plasma-expert/reference/sources/ufn-2000-paper.txt

=== PAGE 1 ===
Abstract. Physical processes determining the ability of light-
ning to change its trajectory by choosing high constructions to
strike are discussed. The leader mechanism of lightning propa-
gation is explained. The criterion for a viable ascending (up-
ward) leader to originate from a construction is established. The
mechanism of the weak long-distance interaction between the
ascending counter leader originating from a grounded construc-
tion and the descending (downward) leader from a cloud is
analyzed. Current problems concerning lightning protection
and lightning triggering by a laser spark are discussed, the
latter being of special interest owing to a recent successful
experiment along this line.
1. Introduction
Experiments to initiate a high-voltage discharge employing a
laser-produced plasma and to direct the discharge along the
channel of a long laser spark [1 ± 12] as well as the advent of
lasers appropriate for this purpose have lent impetus to
attempts to control lightning with lasers. Research in this
field, which is being pursued in the USA, Japan, Canada, and
Russia [13 ±31], until recently did not go beyond the scope of
laboratory investigations, though goal-seeking. In recent
years, however, a start was made on natural experiments in
Japan. As a result of repeated attempts, two events of
successful lightning triggering with the aid of a laser plasma
produced near the summit of a tall tower were recorded in
1997 [17, 18, 21]. These undeniably impressive results raised
the expectations of many that the dawn of an era of laser
techniques in lightning protection is near. Of prime impor-
tance in this connection is a clear understanding of the
lightning processes and a statement of what is definitely
known about the basic lightning mechanisms and what
invites elucidation or comprehensive investigation. This will
facilitate the search for efficient ways of controlling lightning
by laser action in an effort to promote both research and
lightning protection. At the same time, this will guard against
excessively optimistic expectations, especially where engi-
neering practice is involved.
Below we will consider some key physical mechanisms of
the lightning process, discuss the potential of laser triggering
of lightning and the requirements on the control laser spark,
and highlight the currently topical problems of lightning and
lightning protection physics that might be solved with the aid
of lasers.
2. How the lightning leader works
Of prime interest for both lightning physics and practical
lightning protection is descending lightning which originates
in a cloud and propagates towards the ground. In conse-
quence of the lightning ± ground contact, the cloud or part of
it (a charged cell) eventually discharge. Usually, a lightning
flash consists of several sequential components spaced at tens
of milliseconds, which travel through a common channel (and
EÂ M Bazelyan G M Krzhizhanovski|¯ Power Engineering Institute,
Leninski|¯ prosp. 19, 117927 Moscow, Russian Federation
Tel.: (7-095) 955-31 39; Fax: (7-095) 954-42 50
Yu P Ra|¯zer Institute for Problems of Mechanics,
Russian Academy of Sciences,
pros. Vernadskogo 101, 117526 Moscow, Russian Federation
Tel.: (7-095) 434-01 94; Fax: (7-095) 938-20 48
E-mail: raizer@ipm.msk.ru
Received 23 March 2000; revised 19 April 2000
Uspekhi Fizicheskikh Nauk 170 (7) 753 ± 769 (2000)
Translated by E N Ragozin; edited by A Radzig
PHYSICS OF OUR DAY
PACS numbers: 52.80. ± s, 52.80.Mg, 51.50.+v, 52.90.+z
The mechanism of lightning attraction and the problem
of lightning initiation by lasers
EÂ M Bazelyan, Yu P Ra|¯zer
DOI: 10.1070/PU2000v043n07ABEH000768
Contents
1. Introduction
701
2. How the lightning leader works
701
3. Initiation of descending lightning in a cloud
704
4. Build up of the leader of descending lightning and potential delivered to the ground
705
5. Attraction of lightning. Ascending counter leader
707
6. Physical mechanism for the attraction of lightning
708
7. Adverse effect of the corona on the initiation of ascending and counter leaders and the possibilities
to overcome it
709
8. Demands for, capabilities of, and modern trends in lightning protection
711
9. Laser triggering of lightning
712
10. Requirements on a laser-produced channel
714
11. Conclusions
715
References
716
Physics ± Uspekhi 43 (7) 701 ± 716 (2000)
#2000 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences

=== PAGE 2 ===
sometimes through different ones). The overall flash duration
may be as long as a second; sometimes the `component' flicker
of a channel is discernible to the human eye. The first
component, which makes its way through the unperturbed
air, is similar in nature to the laboratory spark leader which
breaks down the long gap, say, between a high-voltage rod
and a grounded plane.
