 9.S.1. NO/N2/02 system without H20.
--- Page 638 ---
Chemical Decontamination
623
I RNO I
NO
oa~~tHj
Figure 9.8.2. NOjN2j02 system with H20 and NH3 as an additive.
reacts with OR to form RN03 and, further, NR4N03 is produced by the
reaction between RN03 and ammonia. When ammonia is subjected to elec-
tron impact in NTP, ammonia radicals are generated. This reaction scheme is
shown in figure 9.S.3. NO reacts with ammonia radicals (NR3, NR2 and NR)
Figure 9.8.3. NOjNH3 system.
--- Page 639 ---
624
Current Applications of Atmospheric Pressure Air Plasmas
I CH41
e
0
NO
O2
~
NO
NO
Figure 9.8.4. Hydrocarbon system.
produced by electron impact. NH2 radicals are a major contributor to
oxidize NO to N02, through which NH4N03 that is used for fertilizer is
produced.
NO decomposition by hydrocarbons is shown schematically in figure
9.8.4. When hydrocarbons are added, the reaction by peroxy radicals
(R-OO) is a major pathway to decompose NO [1-4], although the reactions
are complicated. CHi (i = 1-3) radicals (CH3, CH2, CH etc.) are also
produced by electron impact in NTPs to decompose NO through HCN,
NCO and HCO radicals [5].
There are many kinds of hydrocarbons such as CH4, C2H2, C2H4, C3H6
and C3HS' However, reactions generated are commonly used to produce
peroxy radicals R-OO. H02 is an example of a peroxy radical [3], i.e.
R+O+O+M -
R-OO+M.
(9.8.2.1)
R-OO strongly oxidizes NO into N02 as shown in equation (9.8.2.2) [6].
R-OO + NO -
R-O + N02 •
(9.8.2.2)
The detailed R -00 species of C3H6 is described in references [2] and [6] and
C3Hs in reference [6].
N02 reacts with OH radicals to make HN03. A part ofN02 is changed
into CO2, where N02 is reacted with deposited soot at the proper tempera-
ture. Oxygen radicals preferably react with hydrocarbon molecules thereby
initiating a reaction chain forming several oxidizing radicals [7].
--- Page 640 ---
Chemical Decontamination
625
Carbon dioxide, CO2, is also included in exhaust gases [8]. CO2 hardly
contributes to the decomposition of NO, because the majority of the energy
deposited from the non-thermal plasma may be lost to the vibrational and
rotational excitations of CO2 • Although it is thought that electrons impact
CO2 to make CO, NO can be reduced only at very high temperatures as
shown in equations (9.8.2.3) and (9.8.2.4) [9].
e+C02 -
CO+O+e
CO + NO -
CO2 +!N2 •
(9.8.2.3)
(9.8.2.4)
NO is reproduced by the reaction between CO2 and nitrogen radicals as
shown in equation (9.8.2.5) [10].
N + CO2 -
NO + CO.
(9.8.2.5)
NOs are reproduced by N02 reduction by oxygen and hydrogen radicals,
and reactions between nitrogen and OH radicals as shown in equations
(9.8.2.6}-(9.8.2.8).
N02 +0 -
NO+02
N02 + H -
NO + OH
N +OH -
NO+H.
(9.8.2.6)
(9.8.2.7)
(9.8.2.8)
In summary, NO is converted into final products through the production of
N02 by additives in a NO stream field. The energetic electron impact is the
origin of these reactions. Electrons directly impact to NO or produce radicals
to convert NO into N02. N02 further changes to NH4N03 when ammonia is
added. NO is also reproduced by oxygen and hydroxyl radicals.
9.S.3 Non-thermal plasmas for de-NOx
Plasma reactors that have been utilized for NOx remediation are: (1) di-
electric barrier discharge, (2) corona discharge, (3) surface discharge, (4)
glow discharge and (5) microwave discharge. Reactor groups are subdivided
according to their power source: dc and pulsed. Electrode configurations in
corona discharge and dielectric barrier discharge are (1) plate, (2) needle or
multi-needle, (3) thin wire and (4) nozzle. A grounded electrode is placed
in parallel or coaxial form near these electrodes.
Hybrid systems combining plasma with electron beam [11, 12] or catalysts
were also developed [13-15]. As indirect decomposition systems, radical shower
systems were developed using ammonia gases [16,17] and methane gases [18].
9.8.3.1
Efficiency
The efficiency of NOx reduction using pulsed or stationary NTPs is a
complex function of parameters that include pulse width, pulse polarity,
--- Page 641 ---
626
Current Applications of Atmospheric Pressure Air Plasmas
current density, repetition rate and reactor size. For de-NOx , removal
efficiency TlNO, and energy efficiency TIE are often used to evaluate the decom-
position system. These are defined as equations (9.8.3.1) and (9.8.3.2).
TlNo, = [NO]before - [NO]after x 100
(%)
(9.8.3.1)
.
[NO] before
- L
[NO] before
TlNo, x ~
x ~
TIE -
X
106
X 100
22.4
P
(gjkWh)
(9.8.3.2)
where [NO]before and [NO]after are NO concentrations before and after the
process in units of ppm. L is NO flow rate in units of l/min, the molecular
weight of NO is 30 g, and P is consumed energy in units of kWh. The elec-
trical conversion efficiency that refers to the efficiency for converting wall
plug electrical power into the plasma is important in the evaluation of the
total efficiency for the decomposition of NO".
9.8.3.2
Plasma reactors
Figures 9.8.S(a)-(f) show schematics offundamental plasma reactors for NO
decomposition. Figure 9.8.S(a) shows a DBD reactor. The electrode is coated
with dielectric materials. To prevent charging-up of the dielectric materials,
the power source is ac or burst ac signals with a frequency of 50 Hz to several
tens to hundreds of kHz. For the electrode arrangement, parallel plate, multi-
point [19] and coaxial types [16] are used. A series of filamentary discharges
are produced at the gap. Figure 9.8.S(b) shows a coaxial electrode configura-
tion [20] for generating corona discharge. The central electrode consists of a
thin wire. By applying a high voltage, corona discharges are produced
around the wire by stationary (ac and dc) and pulsed discharges [21-24].
For dc corona discharge, a polar effect appears (positive and negative
corona discharges). The electrode configurations are a wire [20], pipe and
Electrode
Dielectric
Figure 9.8.5. (a) Dielectric barrier discharge reactor.
--- Page 642 ---
Gas flow
t
Electrode
Discharge
Wire
Figure 9.8.5. (b) Corona discharge reactor.
Chemical Decontamination
627
r~
Gas flow
nozzle electrodes [17]. For generating pulsed corona discharges, there are
several types of electrode arrangement, i.e. point-to-plate [25], wire-to-
plate [26, 27], wire-to-cylinder [28, 29], nozzle-to-plate [30] and pin-to-plate
[31, 32]. For power sources, dc/ac superimposed source [33] and bi-polar
polarity of pulsed source [28, 34] are also used. Streamer corona discharge,
which is generated with a voltage rise time of 10-50 ns and a duration of
50-500ns FWHM (full-width at half-maximum), can decompose pollutant
gases.
The catalyst coated-electrode configuration to facilitate de-NOx is
shown in figure 9.8.5(c). NOx gases flow in the plasma and the catalyst to
undergo decomposition.
Figure 9.8.5(d) shows a tubular packed-bed corona reactor. The pellets
of dielectric materials are coated with or without catalyst. The catalyst is
activated by energetic particles, i.e. electrons, photons, excited molecules,
ions etc. [14]. By applying a high ac voltage to pellets filled in a chamber,
Gas flow
Catalyst
Discharge
Wire
Figure 9.8.5. (c) Corona discharge--catalyst reactor.
Gas flow
--- Page 643 ---
628
Current Applications of Atmospheric Pressure Air Plasmas
Gas flow
Discharge
Wire
Figure 9.S.S. (d) Packed-bed corona discharge reactor.
micro-discharges in the gap and/or on the surface are generated. This is
called a packed bed discharge, which is also expected to have a catalytic
effect at the surface of pellets [35].
Figure 9.8.5(e) shows a radical injection NTP system: a pipe electrode
with nozzle pipes from which gas additives flow, that are spouted to generate
Gas now
Electrode
,
(ACIDC)
R~
NOx
Figure 9.S.S. (e) Radical injection reactor.
--- Page 644 ---
Induction
Electrode
Outer
Figure 9.S.5. (f) Surface discharge reactor.
Chemical Decontamination
629
Discharge
Electrode
(grounded)
streamer corona discharges in the NOx stream field. Thus, the NOx is directly
exposed to the corona discharge [30]. On the other hand, radicals are
supplied to the NOx stream field by DBD generated in a separate chamber
from the NOx stream field. In this case, NOx is not exposed to the plasma.
DBD is generated by an intermittent power source so as to control the
discharge power. Ammonia radicals are injected into the NO stream field
[16]. Remediation by radical shower systems is achieved using dielectric
barrier discharges and corona discharges. Plasma-induced radicals from
ammonia [16, 17, 36, 37], methane [18, 36] and hydrogen [36], are injected
into the NOx stream region or via the corona zone.
Figure 9.8.5(f) shows a reactor of surface discharge. One of the elec-
trodes is inside the ceramics. By applying a high ac voltage, surface discharge
(a kind of dielectric barrier discharge) is generated at a surface of the inner
ceramics [38].
Microwave discharges at atmospheric pressure are also used for NOx
removal [39, 40] and are effective to decompose N2/NO and N2/02/NO
mixtures [40]. Because the gas temperature becomes high when operating
stationary discharges, a pulsed mode operation is employed [39]. NO is
also decomposed into N2 and O2 by a microwave discharge in a NO/He
mixture [41]. Micro-structured electrode arrays allow generation of a large-
area glow discharge, which removes two nitrogen oxides (NO and N20).
DC or rf power is applied to the arrays [42].
A hybrid system using NTP and an electron beam is effective in simul-
taneous removal of NO and S02 [12]. An electron beam is used together with
a corona discharge ammonia radical injection system.
--- Page 645 ---
630
Current Applications of Atmospheric Pressure Air Plasmas
9.8.4 Parametric investigation for de-NOx
In the de-NOx process by NTPs, optimization of the following parameters is
desired: (1) energy efficiency, (2) removal efficiency, (3) process cost, (4)
controllability, (5) by-products and (6) lifetime of the system and maintenance.
These parameters are directly influenced by: (1) power source (output voltage,
pulse width and polarity etc.), (2) electrode configuration, (3) catalyst, (4)
radical species, (5) additives, (6) reactor size etc.
In addition to the conventional electrode configurations mentioned
above, pyramid [19, 43] and multi-needle geometry [44] have been employed
to lower the operating voltage. In the pyramid type, tip angle and height were
varied [19]. In the multi-needle type, gap length was varied [44]. These
parameters of gap length and height have a close relationship to the
plasma initiation voltage leading to the reduced electric field strength and
the consumed energy in the plasma. When the angle of the tip point becomes
small, energy efficiency decreases due to larger energy consumption. The
lower reduced electric field strength was obtained for a shorter gap length
to lead to a lower rate of ozone production for the multi-needle type. As a
result, the de-NOx rate becomes low.
The influence of height of the pyramid-shaped electrode was also inves-
tigated [43]. It was shown that NO removal rate increases with decreasing
heights, in other words, depth of the groove, at the same gas residence
time. This change of the removal rate may be related to the change of the
discharge modes in DBD and surface discharge.
A heated wire is used for corona discharge generation and energetic
electrons are emitted [20]. A heated corona wire is able to produce energetic
electrons and activate the oxidation by the generated ozone. It was shown
that the average corona currents increased and the corona starting voltages
decreased with an increase in the wire temperature. The relation between de-
NOx rate and wire temperature was investigated. For generating corona
discharge, metallic wires are often used to make a high electric field. The
dependence of de-NOx rate on the wire materials, tungsten and copper,
was examined by a pulsed corona discharge with a wire-to-plate electrode
system. A higher de-NOx rate is obtained by tungsten wire covered with
W03 because a streamer corona discharge is easily generated, while a dc
stationary corona is only generated in the case of copper wire [26].
A pair of reticulated vitreous carbon (10 pores per inch) is used for
generating streamer corona discharge to convert NO into N02. This elec-
trode configuration is advantageous in scaling-up the system and gives rise
to large total NOx removal. At the surface of the carbon electrodes, N02
oxidizes carbon surfaces and finally nitrous acid is formed [9].
Reactor size and power sources are also parameters that influence the
de-NOy characteristics. Instead of the conventional ac and dc power sources
to generate corona discharges, a high voltage (60 kV) and large current
--- Page 646 ---
Chemical Decontamination
631
(approximately 200 A) pulsed power unit was used to generate a lOO ns-
duration streamer corona discharge. The output voltage is from a Blumlein
line generator. The short-duration pulsed power produces high-energy elec-
trons while the temperature of the ions and the neutrals remains unchanged,
and thus the energy consumed is reduced. The maximum energy efficiency
was 62.4 g/kWh [45]. A similar test is carried out using the Blumlein line
system with an output voltage of 40 kV and a current of 170 A [23]. Actual
flue gas from a thermal power plant was used. It was shown that about
90% of the NO was removed at a flow rate of 0.8 liters/min and a repetition
rate of 7 pps [23]. Using a traveling wave transmission in a coaxial cable, a
series of alternative discharge pulses generate pulsed corona discharge. Fila-
ment streamer discharges were generated at an applied reciprocal voltage
with an output of 40 kV. The NO gas with a concentration of 170 ppm was
reduced to one fourth of the original concentration in a time of 0.6 s [46].
The influence of the reactor diameter for pulsed positive corona discharges
on the de-NOx rate is discussed for a concentric coaxial cylindrical configura-
tion of the electrode. As a result, the increase of inner diameter of the reactor
from 10 to 22 mm could be a way to minimize energy losses in the process of
NOx removal from flue gas [47]. Generally, the current through the plasma
increases with increasing an applied voltage. In an ammonia radical injection
system, the corona current shows a hysteresis characteristic against the
applied voltage. This might be based on the NH4N03 aerosol production.
The deposition of aerosol particles also affects the NOx removal rate [30].
The main pathway for NOx removal in catalyst-based technology is
reduction. Selective catalytic reduction (SCR) has been studied using either
ammonia (NH3) or hydrocarbons (HCs) as additional reducing agents.
The combination of NTP, catalyst and the additives are effective to signifi-
cantly reduce nitric oxides (NO and N02) synergistically to molecular
nitrogen. For example, NOx is converted into N2 and H20 through electron
impact in NTP, gas-phase oxidation and catalytic reduction as shown in
equations (9.8.4.1}-(9.8.4.3). This is called plasma-enhanced NHrSCR
[48]. When HCs are used, this is called HC-SCR.
NTP:
e + O2 -
e + 20
(9.8.4.1)
Gas phase oxidation:
0 + NO + M -
N02 + M
(9.8.4.2)
Catalytic reduction:
NO + N02 + 2NH3 -
2N2 + 3H20.
(9.8.4.3)
As catalysts, Pd-AI20 3, Ti02, aluminosilicate, Ag/mordenite, ')'-A1203 and
Zr02 were examined for plasma-enhanced HC-SCR [48, 49].
The pulsed corona plasma reactor was followed by a Co-ZSM5 catalyst
bed of honeycomb type [14]. NO is converted into N02 in the plasma reactor
and then N02 is reduced in the Co-ZSM5 catalyst bed. No formation of
NH4N03 occurs. In the plasma-enhaced SCR system, plasma-treated N02
was reduced effectively with NH3 over the Co-ZSM catalyst at a relatively
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Current Applications of Atmospheric Pressure Air Plasmas
low temperature of 150°C [14]. Ti02 [50] as catalyst is also effective to de-
NO". NTP improves the de-NO" rate with an appropriate content of water
vapor and Na-ZSM-5 catalyst at any temperature [13].
9.8.5 Pilot plant and on-site tests
The de-NOx exhausted from pilot plants and diesel engines can be directly
processed by NTP. A diesel engine exhaust of a vehicle with a 3 liter exhaust
output is used as a stationary NOx source with the engine speed set at 1200
rpm, where the plasma reactor consisting of a coaxial DBD with a screw-type
electrodes is mounted on the vehicle [51]. The DBD deNOx system is applied
to an actual vehicle with an exhaust output of 2.5 liters and the oxidation of
hydrocarbon is recognized, where geometric and electric parameters such as
dielectric surface roughness and gap width of the coaxial reactor are investi-
gated [52]. A pulsed corona discharge process is applied to simultaneously
remove S02 and NOx from industrial flue gas of an iron-ore sintering
plant. The corona reactor is connected to the power source consisting of a
magnetic pulse compression modulator with a system supplying chemical
additives such as ammonia and propylene. The problem regarding the life-
time of the closing switch can be solved by using magnetic pulse compression
technology [53]. Propylene used as the chemical additive was very effective in
the enhancement of NOx removal. The increase in C3H6 concentration gives
rise to an enhancement of NOx [53].
NOx and S02 from coal burning boiler flue gases are simultaneously
removed by dc corona discharge ammonia radical shower systems in pilot
scale tests, where multiple-nozzle electrodes are utilized for generating a
corona discharge. Tests were conducted for the flue gas rate from 1000 to
1500Nm3/h, the gas temperature from 62 to 80°C, the ammonia-to-total
acid gas molecule ratio from 0.88 to 1.3, applied voltage from 0 to 25 kV
and NO initial concentration from 53 to 93 ppm for a fixed S02 of
800 ppm. As a result, approximately 125 g of NOx was removed by 1 kWh
of energy input with 75% of removal efficiency [54]. A plasma/catalyst
continuously regenerative hybrid system is introduced to reduce diesel parti-
culate matter (DPM), NOx , Co etc., contained in diesel exhaust gas from a
passenger diesel car (2500 cm\ A corona discharge is generated in front 'of
a nozzle-type hollow electrode, where ammonia, hydrocarbon, steam,
oxygen, nitrogen etc. are injected. The hybrid system test shows thatIiJPM
and CO were almost removed and NOx reduced to 30% simultaneously by
the system [25].
9.8.6 Effects of gas mixtures
It is known that, in addition to NOx, exhaust systems also release varying
concentrations of N2, O2, CO2, H20 etc. In coal burning electric plant,
--- Page 648 ---
Chemical Decontamination
633
sulfur oxide (S02) and fly ash are also contained. In diesel exhaust gas, soot is
included. One must consider the effect of these mixtures with NOx . These are
molecules and therefore, when present together with NOx in a plasma, the
plasma energy is partly consumed in these mixtures and is expended as
vibrational and rotational energies. This energy expense may not contribute
to the reaction. Thus, de-NOx efficiency can be enhanced using chemicals like
H20, H20 2, 0 3, NH3, or hydrocarbons that are introduced into NTPs as an
additive. As a result, NO and S02 are finally converted into NH3N04 and
(NH4hS04, respectively, where ammonia is used as an additive.
9.8.6.1
Particulate matter, soot, andfly ash
Fly ash is contained in the exhaust gas from coal-burning thermal electrical
power plants. Diesel particulate matter, NOx , CO2, etc., contained in diesel
exhaust gas emitted from a passenger car, were reduced using a dc corona
discharge plasma/catalyst regenerative hybrid system. The effects of
repetitive pulses and soot chemistry on the plasma remediation of NOx are
computationally investigated [55]. It was pointed out that N02 reacts with
deposited soot in the plasma reactor at the proper temperature [25]. An
outer porous electrode made of SiC ceramics is used for decomposition of
soot-containing exhaust gas and acts as both electrode for dielectric barrier
discharge and particulate filter. Toxic and soot containing harmful
substances from exhaust gas are subjected to plasma processing. The flue
gas is let out through the porous electrode which is gas-permeable but filters
hold back the soot particles. Reaction products were CO and CO2. The soot
decomposition was achieved by a cold oxidation process. Thus, the soot is
constantly oxidized during all engine operating conditions [56].
Fly ash including NOx gas was removed using pulsed streamer
discharges, generated by the configuration of wire and cylinder electrodes.
Fly ash with particle sizes from 0.08 to 3000ilm was injected into the
discharge region. The removal rate of NO and NOx including the fly ash
was increased in the presence of moisture. It was explained that the presence
of H20 generates the OH radicals by dissociation [57].
9.8.6.2 S02
S02 is often processed using ammonia as an additional gas. The reaction is
shown as
2S02 + 40H -
2H2S04
H2S04 + 2NH3 -
(NH4hS04·
(9.8.6.1 )
(9.8.6.2)
When S02 reacts with oxygen atoms to form S03, S03 is converted into
H2S04 as
(9.8.6.3)
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634
Current Applications of Atmospheric Pressure Air Plasmas
S02 was simultaneously removed with NOx using dc corona discharge
ammonia radical shower systems as pilot plant tests. Both removal and
energy efficiencies for S02 decomposition increase with increasing
ammonia-to-acid gas ratio and decrease with increasing flue gas temperature.
The maximum removal efficiency exists at an applied power of about 300 W.
Approximately 9 kg of S02 were removed by an energy input of 1 kWh with
99% of S02 removal [54].
S02 and NOx from industrial flue gas of iron-ore sintering plant were
processed using pilot-scale pulsed streamer corona discharges generated by
magnetic pulse compression technology. The sulfuric acid was neutralized
by ammonia in the discharges to finally obtain ammonia sulfate. The
removal of S02 was greatly enhanced when ammonia was added to the
flue gas. The high removal efficiency may be caused by chemical reaction
between S02 and NH3 in the presence of water vapor as well as the hetero-
geneous chemical reaction among S02, NH3 and H20 [53].
Flue gas from a heavy oil-fired boiler contains 200-1000 ppm of S02 and
about 50-200 ppm ofNOx . When processed at a hybrid gas cleaning test plant
using a corona discharge-electron beam hybrid system, up to 5-22% of NOx
and 90-99% of S02 could be removed by operating the corona discharge with
an ammonia radical injection system. It was found that total NOy and S02
reduction rates increase non-monotonically with increasing applied voltage,
hence, corona current or discharge input power [12].
9.8.6.3
O2
When oxygen molecules are mixed with a mixture of N2 and NO, oxygen
atoms are generated by electron impact, followed by formation of ozone
by a reaction with oxygen molecules as shown in equations (9.8.6.4) and
(9.8.6.5),
e+02 -
O+O+e
0+02 +M -
0 3 +M.
Qzone oxidizes NO to form N02 as shown in equation (9.8.6.6),
NO+03 -
N02 +02.
(9.8.6.4)
(9.8.6.5)
(9.8.6.6)
When the N02 with ammonia as additive is used, NH4N03 is formed as
shown in figure 9.8.3. However, because of the excessive concentration of
oxygen molecules, N02 is reduced to NO. In this case, oxygen atoms do
not contribute to remove NOn but reproduce NO as shown in equation
(9.8.6.7),
(9.8.6.7)
Using dielectric barrier discharge with multipoint electrodes [44], NO
removal was carried out. NO removal rate and NO conversion into N02
--- Page 650 ---
Chemical Decontamination
635
were discussed in NO/N2/02 mixed gas, where the oxygen concentration was
varied from I to 4%. Removal rates of NO and NOx increase with increasing
concentration of O2 in gas mixture, but conversion into N03 via N02 from
NO is limited in low NO concentration.
9.8.6.6 H20
Water vapor H20 leads to production of OH and H02 radicals. As H20
vapor concentration increases, more OH and H02 radicals can be generated
to oxide NO to form N02 and further HN03 [7]. Therefore, NO and NOx
(NO + N02) are removed with increasing H20 vapor concentration being
in a range of 1100-32000 ppm [5]. Increase in the de-NO" rate was also
seen in humid (10% H20) gas mixture [58], and in dc corona discharge
over a water surface [59].
9.8.6.5
Hydrocarbon radical injection
Hydrocarbons were used as an additive. NO/NOx is removed with acetylene
(C2H2) as an additive using a coaxial wire-tube reactor with dielectric barrier
discharge, where the feeding gases include N2, O2, NO and C2H2. The effect
of oxygen with concentrations of 0-10% is discussed for de-NOr The rate of
NO converted into N02 increases with increasing oxygen concentration.
Thus, NO to N02 oxidation is largely enhanced as the amount of hydro-
carbon increases. The hydrocarbon acts as a getter of 0 and OH radicals,
with the products reacting with O2 to yield peroxy radicals (H02) which
efficiently convert NO to N02. The conversion of NO into N2 by NH and
N radicals produced via HCN, NCO and HCO radicals is shown in figure
9.8.4. The de-NOx rate decreases with increasing the oxygen concentration
from 2.5-10%. This is due to the oxidation to CO or C03 by the reaction
between CHx and oxygen radicals. In low oxygen concentration, acetylene
C2H2 reacts with oxygen radicals to form hydrocarbon radicals that facilitate
to form HCN, NCO and HCO radicals. Thus, oxygen strongly influences the
de-NOx process [5].
9.8.6.6 Ammonia radical injection
An ammonia radical injection system for converting NO into harmless
products was developed [60], where the radicals are generated in a separate
chamber from the NO stream chamber. NO gas is not in the plasma. In
order to confirm the energy efficiency of de-NOx using an intermittent one-
cycle sinusoidal source for generating DBDs, the NO concentration is
increased to 3000 ppm by varying the oxygen concentration from 2-5.6%.
For containing oxygen gas in the NO stream field, lower NO temperature
operation is possible to obtain a higher de-NOx rate. At an applied voltage
--- Page 651 ---
636
Current Applications of Atmospheric Pressure Air Plasmas
slightly higher than the threshold voltage for plasma initiation, the removal
amount of NO reaches maximum, presenting maximum energy efficiency. In
particular, for an oxygen concentration of 5.6% and a duty cycle of 5-10%,
a high energy efficiency is obtained to be 98 g/kWh. This means that the
appropriate electrical power is deposited in the DBD plasma at this duty
cycle. In the system, NO is mainly reduced by NH2 radicals for NO to
convert into NH4N03 through H02 radicals as shown in figure 9.8.3.
9.8.7 Environmentally harmful gas treatments
Volatile organic compounds (VOCs) are converted into CO2 and H20 and
other by-products (e.g. HCl and H2) in the desired reaction stoichiometry
by oxygen and hydroxyl radicals. This stoichiometry is difficult to achieve
by NTPs, because other intermediate products are produced. According to
the process conditions, not only CO and nitric oxide such as N20 but also
phosgene (COC12) may be produced, which may require a second-stage
treatment. The end products include poisonous materials such as phosgene
which must be separated from the gas stream and/or be processed in a
second-stage treatment [61].
The mechanism of decomposition is based on the electron impact on the
harmful gases [62, 63]. Therefore, the simulation model includes a solution of
Boltzmann's equation for the electron energy distribution [61]. It was
reported that more N20 was generated for higher concentration of water
vapor and decomposition energy efficiency. Power sources with frequencies
such as 50 and 60 Hz are often used. In this case, the metal catalyst is
contained in the dielectric barrier discharge to remove the by-product by
facilitating the decomposition of the harmful gases. NTPs are effective to
decompose VOCs and the increase of the decomposition rate is desirable
for a practical flue gas process system.
The parameters influencing their decompositions are (1) electrical char-
acteristics of plasmas (power, energy, applied voltage, frequency, repetition
rates and rise time), (2) water, (3) carrier gases and flow rate, (4) ionization
potential of the target gases, and (5) gas temperatures. These parameters
are closely related to bring high selectivity of the target products [64].
A parametric study for decomposing VOC will be introduced below.
9.8.7.1
Plasma sources
Plasma chemical processes have been known to be highly effective in
promoting oxidation, enhancing molecular dissociation, and producing
free radicals to enhance chemical reactions [65]. VOCs are also processed
using NTPs, in the same way as NO is used. Four types of plasma reactor
have been mainly used for the application of VOC destruction: surface
discharge [66], dielectric barrier discharge [67], ferroelectric packed-bed
--- Page 652 ---
Chemical Decontamination
637
discharge [68], and pulsed corona discharge. Most of the power source
frequency is 50-60 Hz [62, 68, 69]. The destruction is also carried out by dc
discharge [65], capillary tube discharge [65] and microwave discharge
processes as well as electron beam. In order to improve energy efficiency
and control of undesirable by-products, hybrid systems in which NTPs are
combined with catalysts are used [67]. Synergetic effects are expected.