The electric field in this gap is strongly nonuniform. It
focuses near the small-radius rod tip. The air in this region
begins to ionize, which requires a field E > Ei  30 kV cmÿ1,
with the effect that under specific conditions there arises a
thin plasma channel growing towards the plane. Despite the
fact that the channel soon enters the domain of a very weak
external field not nearly strong enough to ionize air, it
continues to grow. Due to the still high conduction of the
channel, the high electrode potential U is transferred without
significant losses to the front end of the channel Ð the tip of
small radius r. The tip is a source of a strong field Em  U=r,
and the adjacent air ionizes. As soon as the new volume of air
acquires a high conduction, the high potential is transferred
to it, and this volume becomes the new tip. The length of the
plasma channel therewith increases. The ionization process in
the vicinity of the tip is inherently the propagation of an
ionization wave. The structureless plasma channel thereby
produced is referred to as a streamer (Fig. 1).
The theory of streamers is in an advanced stage of
development and permits estimation of the main parameters
in agreement with experiment [32]. In air, for a voltage of 10 ±
1000 kV, the streamer travels at a speed vs  107ÿ109 cm sÿ1
and produces, immediately behind the tip, a plasma with an
electron density up to 1014 cmÿ3 in a channel of radius
r  0:1 ± 1 cm. But in cool air electrons attach themselves to
oxygen molecules in 10ÿ7 s and also recombine rapidly with
the resultant complex O‡
4 ions. That is why a cool plasma
channel does not live long and does not grow to very great
lengths. As shown by experiments, in cool normal-density air,
a positive (moving towards the cathode) streamer grows for
as long as the average external field over its length exceeds
Ecr  4:5ÿ5 kV cmÿ1, while Ecr  10ÿ12 kV cmÿ1 for a
negative streamer. Hence, for U ˆ 5 MV Ð a nearly limiting
voltage for laboratory experiments Ð a negative streamer can
grow no longer than U=Ecr  5 m. Meanwhile, spark
discharges longer than 100 m have been obtained at this
voltage in the laboratory (to be more specific, at outdoor
high-voltage test benches), whereas lightning ranges into
kilometers for an average external field of only 100 ±
200 V cmÿ1.
The only way to prevent an air plasma from decaying in so
weak a field is to heat the gas to a high temperature. For
T 5 5000 K, the electron losses due to their attachment are
virtually nonexistent, the electron recombination is moder-
ated owing to the decay of complex ions, and the electron loss
is compensated for by associative ionization involving O and
N atoms, which does not require an electric field. But the
radius of the channel which may be heated is sharply limited,
for only a limited amount of energy can be expended for this
purpose. As is well known, in charging a capacitor with
capacitance C to a voltage U, an energy CU 2=2 dissipates,
which is equal to the electric energy to be stored. About the
same is the case with a growing long line with distributed
parameters, typified by the channel [32]. The capacitance of a
unit length of the channel of radius r and length L 4 r is
approximately equal to
C1 
2pe0
ln…L=r† ˆ 0:555
ln…L=r† pF cmÿ1 :
…1†
The capacitance of a unit length of its tip, if it is taken to be
a hemisphere, C1t  2pe0r=r ˆ 2p0e0 is ln…L=r† times larger
and does not depend on the radius at all. No more energy than
C1tU2=2 ˆ pe0U2 can be spent to form a unit length of the
channel, including its heating. For instance, 28 kJ cmÿ1 if
U ˆ 10 MV, which is typical of weak lightning. This energy
can heat an air column of radius r  1 cm to 5000 K (at a
pressure of 1 atm, the specific enthalpy is equal to 12 kJ gÿ1).
In laboratory conditions for U  1 MV, r  1 mm.