Deposition of by-products is not desirable during the process. Pevovskite
oxides such as barium titanate (BaTi03) act as a highly dielectric compound
[68]. The perovskite oxides can be catalytically activated by free radicals of
ultraviolet irradiation from the plasma [68].
Uniform generation of the corona discharge contribute to reduce
toluene. The higher destruction efficiency of toluene is attributed to more
uniform corona-induced plasma activities throughout the reactor volume.
The size of the pellets contributes to the plasma uniformity [62].
9.8.7.2 Processes
Halogen gases such as chlorine and fluorine are finally converted into CO2
and halogenated hydrogen, respectively. It was found that the destruction
efficiency decreases in the order of toluene, methylene chloride and tri-
chlorotrifluoroethane (CFC-1l3: CF2CICFCI2). CFCl13 has the strongest
bonding and is stable [62]. Toluene (C6HSCH3) is reduced by a dielectric
barrier discharge, where the reactor consists of a coaxial cylindrical electrode
system. Packed Ti02 pellets or coated Ti02 on the inner electrode surface are
used. Ti02 as catalyst is activated using plasma with coaxial electrodes. The
energy efficiency is improved due to synergetic effects between plasma and
activated catalyst [67]. The mechanism of toluene destruction involves not
only plasma-induced destruction in the gas phase but also the adsorption/
desorption of toluene on the Ti02 as well as catalytic reaction [67].
Abatement of CFC-l13 (which is one of the fluorocarbons) was first
reported using ferroelectric packed bed discharge [62] and surface discharge
[66]. In the surface discharge case [66], CFC-1l3 with a concentration of
1000 ppm was processed at a destruction rate of 98 % for a discharge
power of 70W. Recently, CHF3 gas was reduced in H20/He plasma
(13.56 MHz) and disappeared at 700W. The by-products were CHF3, CF4,
H20, CO2 and SiF4 [70]. In CF4 destruction under identical experimental
conditions as in the CH3 case, the maximum destruction efficiency using
Hr 0 2/He as a carrier gas is higher by a factor of approximately 2 than
that using 02/He gas. Hydrogen atoms contribute to the CF4 destruction.
The by-products were CO2, HF and H20 [70]. Ar diluted CF4 as per fluor-
ocarbon was abated using atmospheric pressure microwave plasma (2.45
GHz) with TMolO mode. 10 sccm CF4 with 100 sccm Ar in 2 lpm O2 and
10 lpm N2 flow was treated. CO2, COF2, H20 and NO were identified as
the by-products [71].
--- Page 653 ---
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Current Applications of Atmospheric Pressure Air Plasmas
The principal processes of the destruction of toluene are electron and
radical dissociation in the discharges, although charge transfer of toluene
with ions and recombination of toluene ions may also be responsible. Ti02
activated by plasma may induce various reactions on the surface of the
Ti02, resulting in an enhanced toluene destruction. Ti02 plays a role to
enhance the destruction efficiency based on the following reactions: (1)
photocatalyst process by ultraviolet light emission from plasma [67], (2)
direct activation by fast energetic electrons and active species, (3) oxidation
by oxygen radicals produced by the destruction of 0 3 on Ti02 catalyst [72]
and (4) chemical reactions by OH and H02 radicals [72]. Toluene was
mostly reduced to CO, COb H20 by OH radicals, 0 3 and ° [62, 65, 67,
73]. Ozone generation is dependent on the heat by the gas discharge. In the
presence of air or nitrogen, nitrogen atoms are produced in the direct and/
or sensitized cleavage of nitrogen molecules and produce N20, NO and
N02 [68]. N20 concentration is significant [68]. In air, triplet oxygen mole-
cules are the most reactive oxygen source in the presence or absence of
water, and carbon balance can be improved with suppression of by-products
due to promoted autoxidation processes [68].
The principal processes of the VOC destruction are electron and radical
impact dissociation of molecules. For toluene, the reaction of toluene with
OH radicals is effective to make H20 as a final product [65] and water can
be reduced in NTP to give OH radicals and hydrogen atoms. The effect of
water was discussed in the destruction of butane. In low voltage application,
higher destruction efficiencies were obtained under wet conditions compared
with dry conditions. However, at higher voltages, water had almost no or
some negative effect on butane destruction efficiency [68]. This is much
different from NO destruction. Benzene was reduced using alumina-hybrid
and catalyst-hybrid plasma reactors. It was found that Ag-, Cu-, Mo-, Ni-
supported Al20 3 can suppress the N20 formation [74].
Carbon tetrachloride (CCI4) was reduced using catalysis-assisted plasma
technology. Catalysts such as Co, Cu, Cr, Ni and V were coated on 1 mm
diameter BaTi03 pellets. For high frequency operation at 18 kHz, the best
CCl4 destruction was achieved with the Ni catalyst although the destruction
ofCCl4 is based on the direct electron impact and short-lived reactive species
[63, 75]. That is,
e + CCl4 ---- Cl- + CCI3 .
(9.8.7.1)
CCl4 is reproduced by three-body reaction through CCI3,
CI + CCl3 + M ---- CCl4 + M.
(9.8.7.2)
On the other hand, O2 scavenges the CCl3 through the reaction
CCl3 + O2 ---- CCI30 2 .
(9.8.7.3)
Methylene chloride (CH2CI2) was destroyed by a packed bed plasma rector.
Because the chlorine in methylene chloride is strongly bonded with carbon, it
--- Page 654 ---
Chemical Decontamination
639
is much more stable chemically than toluene, and it is expected that higher
electron energies are necessary to reduce methylene chloride [62]. Tri-
chloroethylene (C2HCI3, or TCE) was reduced in DBD [61] and in a capillary
discharge [65]. The majority of the CI from TCE was converted into HCl, C12,
and COC12 [61] and CO2, CO, N02 are also identified [65]. The destruction
efficiency of TCE is smaller in humid mixtures compared to dry mixtures due
to interception of reactive intermediates by OH radicals [61]. The reaction to
form COCl2 is as follows:
C2HC13 + OH -
C2Cl3 + H20
(9.8.7.4)
C2HCl3 + CI -
C2Cl3 + HCI
(9.8.7.5)
(9.8.7.6)
TCE reacts with hydroxyl radicals, but the rate coefficient is no larger than
that with 0 atoms. There are intermediates such as CHOCl, CCl2 and CIO
due to 0 and OH radicals produced by electron impact dissociation of O2
and H20. The ClO radical is attributed with an important role in oxidizing
TCE [61, 76]. TCE can be dissociated or ionized by a direct electron
impact to form C2C13, C2HCI2, C2HClj etc. It was pointed out that negative
ions such as Cl- and C-might play an important role in the destruction
process [65]. These form terminal species such as CO, CO2, HCI and
COCl2 [61]. N02 is also produced after the process [65].
9.8.8 Conclusion
Processing of exhaust gases emitted from motor vehicle and different
factories and harmful gases emitted from various industries is increasingly
necessary to preserve our earth environment, thus improving our living
conditions. For practical use of the NTP system, we must make greater
effort to increase the process efficiency and reduce unit cost. In order to
realize an easy handling unit, not only modification of the conventional
process is needed but also development of new systems, in particular new
plasma sources, is very important. Combinations of different systems are
effective in bringing fruitful processing results.
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Pressure Low Temperature Plasma Chemistry, 360-364
[59] Fujii T, Aoki Y, Yoshioka N 'and Rea M 2001 J. Electrostatics 51/52 8-14
[60] Nishida M, Yukimura K, Kambara S and Maruyama T 2001 Jpn. J. Appl. Phys. 40
1114-1117
[61] Evans D, Rosocha L A, Anderson G K, Coogan J J and Kushner M J 1993 J. Appl.
Phys. 74 5378-5386
[62] Yamamoto T, Ramanathan K, Lawless P A, Ensor D S, Newsome J R, Plaks Nand
Ramsey G H 1992 IEEE Trans. Industry Applications 28 528-534
[63] Yamamoto T, Mizuno K, Tamori I, Ogata A, Nifuku M, Michalska M and Prieto G
1996 IEEE Trans. Industry Applications 32100-105
[64] Kozlov K V, Michel P and Wagner H-E 2000 Proc. HAKONE VII, International
Symposium on High Pressure Low Temperature Plasma Chemistry, 262-266
[65] Kohno H, Berezin A A, Chang J S, Tamura M, Yamamoto T, Shibuya A and Honda
S 1998 IEEE Trans. Industry Applications 34 953-966
[66] Oda T, Takahashi T, Nakano H and Masuda S 1993 IEEE Trans. Industry
Applications 29 787-792
[67] Kanazawa S, Li D, Akamine S, Ohkubo T and Nomoto Y 2000 Trans. Institute of
Fluid-Flow Machinery, No 107,65-74
[68] Futamura S, Zhang A, Prieto G and Yamamoto T 1998 IEEE Trans. Industry
Applications 34 967-974
[69] Proeto G, Prieto 0, Gay C R and Yamamoto T 2003 IEEE Trans. Industry
Applications 39 72-78
[70] Kogoma M, Abe T and Tanaka K 2002 Proc. HAKONE VIII, International
Symposium on High Pressure Low Temperature Plasma Chemistry, 303-
307
[71] Hong J, Kim S, Lee K, Lee K, Choi J J and Kim Y-K 2002 Proc. HAKONE VIII,
International Symposium on High Pressure Low Temperature Plasma
Chemistry, 360-363
[72] Kim H H, Tsunoda K, Katsura S and Mizuno A 1999 IEEE Trans. Industry
Applications 35 1306-1310
[73] Ponizovsky A Z, Ponizovsky L Z, Kryutchkov S P, Starobinsky V Ya, Battleson D,
Joyce J, Montgomery J, Babko S, Harris G and Shvedchikov A P 2000 Proc.
HAKONE VII, International Symposium on High Pressure Low Temperature
Plasma Chemistry, 345-349
[74] Ogata A, Yamanouchi K, Mizuno K, Kushiyama S and Yamamoto T 1999 IEEE
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VIII, International Symposium on High Pressure Low Temperature Plasma
Chemistry, 342-346
--- Page 658 ---
Biological Decontamination
643
9.9 Biological Decontamination by Non-equilibrium
Atmospheric Pressure Plasmas
In this section, a review of various works on the germicidal effects of atmos-
pheric pressure non-equilibrium plasmas is presented. First, a few of the
variety of plasma sources, which have been used by various research
groups, will be briefly presented. In-depth discussion of these sources and
others can be found in chapter 6. Analysis of the inactivation kinetics for
various bacteria seeded in (or on) various media and exposed to the
plasma generated by these devices is then outlined. Three basic types of
survivor curves have been shown to exist, depending on the type of microor-
ganism, the type of medium, and the type of exposure (direct versus remote)
(Laroussi 2002). Lastly, insights into the roles of ultraviolet radiation, active
species, heat, and charged particles are presented. The most recent results
show that it is the chemically reactive species, such as free radicals, that
play the most important role in the inactivation process by atmospheric
pressure air plasmas.
It is important to stress to the reader that only experiments carried out at
pressures around 1 atm are the subjects of this presentation. For comprehen-
sive studies conducted at low pressures, the reader is referred to Moreau et al
(2000) and Moisan et al (2001). In addition, works that used etching-type gas
mixtures, such as 02/eF 4, or which used plasmas only as a secondary
mechanism to assist a chemical-based sterilization method will not be
covered. To learn about these, the reader is referred to Lerouge et al
(2000), Boucher (1980) and Jacobs and Lin (1987).
9.9.1
Non-equilibrium, high pressure plasma generators
Here, a few methods that have been used to generate relatively large volumes
of non-equilibrium plasmas, at or near atmospheric pressure (sometimes
referred to as 'high' pressure) are briefly presented. This is far from being
a comprehensive list of all existing methods. The devices presented here
were chosen mainly because they have been used extensively to study the
germicidal effects of low-temperature high-pressure plasmas. More detailed
analysis of the physics of these devices can be found in chapter 6 of this book.
9.9.1.1
DBD-based diffuse plasma source
One of the early developments of diffuse glow discharge plasma at atmos-
pheric pressure was reported by Donohoe (1976). Donohoe used a large
gap (cm) pulsed barrier discharge in a mixture of helium and ethylene to
polymerize ethylene (Donohoe and Wydeven 1979). Later, Kanazawa et al
(1988) reported their development of a stable glow discharge at atmospheric
pressure by using a dielectric barrier discharge (DBD). The most common
--- Page 659 ---
644
Current Applications of Atmospheric Pressure Air Plasmas
configuration of the DBD uses two parallel plate electrodes separated by a
variable gap. The experimental set-up of a DBD is shown in chapter 6
(section 6.6, figure 6.4.1). At least one of the two electrodes has to be covered
by a dielectric material. After the ignition of the discharge, charged particles
are collected on the surface of the dielectric. This charge build-up creates a
voltage drop, which counteracts the applied voltage, and greatly decreases
the voltage across the gap. The discharge subsequently extinguishes. As the
applied voltage increases again (at the second half cycle of the applied
voltage) the discharge re-ignites.
Laroussi (1995, 1996) reported the use of the DBD-based glow discharge
at atmospheric pressure to destroy cells of Pseudomonasfluorecens. He used
suspensions of the bacteria in Petri dishes placed on a dielectric-covered
lower electrode. The electrodes were placed within a chamber containing
helium with an admixture of air. He obtained full destruction of concentra-
tions of 4 x 106 jml in less than 10 min. Subsequently, gram-negative bacteria
such as Escherichia coli, and gram-positive bacteria such as Bacillus subtilis
were inactivated successfully by many researchers using various types of
high pressure glow discharges (Kelly-Wintenberg et a11998, Herrmann et al
1999, Laroussi et a11999, Kuzmichev et aI2001).
9.9.1.2
The atmospheric pressure plasma jet
The atmospheric pressure plasma jet (APPJ) (Scutze et a11998) is a capaci-
tively coupled device consisting of two co-axial electrodes between which a
gas flows at high rates. Figure 9.9.1 is a schematic of the APPJ. The outer
electrode is grounded while the central electrode is excited by rf power at
13.56 MHz. The free electrons are accelerated by the rf field and enter into
collisions with the molecules of the background gas. These inelastic collisions
produce various reactive species (excited atoms and molecules, free radicals,
etc.) which exit the nozzle at high velocity. The reactive species can therefore
react with a contaminated surface placed in the proximity (cm) of the nozzle
1
Feed gas inlet
Effluent
RF electrode
Ground Electrode
Figure 9.9.1. The atmospheric pressure plasma jet (Scutze et aI1998).
--- Page 660 ---
Biological Decontamination
645
(Herrmann et aI1999). As in the case of the diffuse DBD, the stability of the
APPJ plasma (as well as its non-thermal characteristic) depends on using
helium as a carrier gas. Herrmann used the APPJ to inactivate spores of
Bacillus globigii, a simulant to anthrax (Bacillus anthracis) (Herrmann et al
1999). They reported the reduction of seven orders of magnitude of the
original concentration of B. globigii in about 30 s.
9.9.1.3
The resistive barrier discharge
The concept of the resistive barrier discharge (RBD) is based on the DBD
configuration. However, instead of a dielectric material, a high resistivity
sheet is used to cover at least one of the electrodes (see section 6.4, figure
6.4.7). The high resistivity layer plays the role of a distributed ballast
which limits the discharge current and therefore prevents arcing. The advan-
tage of the RBD over the DBD is the possibility to use dc power (or low
frequency ac, 60 Hz) to drive the discharge. Using helium, large volume
diffuse cold plasma at atmospheric pressure can be generated (Laroussi
et aI2002a).
Using the RBD, up to four orders of magnitude reduction in the original
concentration of vegetative B. subtilis cells in about 10 min was reported
(Richardson et al 2000). Endospores of B. subtilis were also inactivated,
but not as effectively as the vegetative cells. In these experiments, a gas
mixture of helium: oxygen 97: 3 % was used.
9.9.2 Inactivation kinetics
The concept of inactivation or destruction of a population of microorgan-
isms is not an absolute one. This is because it is impossible to determine if
and when all microorganisms in a treated sample are destroyed (Block
1992). It is also impossible to provide the ideal conditions, which inactivate
all microorganisms: some cells can always survive under otherwise lethal
conditions. Therefore, experimental investigation of the kinetics of cell
inactivation is paramount in providing a reliable temporal measure of
microbial destruction.
9.9.2.1
Survivor curves and D-value
Survivor curves are plots of the number of colony forming units (CFU s) per
unit volume versus treatment time. They are plotted on a semi-logarithmic
scale with the CFUs on the logarithmic vertical scale and time on the
linear horizontal scale. Figure 9.9.2 shows an example of a survivor curve
obtained by exposing a culture of E. coli to an atmospheric pressure glow
discharge in a helium/air mixture (Laroussi and Alexeff 1999). A line,
such as shown in figure 9.9.2, indicates that the relationship between the
--- Page 661 ---
646
Current Applications of Atmospheric Pressure Air Plasmas
1e+7
1ei6
1e+5
1e+4
E
en 1e+3
::::>
u.
0
1e+2
1e+1
1e+O
1e-1
0.0
0.5
1.0
1.5
2.0
2.5
Treatrrent TirTe (mnutes)
Figure 9.9.2. Survivor curve of E. coli exposed to DBD plasma.
concentration of survivors and time is given by
10g[N(t)/Nol = -kt
3.0
3.5
4.0
where No is the initial concentration and k is the 'death rate' constant.
One kinetics measurement parameter, which has been used extensively
by researchers studying sterilization by plasma, is what is referred to as the
'D' (decimal) value. This parameter was borrowed from studies on heat
sterilization. The D-value is the time required to reduce an original concen-
tration of microorganisms by 90%. Since survivor curves are plotted on
semi-logarithmic scales, the D-value is determined as the time for a 10gIO
reduction. Sometimes the D-value is referred to as the 'log reduction time'
(Block 1992) and expressed as follows:
Dv = t/(logNo -logNs)
where t is the time to destroy 90% of the initial population, No is the initial
population, and Ns is the surviving population (Block 1992).
Another parameter, which is of great importance for practical systems,
is the inactivation factor (IF). The IF is the percentage kill of a microbial
population by a particular treatment (Block 1992). The IF is generally deter-
mined for spores (highly resistant microorganisms), by taking the ratio of the
initial count to the final extrapolated count (Block 1992). Since the IF
depends on the initial count (before treatment, what is referred to as the
--- Page 662 ---
Biological Decontamination
647
'bioburden'), its value reveals the expected number of viable microorganisms
after the treatment. Therefore, the IF of a treatment method directly reflects
its sterilizing effectiveness, given a certain bioburden.
9.9.2.2
Survivor curves of plasma-based inactivation processes
To date, the experimental work on the germicidal effects of cold, atmospheric
pressure plasmas has shown that survivor curves take different shapes
depending on the type of microorganism, the type of the medium supporting
the microorganisms, and the method of exposure (direct exposure: samples
are placed in direct contact with the plasma; remote exposure: samples are
placed away from the discharge volume or in a second chamber. The reactive
species from the plasma, but not the plasma itself, are allowed to diffuse and
come in contact with the samples) (Laroussi 2002).
Herrmann (APPJ, remote exposure), Laroussi (diffuse DBD-type
discharge, direct exposure), and Yamamoto (corona discharge with H20 2,
remote exposure) reported a 'single slope' survivor curve (one-line curve)
for B. globigii on glass coupons (dry samples), for E. coli in suspension,
and for E. coli on glass, respectively (Herrmann et al 1999, Laroussi et al
2000, Yamamoto et al 2001). The D-values ranged from 4.5 s for the B.
globigii on glass (APPJ), to 15 s for E. coli on glass (Corona with H20 2
plasma), to 5 min for E. coli in liquid suspensions (DBD-type plasma).
Two-slope survivor curves (two consecutive lines with different
slopes) were reported by Kelly-Wintenberg (DBD-type, direct exposure)
for S. aureus and E. coli on polypropylene samples, and by Laroussi for
Pseudomonas aeruginosa in liquid suspension (Kelly-Wintenberg et a11998,
Laroussi et al 2000). The curves show that the D-value of the second line
(D2) was smaller (shorter time) than the D-value of the first line (Dd.
Montie also reported the same type of survivor curve for E. coli and B.
subtilis on glass, agar, and polypropelene (all under direct exposure to a
DBD-type discharge) (Montie et al 2000). Montie claimed that D J was
dependent on the species being treated and that D2 was dependent on the
type of surface (or medium) supporting the microorganisms (Montie et al
2000). A given explanation of the 'bi-phasic' nature of the survivor curve
was the following. During the first phase, the active species in the plasma
react with the outer membrane of the cells, inducing damaging alterations.
After this process is advanced enough, the reactive species can then quickly
cause cell death, resulting in a rapid second phase (Kelly-Win ten berg et al
1998).
Multi-slope survivor curves were also reported for E. coli and P. aerugi-
nosa on nitrocellulose filter (diffuse DBD-type, direct exposure) and for B.
stearothermophilus on stainless steel strips (pulsed barrier discharge,
remote exposure) (Laroussi et al 2000, Kuzmichev et al 2001). Each line
has a different D-value. Similar survivor curves (three phases) were reported
--- Page 663 ---
648
Current Applications of Atmospheric Pressure Air Plasmas
in low pressure studies (Moreau et al 2000, Moisan et al 2001). Moisan
explains that the first phase, which exhibits the shortest D-value, is mainly
due to the action of ultraviolet radiation on isolated spores or on the first
layer of stacked spores. The second phase, which has the slowest kinetics,
is attributed to a slow erosion process by active species. Finally the third
phase comes into action after spores and debris have been cleared by
phase 2, hence allowing ultraviolet to hit the genetic material of the still
living spores. The D-value of this phase was observed to be close to the D-
value of the first phase. It is important to note that the explanation given
above would not apply to the case of atmospheric pressure air plasmas,
which generate a negligible ultraviolet power output at the germicidal wave-
lengths (200-300 nm).
9.9.3 Analysis of the inactivation factors
This section presents a discussion on the contributions of the various agents
emanating from non-equilibrium air plasmas to the killing process. These are
the heat, ultraviolet radiation, reactive species, and charged particles. Note
that in general various gas mixtures can be used to optimize the generation
of one inactivation agent or another and ultimately to optimize the killing
efficiency. The following results and discussions, however, are limited to
the case of atmospheric pressure air (containing some degree of humidity).
As a plasma generation device, a DBD is used.
9.9.3.1
Heat and its potential effect
High temperatures can have deleterious effects on the cells of microorgan-
isms. A substantial increase in the temperature of a biological sample can
lead to the inactivation of bacterial cells. Therefore, heat-based sterilization
techniques were developed and commercially used for applications that do
not require medium preservation. In heat-based conventional sterilization
methods, both moist heat and dry heat are used. In the case of moist heat,
such as in an autoclave, a temperature of 121°C at a pressure of 15 psi is
used. Dry heat sterilization requires temperatures close to 170 °C and treat-
ment times of about 1 h.
To assess if heat plays a role in the case of decontamination by an air
plasma, a thermocouple probe was used to measure the temperature increase
in a biological sample under plasma exposure. In addition, the gas tempera-
ture in the discharge can be measured by evaluating the rotational band of
the 0-0 transition of the second positive system of nitrogen. Figure 9.9.3
shows that the gas temperature and the sample temperatures in a DBD air
plasma undergo only a small increase above room temperature (Laroussi
and Leipold 2003). Based on these measurements no substantial thermal
effects are expected.
--- Page 664 ---
Biological Decontamination
649
350
340
0
0
Gas Temperature
~
.II.
Sample Temperatura
!!! 330
.II.
0
.II.
:::l -
.II.
.II.
I!! 2t 320
0
E
~ 310
0
rn
to
(!)
300
0
290
0
2
4
6
8
10
12
Flow Rate [I/min]
Figure 9.9.3. Gas and sample temperature versus air flow rate at a power of 10 w.
9.9.3.2
Ultraviolet radiation and its potential effect
Among ultraviolet effects on cells of bacteria is the dimerization of thymine
bases in their DNA strands. This inhibits the bacteria's ability to replicate
properly. Wavelengths in the 220-280 nm range and doses of several
mW s/cm2 are known to have the optimum effect. Figure 9.9.4 shows the
emission spectrum between 200 and 300 nm from a DBD air plasma
0.25
I
I
I
I
-
0.20 I-
::i
.!!!.
iii
c: 0.15 I-
0)
U5 ...
. ~ 0.10 -
0.
:2
:::l
E
0
0.05 -
15
.s::.
a..
J
0.00
.II
I
I
I
200
220
240
260
280
300
Wavelength [nm]
Figure 9.9.4. Emission spectrum of an air plasma in the ultraviolet region.
--- Page 665 ---
650
Current Applications of Atmospheric Pressure Air Plasmas
(Laroussi and Leipold 2003). ultraviolet emission at wavelengths greater
than 300 nm was also detected. The spectrum is dominated by N2 rotational
bands 0-0 transition (337nm) and NO,6 transition around 304nm. Measure-
ments of the ultraviolet power density by a calibrated ultraviolet detector, in
the 200-31Onm band, showed that less than 1 mW/cm2 was emitted, under
various plasma operating conditions. Therefore, according to these measure-
ments, the ultraviolet radiation has no significant direct influence on the
decontamination process of low temperature air plasmas. This is consistent
with the results of several investigators (Laroussi 1996, Herrmann et al
1999, Kuzmichev et aI2001).
9.9.3.3
Charged particles and their potential effects
Mendis suggested that charged particles may playa very significant role in
the rupture of the outer membrane of bacterial cells. By using a simplified
model of a cell, they showed that the electrostatic force caused by charge
accumulation on the outer surface of the cell membrane could overcome
the tensile strength of the membrane and cause its rupture (Mendis et al
2000, Laroussi et al 2003). They claim that this scenario is more likely to
occur for gram-negative bacteria, the membrane of which possesses an
irregular surface. Experimental work by Laroussi and others has indeed
shown that cell lysis is one outcome of the exposure of gram-negative
bacteria to plasma under direct exposure (Laroussi et al 2002b). However,
it is not clear if the rupture of the outer membrane is the result of the charging
mechanism or a purely chemical effect. Figure 9.9.5 shows SEM micrographs
of controls and plasma-treated E coli cells (Laroussi et aI2002b). The micro-
graph of the plasma-treated cells shows gross morphological damage.
9.9.3.4
Reactive species and their inactivation role
In high-pressure non-equilibrium discharges, reactive species are generated
through electron impact excitation and dissociation. They play an important
(a)
(b)
Figure 9.9.5. SEM micrographs of controls (a) and plasma-treated bacteria (b) E. coli cells.
The plasma-treated cells show gross morphological damage.
--- Page 666 ---
Biological Decontamination
651
role in all plasma-surface interactions. Among the radicals generated in air
plasmas, oxygen-based and nitrogen-based species such as atomic oxygen,
ozone (03), NO, N02, and the hydroxyl radical (OR) have direct impact
on the cells of microorganisms, especially when they come in contact with
their outer structures such as the outer membrane. Membranes are made of
lipid bilayers, an important component of which is unsaturated fatty acids.
The unsaturated fatty acids give the membrane a gel-like nature. This allows
the transport of the biochemical by-products across the membrane. Since
unsaturated fatty acids are susceptible to attacks by hydroxyl radical (OR)
(Montie et al 2000), the presence of this radical can therefore compromise
the function of the membrane lipids. This will ultimately affect their vital
role as a barrier against the transport of ions and polar compounds in and
out of the cells (Bettelheim and March 1995). Imbedded in the lipid bilayer
are protein molecules, which also control the passage of various compounds.
Proteins are basically linear chains of aminoacids. Aminoacids are also
susceptible to oxidation when placed in the radical-rich environment of the
plasma. Therefore, oxygen-based and nitrogen-based species are expected to
playa crucial role in the inactivation process.
The following are measurements of nitrogen dioxide (N02), hydroxyl
(OR), and ozone (03) obtained from a DBD operated in atmospheric
pressure air (Laroussi and Leipold 2003). Figure 9.9.6 shows the concentra-
tion of N02 in the DBD, as measured by a calibrated gas detection system.
The presence of OR was measured by means of emission spectroscopy,
looking for the rotational spectrum of OR A-X (0--0) transition. This
molecular band has a branch at about 306.6 nm (R branch) and another
one at 309.2nm (P branch). Figure 9.9.7 shows the emission spectrum in
900
I
800
..
E 700
Co
..
.3,
N
600
0
•
z
500
c::
•
..
..
..
0
•
:;:::
400
!!!
•
•
..
.....
c:
300
..
lOW
Q)
•
0
• 5W
c:
200
0
1.5W
0
•
U
0
100
0
0
0
0
0
0
0
8
10
12
14
Gas Flow [11m in]
Figure 9.9.6. Concentration of nitrogen dioxide versus air flow rate, for different powers.
--- Page 667 ---
652
Current Applications of Atmospheric Pressure Air Plasmas
8
OH R-Branch
307
308
Wavelength [nm]
OH P-Branch
309
Figure 9.9.7. Emission spectra from a humid air discharge showing OH lines.
the range between 306 and 310 nm and it indicates the OR band heads.
Figure 9.9.8 shows the relative concentration of OR in the discharge as a
function of power and air flow rate. Ozone concentration produced by the
DBD in atmospheric air was measured for varying flow rate and at various
Figure 9.9.8. Relative concentration of OH versus power and air flow rate.
--- Page 668 ---
Biological Decontamination
653
power levels by ultraviolet absorption spectroscopy and by a chemical titra-
tion method. Concentrations up to 2000 ppm could be obtained. Ozone
germicidal effects are caused by its interference with cellular respiration.
9.9.4 Conclusions
Research on the interaction of both low-pressure and high-pressure non-
equilibrium plasmas with biological media has reached a stage of maturity,
which indicates that this emerging field promises to yield valuable technolo-
gical novelty. In the medical field, the use of plasma to sterilize heat-sensitive
re-usable tools in a rapid, safe, and effective way is bound to replace the
present method which relies on the use of ethylene oxide, a toxic gas. In
the food industry, the use of plasmas to sterilize packaging will lead to
safer food with a longer shelf life. In space applications, plasma is considered
as a potential method to decontaminate spacecraft on planetary missions.
The goal in this application is to avoid transporting microorganisms from
Earth to the destination planet (or moon). Air plasma is also a potential tech-
nology that can be used for the destruction of biological warfare agents.
Extensive research on the use of high-pressure low-temperature plasmas
to inactivate microorganisms is a relatively recent event. There are still a lot
of basic issues that need more in depth investigations. Among these are the
effects of plasma on the biochemical pathways of bacteria. A clear under-
standing of these will lead to new applications other than sterilization/decon-
tamination. However, for practical devices intended for the destruction of
pathogens, all the available results indicate that non-equilibrium plasmas
generated in atmospheric pressure air offer a very efficient decontamination
method. This is mainly due to the efficient production of oxygen-based and
nitrogen-based reactive species, which interact directly with the cells and
can cause them irreversible damage.
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Current Applications of Atmospheric Pressure Air Plasmas
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gas composition on spore mortality and etching during low-pressure plasma steri-
lization' J. Biomed. Mater. Res. 51 128-135
Mendis D A, Rosenberg M and Azam F 2000 'A note on the possible electrostatic disrup-
tion of bacteria' IEEE Trans. Plasma Sci. 28(4) 1304-1306
Moisan M, Barbeau J, Moreau S, Pelletier J, Tabrizian M and Yahia L'H 2001 'Low
temperature sterilization using gas plasmas: a review of the experiments, and an
analysis of the inactivation mechanisms' Int. J. Pharmaceutics 226 1-21
Montie T C, Kelly-Wintenberg K and Roth J R 2000 'An overview of research using the
one atmosphere uniform glow discharge plasma (OAUGDP) for sterilization of
surfaces and materials' IEEE Trans. Plasma Sci. 28(1) 41-50
Moreau S, Moisan M, Barbeau J, Pelletier J, Ricard A 2000 'Using the flowing afterglow of
a plasma to inactivate Bacillus subtilis spores: influence of the operating conditions'
J. Appl. Phys. 881166-1174
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655
Richardson J P, Dyer F F, Dobbs F C, Alexeff I and Laroussi M 2000 'On the use of the
resistive barrier discharge to kill bacteria: recent results' in Proc. IEEE Int. Can!
Plasma Science, New Orleans, LA, p 109
Scutze A, Jeong J Y, Babyan S E, Park J, Selwyn G S and Hicks R F 1998 The
atmospheric pressure plasma jet: a review and comparison to other plasma sources'
IEEE Trans. Plasma Sci. 26(6) 1685-1694
Yamamoto M, Nishioka M and Sadakata M 2001 'Sterilization using a corona discharge
with H20 2 droplets and examination of effective species' in Proc. 15th Int. Symp.
Plasma Chem., Orleans, France, vol II, pp 743-751
9.10 Medical Applications of Atmospheric Plasmas
This section concludes the chapter devoted to practical aspects of atmospheric
plasmas. At this point, the reader is provided with state of the art information
on available plasma sources and their applications in inorganic/material
technology, gas cleaning, combustion, etc. The remaining issue is the role of
plasma in health care.
Several biomedical applications of plasmas have been already identified,
including surface functionalization of scaffolds, deposition of bio-compatible
coatings, and bacterial decontamination. For in vivo treatment, plasma-
based devices have been successfully used in wound sealing and non-specific
tissue removal. Since the modern plasma sources have become quite friendly
and 'bio-compatible', the area of applications is expanding rapidly and many
novel medical techniques are under preparation. The most recent develop-
ment is in vivo bacterial sterilization and tissue modification at the cellular
level. All these techniques will be described in this section.
9.10.1
A bio-compatible plasma source
A plasma can be considered 'bio-compatible' when it combines therapeutic
action with minimum damage to the living tissue. In non-specific tissue
removal, the penetration depth and the degree of devitalization must be
controllable. In refined/selective tissue modification there are more restrictions
on the thermal, electrical and chemical properties of the plasma. In this
paragraph the necessary safety requirements will be briefly discussed.
9.10.1.1
Thermal properties of a non-equilibrium plasma
Surface processing of materials usually involves non-thermal plasmas. 'Non-
thermal' does not imply that such plasmas cannot inflict thermal damage; it
means that they are non-equilibrium systems with electron temperature 100
to 1000 times higher than neutral gas temperature. In table 9.10.1.1 typical
--- Page 671 ---
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Current Applications of Atmospheric Pressure Air Plasmas
Table 9.10.1.1.
Plasma source
Type
Gas
T(K)
Ref.
Atmospheric
RF capacitively
Helium, argon
400
Park et at (2002)
pressure plasma
coupled
jet (APPJ)
Atmospheric
AC/DC glow
Air
800-1500 Lu and Laroussi
glow
above water
(2003)
Cold arc-plasma
AC 10-40kHz
Air, N2, O2
520
Toshifuji et at
jet
(2003)
Microwave torch 2.45GHz
Argon + O2
2200
Moon and Choe
(2003)
AC plasma
AC
Helium+02
800-900
Moon and Choe
(2003)
DBD
Dielectric barrier N2 +02 +NO
300
Baeva et at (1999)
Pulsed DBD
Dielectric barrier Argon+H20
350-450
Motret et at (2000)
Atmospheric
DC glow with
Air
2000
Mohamed et at
glow
micro-hollow
(2002)
cathode electrode
Plasma needle
RF capacitively
Helium+N2
350-700
Stoffels et at (2002)
coupled, mm size
RF micro-plasma Helium (+H2O)
300
Stoffels et at (2003)
gas temperatures in several types of non-thermal plasmas are given. Most of
these results have been obtained using spectroscopic methods: optical emis-
sion and CARS (Baeva et aI1999). Moon and Choe (2003) have calibrated
optical emission spectroscopy against thermocouples. Stoffels et al (2002,
2003) has also used both methods; some details are given in section 9.10.3
where the plasma needle is characterized.
Most of these sources can be used for non-specific treatment, like burning
and coagulation (see section 9.10.2). For this purpose the temperature may be
quite high as long as there is no carbonization or deep damage. In other appli-
cations, like specific treatment without tissue devitalization, temperature is an
essential issue. The tissue may be warmed up to at most a few degrees above
the ambient temperature, and exposure time must be limited to several
minutes. Discharges suitable for this kind of treatment are the micro-plasmas
(plasma needle) and possibly some kinds of DBDs.
9.10.1.2
The influence of electricity
The influence of electric fields on living cells and tissues has been elaborately
studied in relation to electrosurgery and related techniques. High electric
--- Page 672 ---
Medical Applications of Atmospheric Plasmas
657
fields are surely a matter of concern for the health of the patient, because they
may interact with the nervous system, disturb the heartbeat, and cause
damage to the individual cells.
Much attention has been given to alternating (high-frequency) currents
passing through the body. For detailed data the reader should refer to works
like Gabriel et al (1996) (dielectric properties and conductivity of tissues),
Reilly (1992) (nerve and muscle stimulation) and Polk and Postow (1995)
(electroporation and other field-induced effects). These studies have revealed
that the sensitivity of nerves and muscles decreases with increasing ac
frequency. The threshold current that causes irritation is as high as 0.1 A
at 100 kHz. It implies that for medical applications high-frequency sources
should be employed. At present, most of the electro surgical equipment
operates at 300 kHz or higher; the plasma needle is sustained by rf excitation.
Under these conditions no undesired effects are induced.
9.10.1.3
Toxicity
Plasma is a rich source of radicals and other active species. Reactive oxygen
species (ROS) (0, OH and H02, peroxide anions O2 and H02, ozone and
hydrogen peroxide) may cause severe cell and tissue damage, known under
a common name of oxidative stress. On the cellular level, several effects
leading to cell injury have been identified: lipid peroxidation (damage to
the membrane), DNA damage, and protein oxidation (decrease in the
enzyme activity). On the other hand, free radicals have various important
functions, so they are also produced by the body. For example, macrophages
generate ROS to destroy the invading bacteria, and endothelial cells (inner
artery wall) produce nitric oxide (NO) to regulate the artery dilation. The
natural level of radical concentration lies in the J.lM range (Coolen 2000).
The density of radical species in the plasma can be determined using
a variety of plasma diagnostics. However, for applications in biology/
medicine, standard gas-phase plasma characterization is not very relevant.
Instead, one has to identify radical species that penetrate the solution and
enter the cell. Biochemists have some standard methods for radical detection,
e.g. laser-induced fluorescence in combination with confocal microscopy.
Special organic probes are used, which become fluorescent after reaction
with free radicals. This yields detection limits below 0.01 J.lM in a solution,
and allows three-dimensional profiling with a resolution of about 0.2 J.lm.
9.10.2
In vivo treatment using electric and plasma methods
9.10.2.1
Electrosurgery
From very early times it was believed that electricity might have some healing
properties. In the 17th century some cases of improving the heart function,
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Current Applications of Atmospheric Pressure Air Plasmas
waking up from swoon, etc. were reported. About 200 years later the
technology of artificial generation of electricity was ready for advanced
medical applications. In 1893, d'Arsonval discovered that high-frequency
current passing through the body does not cause nerve and muscle stimula-
tion (d'Arsonval1893). Soon after, high-frequency devices were introduced
for cutting of tissues.
At present, electrosurgery has a solid, established name in medicine: the
electrical cutting device replaces the scalpel in virtually all kinds of surgery. A
detailed list of applications can be found in the database of ERBE (http://
www.erbe-med.de). a leading company producing equipment for electric,
cryogenic and plasma surgery. The electrosurgical tools manufactured by
ERBE are powered by high-frequency generators, either at 330 kHz or at
1 MHz. The reason for using these frequencies has been already discussed
in the previous section: they are well above 100 kHz, the lower limit for
electric safety. The devices can supply reasonably high powers-up to 200
or 450 W, dependent on the type and application. The power can be (auto-
matically) regulated during the operation, to obtain the desired depth of
the incision. Various electrode designs and configurations are used: a
monopolar high-frequency powered pin (in this case the current is flowing
through the patient's body), a bipolar coaxial head, and a tweezers-like
design (see figure 9.10.1). In the latter case the arms of the tweezers have
opposite polarities, and the distance between their tips can be varied. The
quality of cuts for all these configurations is about the same.
The features that have made electric devices so successful and desired
are: good cutting reproducibility, high precision, good control of depth,
A
c
B ~
c
D
Figure 9.10.1. Electrosurgery devices and techniques developed by ERBE (http://
www.erbe-med.de/): (a) a monopolar cutting device, (b) bipolar cutting/coagulation
tweezers, (c) tissue cutting using coaxial bipolar device, (d) tissue coagulation using bipolar
tweezers.
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Medical Applications of Atmospheric Plasmas
659
and the possibility of local coagulation. The latter is especially important in
achieving hemostasis and thus preventing blood loss, formation of thrombus,
and contamination of tissues during surgery. Electrical coagulation is also
used on its own, when no incision is necessary-for this purpose a bipolar
tweezers-like device is used (see figures 9.1O.1b,d). The current flowing
through the tissue induces ohmic heating that allows for fast and superficial
coagulation. This method is often used to seal small blood vessels.
9.10.2.2 Argon plasma coagulation
The step from electric to plasma surgery is readily made. The electric
methods discussed above are based on local tissue heating. Devitalization
by heat is a rather unsophisticated effect, which can be achieved by exposure
to any heat source. Atmospheric plasma generated by a high-power electric
discharge is one of the options. Needless to say, for these applications it is not
required that the gas temperature in the plasma be low. On the contrary,
controlled burning of the diseased tissue is an essential part of the therapy.
The aim of the treatment is coagulation and stopping the bleeding, and some-
times even total desiccation and devitalization of the tissue.
An adequate discharge has been developed by ERBE, and the corre-
sponding surgical technique is called argon plasma coagulation (APC). The
design of the APC source resembles somewhat the APPJ (Park et al 2002),
because the latter is also a plasma generated in a tube with flowing argon.
The APC source has not been characterized, but considering the parameters
(frequency of 350 kHz, operating voltage of several kV and power input of
50 W) it seems to be a classical ac atmospheric jet. The gas temperature
within the plasma can easily reach several hundreds of degrees Celsius.
A schematic view of an APC device (figure 9.10.2) shows a tube through
which argon is supplied. The flow rate is adjustable between 0.1 and 0.91/min.
The powered electrode is placed coaxially inside the tube (monopolar
Figure 9.10.2. An argon plasma coagulation device, developed by ERBE. Argon flow is
blown through the tube, in which the high frequency electrode is placed. The plasma
flame stretches out of the tube.
--- Page 675 ---
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Current Applications of Atmospheric Pressure Air Plasmas
configuration). Like in monopolar electrosurgery, the patient is placed on a
conducting sheet and the high-frequency current flows through the body. The
APe electrode generates argon plasma, which stretches about 2-10 mm from
the tip. Since the plasma is conductive, the current can flow to the tissue, but
the electrode does not touch it. This is one of the most important advantages
of APe: the energy is transferred in a non-contact way, so the problems with
tissue sticking to the metal device, heavy burning and tearing can be avoided.
Another unique feature of APe is its self-limiting character. Since the
desiccated tissues have a lower electrical conductivity than the bleeding
ones, the plasma beam will turn away from already coagulated spots
toward bleeding or still inadequately coagulated tissue in the area receiving
treatment. The argon plasma beam acts not only in a straight line (axially)
along the axis of the electrode, but also laterally and radially and 'around
the corner' as it seeks conductive bleeding surfaces. This automatically
results in evenly applied, uniform surface coagulation. The tissues are not
subjected to surface carbonization and deep damage, and the penetration
depth is at most 3-4 mm. It should be mentioned that the action 'around
the corner' is typical for all plasmas, but it cannot be achieved in e.g. laser
surgery. Superficial scanning of irregular surfaces, small penetration
depths, and low equipment costs, make plasma devices competitive with
lasers.
It is not entirely clear what causes the coagulation of the treated tissue. It
may be the heat transferred directly from the hot gas as well as the heat gener-
ated within the tissue by ohmic heating. It is also plausible that argon ions
bombarding the tissue contribute to desiccation.
Although the exact physical mechanism of coagulation is not yet
completely understood, the APe device has been successfully applied in
many kinds of surgery. The most obvious application is open surgery-
promoting hemostasis in wounds and bleeding ulcers. Treatment of various
skin diseases has been discussed by Brand et al (1998). Devitalization of
mucosal lesions in the oral cavity (e.g. leucoplakia) has been also performed.
However, the most obvious techniques are not necessarily the most
frequently applied ones. Since ERBE has developed a flexible endoscopic
probe, the way to minimally invasive internal surgery has been opened.
The area of interest is enormous, and most of the APe applications involve
endoscopy. In gastroenterology there are many situations where large
bleeding areas must be devitalized. APe treatment has been used to destroy
gastric and colon carcinoma or to remove their remains after conventional
surgery, to reduce tissue ingrowth into supporting metal stents (e.g. stents
placed in the esophagus), to treat watermelon stomach and colitis. APe
techniques are also frequently used for various operations in the tracheo-
bronchial system-removal of tumors, opening of various blockages
(stenoses) in the respiratory tract (e.g. scar stenoses), etc. In the nasal
cavity, APe can reduce hyperplasia of nasal concha (which causes
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Medical Applications of Atmospheric Plasmas
661
respiratory problems) and hemorrhaging. More examples and detailed
information about the medical procedures can be found on the website of
ERBE. In all mentioned cases, the physicians are positive about the
immediate body reaction and post-treatment behavior. Of course, during
the operation the surgeon has to be careful not to cause membrane/tissue
perforation by applying high powers and/or prolonging the treatment too
much. When the treatment is performed correctly, the devitalized (necrotic)
tissue dissolves and the healing proceeds without complications.
9.10.2.3
Spark erosion and related techniques
Spark erosion is a special and unconventional application of plasma in
surgery. It is remarkable for two reasons: first, as an attempt to treat athero-
sclerosis, a complex cardiovascular disease that plagues most of the Western
world, and second, as an example to show that a quite powerful discharge
can be induced in vulnerable places, like blood vessels. In the following
passage a brief description of atherosclerosis, its pathogenesis and current
treatment methods will be given, followed by a discussion of the spark
erosion technique.
Atherosclerosis is a chronic inflammatory disease, where lipid-rich
plaque accumulates in arteries. The consequences are plaque rupture and/
or obstruction of the arteries. The occluded artery cannot supply blood to
a tissue. This results in ischemic damage and infarct (necrosis). For example,
direct obstruction of a coronary artery causes irreversible damage to a part of
the heart muscle, and a myocardial infarct (heart attack). Plaque rupture
produces thrombus that can cause vascular embolization and infarct far
away from the actual site of plaque. Complications include stroke and
gangrene of extremities. At present it is the principal cause of death in the
Western world (Ross 1999).
Atherosclerotic obstructions are usually removed surgically (Guyton
and Hall 2000), by inflating and stretching the artery (balloon angioplasty).
In severe cases an additional blood vessel must be inserted (bypass
operation). However, there is no universal cure, because restenosis after
balloon angioplasty occurs within six months in 30-40% of treated cases,
and the bypasses are less stable than original arteries.
In surgical treatment the plaque must be removed, but in a way that
causes least damage to the artery, so as to minimize restenosis. Recently,
laser methods have been applied with reasonable success. However, as
mentioned earlier, lasers cannot act 'around the corner', which in this case
is essential. In 1985 Slager presented a new concept, which lies between
electrosurgery and plasma treatment (Slager et al 1985). This technique,
called spark erosion, is based on plaque vaporization by electric heating.
The tool developed by Slager is similar to the monopolar device used in
APC, but no feed gas is used. Instead, the electrode is immersed directly in
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662
Current Applications of Atmospheric Pressure Air Plasmas
Figure 9.10.3. A crater in the atherosclerotic plaque, produced by tissue ablation using the
spark erosion technique (Slager et aI1985).
the blood stream and directed towards the diseased area. Alternating current
(250 kHz) is applied to the electrode tip in a pulsed way, with a pulse duration
of lOms. The voltages are up to 1.2kV. Under these conditions, the tissue is
rapidly heated and vaporized. The produced vapor isolates the electrode
from the tissue, so that further treatment is performed in a non-contact
way. After vaporization, electric breakdown in the vapor occurs and a
small « Imm) spark is formed. Spark erosion allows removing substantial
amounts of plaque--craters produced can have dimensions of up to
1.7mm. The crater edges are smooth and the coagulation layer does not
exceed 0.I-O.2mm (see figure 9.10.3).
It is not yet clear whether spark erosion will become competitive with
lasers and mechanical methods in treatment of atherosclerosis. One possible
problem is formation of vapor bubbles, which may lead to vascular
embolization. Nevertheless, the spark-producing electrode can be used in
open-heart operations, e.g. in surgical treatment of hypertrophic obstructive
cardiomyopathy (Maat et al 1994). The cutting performance is similar to
electrosurgery but, as in plasma techniques, the treatment is essentially
non-contact.
Compared to argon plasma coagulation, thermal effects in spark surgery
are minor. The spark plasma is much smaller than the argon plasma, so that
heating is more local. Since there is no gas flow, no heat is transferred by
convection, and pulsed operation suppresses the thermal load. The physical
characterization of spark-like discharges was performed by Stalder et al
(2001) and Woloszko et al (2002). The spark generated by these authors
was similar to the discharge employed by Slager, but they focused on the
plasma interactions with electrolyte solution. The electron density in such
--- Page 678 ---
Medical Applications of Atmospheric Plasmas
663
plasmas is in the order of 1018 m -3, and the electron temperature is about
4eV. The gas temperature is about 100°C above the ambient.
9.10.3 Plasma needle and its properties
In the medical techniques described above the action of plasma is not
refined-it is based on local burning/vaporization of the tissue. Using the
analogy to material science, APC and spark erosion can be compared to
cutting and welding. However, plasmas are capable of much more sophisti-
cated surface treatment than mere thermal processing. If the analogy to
material science holds, it is expected that fine tissue modification can be
achieved using advanced plasma techniques.
However, the construction of non-thermal and atmospheric plasma
sources suitable for fine tissue treatment is not trivial. Moreover, most
plasmas must be confined in reactors, so they cannot be applied directly
and with high precision to a diseased area. In the following section another
approach will be presented: a flexible and non-destructive micro-plasma for
direct and specific treatment of living tissues.
9.10.3.1
Plasma needle
Small-sized atmospheric plasmas are usually non-thermal. This is simply a
consequence of their low volume to surface ratio. Energy transfer from
electrons to gas atoms/molecules occurs in the volume, and the resulting
heat is lost by conduction through the plasma boundary surface. A simple
balance between electron-impact heating and thermal losses can be made
for a spherical glow with a radius L:
me
4
3
b.T
2
ma VeanekBTe 3' 7fL = '" L 47fL
where me a is the electron/atomic mass, Vea is the electron-atom collision
frequency and '" is the thermal conductivity of the gas. This allows estimation
of a typical plasma size:
L=
ma
3",b.T
me VeanekBTe'
Dependent on the plasma conditions, the typical length scales of non-thermal
plasmas with b.T < 10° C are of the order of 1 mm.
A plasma needle (Stoffels et al 2002) fulfills the requirements of being
small, precise in operation, flexible and absolutely non-thermal. This is a
capacitively coupled rf (13.56 MHz) discharge created at the tip of a sharp
needle. The experimental scheme, including a photograph of the flexible
hand-held plasma torch, is shown in figure 9.10.4. Like most atmospheric
--- Page 679 ---
664
Current Applications of Atmospheric Pressure Air Plasmas
waveform
RF amplifier
power
meter
Figure 9.10.4. A schematic view of the plasma needle set-up. In the photograph of the
flexible torch: rf voltage (right throughput) is supplied to the electrode (needle), confined
in a plastic tube, through which helium is blown (bottom throughput).
discharges, the needle operates most readily in helium: the voltage needed for
ignition is only 200 V peak-to-peak. In fact, using helium as a carrier gas has
other advantages. The thermal conductivity (144 W/m/K) is very high, and
consequently the plasma temperature can be maintained low. Moreover,
helium is light and inert, and possible tissue damage due to ion bombardment
and toxic chemicals can be thus excluded. The therapeutic working of the
plasma depends on the additives. As said in section 9.10.1, small doses of
active species may be beneficial, while large doses inflict damage. In case of
a plasma needle, the amount of active species is easy to regulate. The right
dose can be administered by adjusting the plasma power, distance to the
tissue, treatment time and gas composition. So far, helium plasmas with
about 1 % of air have been used.
The glow can be applied directly to the tissues. In figure 9.10.5 one can
see how the plasma interacts with human skin: it spreads over the surface
without causing any damage or discomfort.
Prior to tests with living cells and tissues the needle has been character-
ized in terms of electrical properties, temperature and thermal fluxes. In
figure 9.1O.6(a) the temperature versus plasma power is shown for a needle
with 1 mm diameter: the power lies in the range of several watts and the
temperatures rise far above the tolerance limits for biological materials.
For a thinner needle (0.3mm) the power dissipation is only 10-100mW
and the temperature increase is at most a couple of degrees (figure
9.1O.6(b). Thus, the needle geometry is important for its operation.
The flux of radicals emanated by the plasma into a liquid sample has been
determined using a fluorescent probe (see section 9.10.1). In figure 9.10.7 the
--- Page 680 ---
Medical Applications of Atmospheric Plasmas
665
Figure 9.10.5. Plasma generated in the flexible torch stretches out to reach the skin.
550
Q' 500
...-'
.... -
';' 450 ~
~ 400
.,
~ 350
.,
... 300
250
0
2
4
6
8
10
(a)
power(W)
30
g 28
!:!
~ 26
!:i
0.. B 24
0.15 W
•
22
3
5
7
9
(b)
distance to needle (mm)
Figure 9.10.6. (a) Temperature of the plasma determined using a spectroscopic method for
a 1 mm thick needle. (b) Temperature of the surface (thermocouple) as a function of the
distance between the needle and the thermocouple for a 0.3 mm thick needle.
--- Page 681 ---
666
Current Applications of Atmospheric Pressure Air Plasmas
9
8
7
:i 6
'::5
.!!
. ~ 4
"g
I! 3
2
o •
o
•
.-
•
2
3
•
•
•
•
•
4
5
6
7
8
time (min)
9
Figure 9.10.7. Active radical concentration in a 400 ~l water sample treated with the
plasma needle, as a function of exposure time. The plasma power is about 50mW, the
needle-to-surface distance is 1.5 mm.
concentration of ROS as a function of exposure time is shown for a helium
plasma with 1 % air. The estimated radical density in the gas phase is
1019 m -3. The ROS concentration in the liquid lies in the 11M range. This
amount can trigger cell reactions, but it is too low to cause tissue damage.
9.10.4 Plasma interactions with living objects
Interactions of non-thermal plasmas with living objects are an entirely new
area of research. Of course, the ultimate goal of this research is introducing
plasma treatment as a novel medical therapy. However, living organisms are
so complicated that one has to begin with a relatively simple and predictable
model system, like a culture of cells. In the following section it will be shown
that even the simplest biological models can exhibit complex reactions when
exposed to an unknown medium.
9.10.4.1
Apoptosis versus necrosis
The essential difference between the non-thermal plasma needle and APC or
spark erosion lies in the manner in which the cells are affected. In fine surgery
cell damage should be minimal. Cell death should be induced only when
necessary, and then it should fit in the natural pathway, in which the body
renews and repairs its tissues.
Cell death is the consequence of irreversible cell injury. It can be
classified in two types described below.
• Necrosis, or accidental cell death. Necrosis is defined as the consequence of
a catastrophic injury to the mechanisms that maintain the integrity of the
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Medical Applications of Atmospheric Plasmas
667
cell. There are many factors that cause necrosis: cell swelling and rupture
due to electrolyte imbalance, mechanical stress, heating or freezing, and
contact with aggressive chemicals (e.g. acids, formaldehyde, alcohols). In
necrotic cells the membrane is damaged, and the cytoplasm leaks to the
outside. Since the content of the cell is harmful to the tissue, the organism
uses its immune reaction to dispose of the dangerous matter, and an
inflammatory reaction is induced. In surgery, mechanical, thermal or
laser methods always cause severe injury and necrosis. The necrotic
tissue is eventually removed by the organism, but the inflammation slows
down the healing and may cause complications, the most common being
restenosis and scar formation.
• Apoptosis, or programmed cell death. Apoptosis is an internal mechanism
of self-destruction, which is activated under various circumstances. This
kind of 'cell suicide' is committed by cells which are damaged, dangerous
to the tissue, or simply no longer functional. Thus, apoptosis takes place
in developmental morphogenesis, in natural renewal of tissues, in DNA-
damaged, virus-infected or cancer cells, etc. Presumably, any moderate
yet irreversible cell damage can also activate apoptosis. Known factors
are ultraviolet exposure, oxidative stress (section 9.10.1) and specific
chemicals. The role of radicals and ultraviolet has given rise to the
hypothesis, that plasma treatment may also induce apoptosis.
Since the intracellular mechanism of apoptosis is rather complex, no
details will be given here. The reader may refer to textbooks on cell biology
(Alberts 1994) or more specific articles (Cohen 1997). The morphological
changes in the cell during apoptosis are easy to recognize. In early apoptosis,
the DNA in the nucleus undergoes condensation and fragmentation and the
cell membrane displays blebs. Later, the cell is fragmented in membrane-
bound elements (apoptotic bodies). Note that the membrane retains its integ-
rity, so no cytoplasm leakage and no inflammatory reaction occur. The apop-
totic bodies are engulfed by macrophages or neighboring cells and the cell
vanishes in a neat manner.
It is clear that apoptosis is preferred to necrosis. Selective induction of
apoptosis can make a pathological tissue disappear virtually without a
trace. Such refined surgery is the least destructive therapeutic intervention.
No inflammation, no complications in healing and no scar formation/
stenosis is expected. In the next paragraph plasma induction of apoptosis
and other cell reactions (without necrosis) will be discussed.
9.10.4.2 Plasma needle and cell reactions
A fundamental study on a model system is necessary to identify and classify
the possible ways in which the plasma can affect mammalian cells. Stoffels
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Current Applications of Atmospheric Pressure Air Plasmas
et al (2003) used two model systems: the Chinese hamster ovarian cells
(CHO-KI) and the human cells MR65. CHO-KI cells are fibroblasts, a
basal cell type that can differentiate in other cells, like muscle cells, chondro-
cytes, adipocytes, etc. Fibroblasts are sturdy and easy to culture, which
makes them a good model at the beginning of a new study. They are also
actively involved in wound repair, so their reactions to plasma treatment
may be of interest in plasma-aided wound healing. The MR65 cells are
human epithelial cells, originating from non-small cell lung carcinoma
(NSCLC). The NSCLC is one of the most chemically resistant tumors.
The usage of MR65 has a twofold advantage: (a) information on epithelial
cells brings one closer to medical applications, like healing of skin ailments,
and (b) induction of apoptosis in tumor cells is anyway one of the major
objectives of plasma treatment. Cells were treated using the plasma needle
under various conditions and observed using phase contrast microscopy or
fluorescent staining in combination with confocal microscopy. Initially,
basic viability staining was used: propidium iodide (PI) and cell tracker
green (CTG). Propidium iodide stains the DNA of necrotic cells red, while
cell tracker green stains the cytoplasm of viable cells green. Apoptosis in
tumor cells was assayed using the M30 antibody. Antibody assays are very
specific. M30 recognizes a molecule, which is a product of enzymatic reaction
that occurs solely in apoptosis-a caspase-cleaved cytoskeletal protein.
When M30 binds to this product, a fluorescent complex is formed. The diag-
nosis is unambiguous. Next to specific antibody assays, cells were observed to
detect morphological changes characteristic for apoptosis. Various cell reac-
tions are briefly described below.
Plasma treatment ofliving cells can have many consequences. Naturally,
a high dose leads to accidental cell death (necrosis). Typically, necrosis
occurs when the plasma power is higher than 0.2 Wand the exposure time
is longer than 10 s (per treated spot). In terms of energy dose, this
corresponds to 20J/cm2, which is very high. However, even upon such
harsh treatment the cells are not disintegrated, but they retain their shape
and internal structure. A typical necrotic spot in a CHO-Kl sample is
shown in figure 9.10.8. Note that the dead cells (red stained) are separated
from the living cells (green) by a characteristic void. This void is ascribed
to local loss of cell adhesion.
A moderate cell damage can activate the apoptotic pathway. In MR65
apoptosis occurs under the threshold dose for necrosis. Simultaneously, cell
adhesion is disturbed. Typical images of plasma-treated cells are shown in
figure 9.10.9. The whole cytoplasm of the cell is stained using the M30
antibody, which detects the enzymatic activity that is displayed during
apoptosis. The percentage of apoptosis after treatment is up to 10%; the
plasma conditions still have to be optimized.
When the power and treatment time is substantially reduced (to 50mW
and I s per spot), neither necrosis nor apoptosis occur. Instead, the
--- Page 684 ---
Medical Applications of Atmospheric Plasmas
669
Figure 9.10.8. A sample of CHO-KI cells after plasma treatment: a necrotic zone (red
stained with PI), an empty space and the viable zone (green stained with CTG).
cells round up and (partly) detach from the sample surface: voids like in
figure 9.10.8 (but without necrotic zone) are created in the sheet of cells.
The cells remain unharmed and after 2-4 h the attachment is restored. It
seems that plasma treatment induces a temporary disturbance in the cell
(a)
(b)
Figure 9.10.9. Apoptosis induced in MR65 cells by plasma treatment, assayed by the M30
antibody method: (a) early apoptosis (caspase activity in the cytoplasma, first changes in
the cell shape), (b) late apoptosis (formation of apoptotic bodies).
--- Page 685 ---
670
Current Applications of Atmospheric Pressure Air Plasmas
metabolism, which is expressed (among others) by loss of adhesion. Further
discussion of possible causes is given elsewhere (Stoffels et al 2003).
Cell detachment without severe damage is a refined way of cell manip-
ulation. The loosened cells can be removed (peeled) from a tissue but, as
they are still alive, no inflammatory response can be induced. The area of
plasma action is always well defined: the influenced cells are strictly localized
and the borders between affected and unaffected zones are very sharp. Thus,
plasma treatment can be performed locally and with high precision.
The last but very important feature of plasma treatment is related to
plasma sterilization. The latter is a well-known effect, demonstrated by
many authors (Moisan et a1200l, Laroussi 2002) and even implemented in
practice. Parallel to plasma-cell interactions, bacterial decontamination
using a plasma needle was studied. It appeared that bacteria are much
more vulnerable to plasma exposure than eukaryotic cells. Bacterial inactiva-
tion to 10-4 of the original population can be achieved in 1-2 min at plasma
power lower than lOmW, while under the same conditions the mammalian
cells remain uninfluenced. This demonstrates the ability of a non-thermal
plasma to selectively sterilize infected tissues.
9.10.4.3
Motivationfor the future
Minimal destructive surgery using non-thermal plasmas is still in its infancy.
So far several potentially useful cell reactions have been identified, but the
way to clinical implementation will probably be long and painstaking.
However, one thing can be stated for sure-non-thermal plasma can be
used for controlled, high-precision cell removal without necrosis, be it by
apoptosis, inhibiting proliferation or cell detachment. There are strong
indications that no inflammatory reaction will be induced. After the
necessary tests are completed, an enormous area of applications will open.
Removal of cancer and other pathological tissues, cosmetic surgery, aiding
wound healing, in vivo sterilization and preparation of dental cavities without
drilling are just a few examples. The plasma needle can be also operated in a
catheter (like in APC) and used endoscopically. An enormous effort must be
invested in developing all these therapies, but considering the benefit for
human health, it is certainly rewarding.
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--- Page 688 ---
Appendix
This Appendix contains three sections with results pertaining to section 5.3.3
which were inadvertently omitted from the manuscript. They have been
added in the proof stage as an Appendix.
( C)
Vibrational distribution of N2 ground state
The V-T, V-V and V-V' rates of the foregoing section were implemented
in the model and the vibrational distribution of the N2 ground and
excited electronic states was determined by solving a system of kinetic
equations at steady state in which the vibrational levels of the N2 ground
and excited electronic states are the unknowns. The total concentration of
N2 was determined with the two-temperature kinetic [12] model and fixed
by replacing the vibrational level v = 0 of the ground electronic state by
the mass conservation equation. The total populations of the other species
were fixed and determined with the two-temperature kinetic model, and
their internal distribution was calculated according to a Boltzmann distri-
bution at the vibrational temperature Tv = Tg and at the electronic
temperature Tel = Te. We now present our calculations of the vibrational
distribution of the N2 ground state at Tg = 2000 K and for different electron
temperatures.
For electron temperatures Te lower than 6000 K, the vibrational distri-
bution is very close to a Boltzmann distribution at the gas temperature
Tg = 2000 K. Figures A.l and A.2 show the calculated vibrational distribu-
tions for a gas temperature of 2000 K and an electron temperature of 9000 K
and 16000K respectively. The Boltzmann distributions at Tv = Tg and
Tv = Te are also shown on these figures.
For Te = 9000 K, the vibrational excitation introduced by VE transfer is
mainly redistributed via V-T relaxation of N2 by collision with N2, and via
Nr N 2 V-V exchange. The N 2-02 and NrNO V-V' processes do not signif-
icantly affect the populations of N2 levels. We checked that this conclusion
remains valid if we assume a different internal distribution for the O2 and
NO molecules.
673
--- Page 689 ---
674
Appendix
1019
-- calculated distribution
1017
1015
1013
?
\,--___
---- Boltzmann at Tv=T;
,
--__ --- Boltzmann at Ty=T.
,
--
,
--
,
--
,
--
,
--
,
--------
~
,
,
5 1011
, , ,
.!:
c:
109
.2
1U
107
"S
C.
0 C. 105
103
101
10-1
0
, , , , , , , , , , , , , , , , , , , , , , , , , ,
., •••• ~ •••• ~ •••• ~ ••• t ••• 1 ..•.... , .... ~ ....•...... ~ ....•... I. ~ ... .l ..... ,. A .. ~ ••• ~ •••• ~ •••••••• A •••• A L ., .... ~.~.,.., .. A ••••••••• ~ ••• ,. , • •• L..A ••• ~ •• L.~ .... l .... t
10
20
30
40
vibrational level v
Figure A.I. N2(X,V) vibrational distribution function at Tg = 2000K and Te = 9000K,
p= I atm.
h
1017
f· \
----
,
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\ ,
\
--
,
109
\
I
\\
. , I
•
,
! , .
-- calculated distribution
---- Boltzmann at Tv=Tg
--- Boltzmann at Tv=T.
.j
-----.... ----------- ..... . j
"
~
107 L
\
i
\,
!
105 L, .... ,
... ,
.... ,
........ ,
.... , ....... , .. ,
... , .. ,
........ ,
.... ,
.... ,
... , ....... ,
.. ~~ •...... , ............ ,
.... ,
.... , . , ... 1...., •.• , .•.• , ...••... , .•.••.•.••... , .... , 1..., .... , ... , ... , .... , .... , ... 1
o
10
20
30
40
vibrational level v
Figure A.2. N2(X, v) vibrational distribution function at Tg = 2000K and Te = 16 OOOK,
p= I atm.
--- Page 690 ---
Appendix
675
Indeed, the rates of NrNO exchange are faster than those of N2-N2
exchange above v = 3 (see figure 5.3.11 in section 5.3.3), but the total concen-
tration of NO is two orders of magnitude lower than the concentration ofN2
and the rates for Nr 0 2 v-v exchange are fast for v> 20 but the population
of those levels is mainly governed by V - T transfer processes. The vibrational
distribution at Te = 9000 K lies between the Boltzmann distributions at
Tv = Tg and Tv = Te, but remains closer to a distribution at Tv = Tg.
For Te = 16 000 K, almost 25% of the O2 molecules are dissociated and
the vibrational excitation is mainly redistributed by V-T relaxation ofN2 by
collision with 0 atoms and by Nr N2 v-v exchange. At this electron
temperature, the vibrational distribution of the first 15 levels is close to the
Boltzmann distribution at Tv = Te.
( D )
Inelastic electron energy losses in air plasmas
Electron inelastic energy losses can now be calculated by summing the contri-
butions of all electron impact collisional processes
Qinel= L
[LL~{(Ej-Ei)]
processes
I
j
(A.l)
where Ej - Ei represents the internal energy gained by heavy species during
the collision (Ej must be greater than Ei) and dnj/dt is the net volumetric
rate of production of heavy species in the final energy level f. In an atmos-
pheric pressure air plasma characterized by a gas temperature between
1000 and 3000 K and electron temperatures up to 17 000 K, the dominant
contribution to electron inelastic energy losses is the electron-impact
vibrational excitation of N2 ground state. The electron impact vibrational
excitation cross-sections of O2 and NO ground states are two orders of
magnitude lower than those of N2, and therefore the contribution of these
molecules is negligible.
The total rate of energy loss can be expressed as
(A.2)
where VI and V2 are the initial and final vibrational levels of the transition,
and where the elementary rate QVIV2 is written as
QVIV2 = (kVIV2 [N2(X, vdl- kV2V1 [N2(X, v2)])ne~Ev2Vl·
(A.3)
In equation (A.3), ne is the concentration of electrons, kV1V2 and kV2V1 are the
excitation and de-excitation rate coefficients and ~EV2Vl stands ~or the differ-
ence of energy between the two vibrational levels V2 and VI· QVIV2 depends
strongly on the N2 ground state internal distribution. Vibrational population
distributions calculated with the method presented in the foregoing section
are used in equation (A.3) to determine the electron inelastic energy losses.
--- Page 691 ---
676
Appendix
106
105
.. ~
E
104
0
~ 103
<f)
CD
!Z
102
.2
1
101
,Q
10°
(j)
as
~ 10-1
c:
0 15 10-2
~
CD 10-3
10-4
....... .J
... .1
0
5000
10000
15000
20000
electron temperature T.(K)
Figure A.3. Predicted inelastic electron power losses in atmospheric pressure air at 2000 K.
The predicted inelastic power losses are shown in figure A.3. At low electron
temperatures and densities, the vibrational levels ofN2 ground state are close
to a Boltzmann distribution at Tv = Tg• The excited vibrational levels have
low population.
Therefore, the power lost by e-V excitation is not balanced by the power
regained from V-e super-elastic de-excitation. As the electron temperature
increases, the electron density also increases and eventually the vibrational
population distribution tends toward Tv = Te. The net power losses do not
increase as rapidly because of the increased importance of super-elastic
collisions. It is sometimes convenient to define an electron 'energy loss
factor' as the ratio of total (elastic + inelastic) energy losses to the elastic
energy losses
De = QeJ ~ QineJ
QeJ
(A.4)
where QeJ is the volumetric power lost by free electrons through elastic
collisions, and QeJ is the sum of contributions of collisions between electrons
and heavy species h = N2, O2 and 0:
.
'" (
)me_
Qel = ne L 3k Te - Th -lleh'
h
mh
(A.5)
In equation (A.5), k is the Boltzmann constant, me and mh are the masses of
electron and heavy species respectively, Th is the kinetic temperature of the
--- Page 692 ---
Appendix
677
1500
>E--K Tg=1800K
*"-* Tg=2000K
-Tg=2900K
...
1000
~
VI
VI
..Q
>.
!?
Ql
I:
Ql
500
9000
14000
electron temperature T. (K)
Figure A.4. Energy loss factor De at Tg = 1800,2000 and 2900 K, as a function of Te.
heavy species (equal to Tg), and Deh represents the average frequency of
collisions between the electrons and heavy particle h. Deh can be expressed
in terms of the number density of neutral species nh, the electron velocity
ge = J8kTe/7fme and the average elastic collision cross-section Q~h:
(A.6)
Figure A.4 shows the calculated electron energy loss factor as a function
of the electron temperature for two values of the gas temperature, Tg = 1800
and 2900 K. As can be seen from this figure, the inelastic loss factor is a rela-
tively weak function of the gas temperature. It increases up to Te = 8000 K as
the net rate of production of N2 molecules in vibrational level V2 > VI
increases with Te, and then decreases due to the transition Tv ~ Tg to
Tv ~ Te. When Tv becomes close to Te, the forward and reverse rates are
practically balanced and the net rate of energy lost by VE transfer
approaches zero.
(E)
Predicted DC discharge characteristics in atmospheric pressure air
The results of the previous subsections enable us to convert the 'S-shaped'
curve of ne vs. Te into electric field vs. current density discharge characteristics.
This result is obtained by combining Ohm's law and the electron energy equa-
tion. The latter incorporates the results of the collisional-radiative model to
account for non-elastic energy losses from the free electrons to the molecular
species. The predicted discharge characteristics for atmospheric pressure air at
--- Page 693 ---
678
Appendix
2000
1800
1012
-1
13
~ 1
1600
nj'10 em
- 1400
..
l
E
0
~ 1200
w
1
,; 1000
1
Q)
u:::
800
I
~g
i
~ 600
400
1
200
j
~0-4
10~
10-2
10-1
10°
101
102
Current Density. j (A.em-2)
Figure A.S. Predicted discharge characteristics for atmospheric pressure air at 2000 K,
2000 K are shown in figure A,S, These discharge characteristics exhibit
variations that reflect both the S-shaped dependence of electron number
density versus Te, and the dependence of the inelastic energy loss factor on
the electron temperature and number density, We have used these predicted
characteristics as a starting point to design the DC glow discharge experi-
ments presented in section 5.2, If these predictions are correct, the produc-
tion of 1013 electron/cm3 requires an electric field of rv 1.35 kV/cm, and a
current density of rvl0.4A/cm2. Thus the power required to produce
1013 electrons/cc in air at 2000 K is approximately 14 kW /cm3 .
--- Page 694 ---
Index
AC corona 60, 61, 62
AC torch 276, 350
Active zone 48,49,50,51
Aerodynamics 3
Afterglow 137
Air chemistry 5, 6, 124-182
Anharmonicity effects 455-458
Anode layer 51, 52, 53, 54
Anti-Stokes scattering 455
Arc discharge 17, 18, 35
Arrhenius plot, 125
Atmospheric layers 4, 5
Atmospheric-pressure glow discharge
(APGD) 255-257
Attachment (dissociative) 99, 127,
201
Attachment coefficient 32, 33
Ball lightning 8, 9
Barrier corona 61, 62, 63
Barrier discharge 276-278, 280, 283, 286,
287, 291, 293, 294, 299, 300, 307,
316,321
Bio-compatibility 655
Biological decontamination 643-653
Boltzmann (Maxwell-Boltzmann)
distribution 86-88, 128, 139, 184,
200,376,450
Breakdown 17,26,29,30,31,32,33,35,
36,37, 38, 39, 63, 68, 69, 71, 185,
247,262-274,279,281,298,300,
303, 304, 307, 348, 354, 359
Brillouin scattering 477
Burst corona 42, 54
Capture 100
Cathode boundary layer (CBL)
discharge 319
CARS (coherent anti-Stokes Raman
spectroscopy) 462, 471
Cathode fall 34, 279, 281,304,307-310,
316-319,324
Cathode layer 34, 38, 48, 49, 50, 51, 54,
282, 308, 329, 336
Cavity ring down spectroscopy (CRDS)
517-535
CBL discharge (cathode boundary layer)
307, 319, 320
Cell reaction 667-670
Charge transfer, 127, 144
Chemical decontamination 621-639
CHEMKIN 205,210
Cleaning 597, 601-605
Cold plasma 19, 21
Collision 13
cross section 190
energy 138
frequency 212
inelastic 199
one-body 94, 95
two-body 96-103, 130
term 106
three-body 130
Collisional-radiative model, 201
Combustion enhancement 577-580
Computer modeling, 183
Corona discharge 12,14,17,41,47,54,
60, 63, 64, 329, 338
Corona-to-spark transition 52, 53
679
--- Page 695 ---
680
Index
CPE discharge (capillary plasma
electrode) 306, 307, 321-324
Cross section 97-100, 125, 127
Current density (electrons) 192,211,225,
243
Current-voltage characteristic 295-297,
300 ,308,311-313
D-value 645, 647
DC corona 42, 47, 54, 61
DC glow discharge (see glow discharge)
Debye length 89, 213
Decay rate 96
Decontamination 3, 14
De-NOx process 622-633
Deposition 597, 615-617
Detachment 55,59, 148
Detailed balance 203
Diagnostics 10, 14
Dicke narrowing 461
Dielectric-barrier discharge (DBD) 12,
14, 17, 68, 184, 277, 260, 245-260
Diffuse discharge 284,297, 301
Diffusion 192
Dispersion relation 566
Dissociation (electron impact) 99, 126,
201,207
Dissociation (heavy particle) 100
Distribution function 79-85
Doppler broadening 447, 448, 461, 469,
512
Drift tube 140
Efficiency (of plasma generation) 6, 7
Electric field 227, 239
Electric potential 241
Electrical conductivity 191, 240
Electromagnetic absorption 565-574
Electromagnetic reflection 565-574
Electromagnetic theory 566-569
Electron 77, 124
Electron-beam sustained plasma 427
Electron density 488-500, 517,
525-528
Electron-driven reactions 99, 100,
127-129
Electron energy distribution function
(EEDF) 125, 184,447,448
Electron impact excitation 99
Electron impact ionization 99
Electron-ion recombination 13,418
Electron lifetime 7
Electron loss reduction 428
Electron temperature (see temperature,
electrons)
Electrosurgery 657-663
Electrostatic precipitation 539-551
Emission bands 447
H2 (Fu1chur band) 447,501-509
N2 (second positive band) 212,
505-509
Nt (first negative band) 447, 501-509
NO 506-508
OH 221
0 2 505
Emission spectroscopy 390, 501- 516
Epstein distribution 567
Equilibrium 124, 139
Equivalent circuit 72
Etching 597, 613-615
Excitation 99, 100, 125, 126
electronic 125
vibrational 127, 148-152, 161
rotational 139
Fine structure effects 512
Flow control 588-589
Functionalization (surface) 597, 607-613
Glow corona 42, 43, 44, 54, 55, 56, 57
Glow discharge 2, 18, 22, 23, 34, 38, 45,
50,59, 184, 199,218,229,245-269,
277,279,245,282-284,286-288,
290,291,298,299,304,307,308,318
319, 324, 328, 329, 334-344, 346
Glow-to-arc transition 295, 318, 319
Guided ion beam 159
Heavy particles 76
Heavy particle reactions 100-102
Heavy particle ionization 201
Heterodyne interferometry 488-500
High temperature flowing afterglow
(HTFA) 138-140, 145-148
Hollow cathode discharge 276, 307,
309-311, 313-315, 31~ 318
--- Page 696 ---
Homogeneous barrier discharge 277,
286,293-305
Humidity 4, 6
Hydrocarbon-air combustion 574-586
Hydrogen Balmer lines 403
Inactivation factors 648-652
Inactivation kinetics 645-648
Instabilities 446
Interferometry 482-488
In-vivo treatment 657-662
Ion 124
Ion concentration 517-535
Ionization 99, 100, 124, 126
direct 124
step-wise 124
Ionization coefficient 30, 32, 33, 38, 46,
48,49
Ionization instability 57, 58
Ion-molecule reactions 136, 140-178
Ion-pair production 99
Ionosphere 7, 138
I - V characteristic 290, 307, 314, 342-345
Kinetic equation 105-117
Kinetic theory 78
Laser ionization 364
Laser pumping 364
Laser scattering 450-481
Laser-sustained plasma 365
Life time 127
Line width 448-450
Gaussian 448-450
Lorentzian 448-450
Natural 509
Resonance 509, 510
Van der Waals 509, 510
Voigt 448-450
Lightning 3, 8
Liquid crystal display (LCD, active
matrix LCD) 262-263
Local thermodynamic equilibrium 221,
400, 501
MATLAB 210
Maxwell's equations 90
Medical application 655-670
Index
681
MHC discharge (microhollow cathode)
230,276,307,309-311,313-315,
317,318,321
Microdischarge 69, 70, 71,72, 184,
258-259,276-279,281,297,
280-283,307,309-318,324,493
Microstructured electrode arrays 309
Microwave absorption 3, 14
Microwave plasma 395
Millimeter wave interferometry 482-488
Modeling 1, 10
Monte Carlo simulation 185, 255,
266-268
Multidimensional modeling 233
Navier-Stokes equations 186
Neutral particle (neutrals) 137
Nonequilibrium air plasma chemistry
154-167
Number density,
electrons 195, 196, 199
ions 241
Ohm's law 211
Ozone 128,276,277,278,280,282,287,
289,290,291,297,316,551-563
Oxidation 605-607
Particle-in-a cell model 185,255,
266-268
Paschen curve 30, 32, 34
Penning ionization 100
Phase shift 565-574
Photo-excitation 102
Photo-detachment 102
Photo-dissociation 102
Photo-ionization 14, 102
Photon 78
Pin-to-plane corona 233
Plasma combustion 3, 14
Plasma display panels 253-255, 263,
265
Plasma needle 663-666,667-670
Plasma mitigation 587-597
Plasma parameters 446
Plasma processing 2, 3, 14
Plasma spikes 589-594
Plasma torch 350-361,395,574-586
--- Page 697 ---
682
Index
Poisson equation 189, 236, 238
Pollution control 3, 14
Power factor 73, 74
Proton transfer reaction 164
Pulsed breakdown 38
Pulsed streamer corona 63
Radiation-driven processes 102-103
Raman scattering 451-455, 459, 469
Raman spectroscopy 374
Rate coefficient 125, 130-135, 200, 214
Rayleigh scattering 459, 469
Recombination 99,127,168-175
Refractive index (index of refraction)
488, 490
Replenishment criterion 45, 48
Replenishment integral 56
Resistive barrier discharge 276, 293, 299,
300
RF discharge 14, 19,21,22
RF plasma torch 362
Runaway electrons 38, 39
Saturation current 543
Scramjet propulsion 574-586
Shock waves 587-597
Space charge 543
Spark formation 51, 59, 60, 64, 329, 341
Spark transition 47,52,53,58
SPECAIR 222
Sputtering 598
Stark broadening 401, 509
Stefan-Boltzmann law 88
Sterilization 3, 14
Stokes scattering 455
Streamer 26,35,42, 54, 56, 63, 281, 297,
298, 304, 324, 348
Streamer breakdown 35, 44, 63,
247-248,276,287,290,291,338
Streamer corona 42, 44, 56, 63
Streamer-to-spark transition 58
Sub-breakdown 386
Supersonic flight 587-597
Surface dissociation 598
Surface ionization 598
Surface treatment 276,287,290,291,
338, 597-618
Temperature,
electron 124, 183, 200
gas 203, 217, 221
ion 124
neutral 124
rotational 124, 200, 221
translational 196
vibrational 124, 136-144, 200
Thermal conductivity 190
Thermal plasma 19,21, 35,42, 124
Thomson scattering 451-455, 459, 469
Torch plasma 351, 354-358
Townsend breakdown 29, 33, 35,
247-248
Townsend criterion 32
Townsend discharge 30, 34, 44, 45, 46,
283,284
Townsend mechanism 35, 36, 281, 348
Trichel pulse 43, 47, 48,50,51, 184,233,
239,243,329,330-335,340
Two-temperature model 200
Ultraviolet radiation 279, 316, 650
UV flash tube 362
Velocity distribution 125, 200
Vibrational distribution functions
465-469
Vibrational enhancement 149
Viscosity 190
Volt -ampere characteristic 44, 46
Voltage-charge Lissajous figure 71
Voltage-current characteristic 313, 320,
321, 333, 335, 337, 338
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