However, a prodigious field U=r  106ÿ107 V cmÿ1
would have been induced near the channel tip for so small a
radius. The electric field around the cylindrical channel,
E  U‰r ln…L=r†Šÿ1,
would
also
be
very
strong
(ln…L=r†  10). An extremely strong ionization wave would
travel through the air surrounding the tip and the channel,
which would immediately increase their radius. But in this
case the amount of energy would fall short of the gas heating.
Being cool, the channel would rapidly lose conductivity and
the electrical link to the voltage source. It would cease to
grow. We arrive at a vicious circle. The voltage should be
augmented to increase the energy deposited into the channel,
but simultaneously the volume of the conducting (and
therefore heated) gas increases owing to the ionization
expansion, with the effect that the specific energy deposition
does not rise. This is precisely the reason why a long
laboratory spark and lightning cannot constitute a structure-
less plasma channel akin to a streamer. They propagate
employing the leader mechanism.
The leader is structurally much more complex. The thin
plasma channel of a leader is embedded in a shell of space
charge (termed a cover) of the same sign as the channel
potential U. The cover radius RL 4 r. The potential U now
falls off at a radial distance of the order of RL rather than r, as
+
+
+
+
x
a
E
x
ncr
n‡ ÿ ne
ne…x†
x
b
Ecr
Em
E…x†
Figure 1. Schematic of the front part of a positive streamer (a), and
qualitative distributions of the electron density ne, the difference between
the densities of positive ions and electrons, n‡ ÿ ne, which determines the
space charge density, and of the field E along the axis in the vicinity of the
tip (b).
702
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 3 ===
was the case with a streamer. That is why the electric fields at
the channel surface and near the leader tip prove to be
moderate even for a very high voltage Ð ranging into tens
of megavolts, as for lightning. Nevertheless, the field around
the tip is high enough to initiate streamers, Et  30 ±
50 kV cmÿ1. The tip serves as a source of a diverging bundle
of numerous streamers which make up a continuous sequence
starting from the tip as from a high-voltage electrode. On
travelling a distance of the order of Rs  U=Ecr, the streamers
come to a halt. For a negative leader for U  10 MV,
Rs  10 m. A streamer zone is thereby formed in front of the
leader tip (Fig. 2). It is occupied with moving streamers and
those already dead. The charge introduced by the streamers
becomes the cover charge. Penetrating into the streamer zone
preformed, the growing leader channel pulls on a cover of
radius RL  Rs.
The channel tip moves to a new position, adding a new
portion to the channel, when the current of many `young', just
emitted and still well conducting streamers is concentrated in
a thin column to heat it to a high temperature providing
retention of the conductivity. This is the most important
phase of the leader process Ð the current contraction to a thin
filament is akin to the effect of constriction in a glow
discharge and is associated with the action of an ionization-
overheating (thermal) instability [33]. The scale for the leader
velocity vL is supposedly the ratio between the length of the
streamers that retain a good conductivity, l  vs=na (vs is the
velocity of streamers in the immediate neighborhood of the
leader tip, and na is the electron attachment frequency), and
the characteristic instability build-up time tins. The bundle of
conducting streamers nearly in contact with each other, in
which the electron density is still relatively high, supposedly
forms what appears in the photographs as a bright leader tip.
The tip radius r is therefore about the same as l. For the values
vs  107 cm sÿ1 and na  107 sÿ1 typical of the streamer zone
of laboratory leaders, one finds l  1 cm. The instability
build-up time in this case is, according to calculations [32], of
the
order
of
tins  10ÿ6
s.
Hence
it
follows
that
vL  l=tins  106 cm sÿ1. Estimated values of r and l agree,
in order of magnitude, with those given by experiments. The
lightning leader velocity vL is higher by an order of
magnitude, since the tip voltage is 1 ± 2 orders of magnitude
higher and all the processes are more intense. The effects and
the processes in the leader tip and in the streamer region are so
complicated that the dependence of the leader velocity on
external factors is hard to represent in the form of a reliable
and physically transparent formula. Neither an adequate
theory, nor adequate numerical calculations exist at present.
The understanding of the phenomena which determine the
leader velocity does not, even qualitatively, go far beyond the
scope of what was just stated. This issue is discussed some-
what more fully in Ref. [32]. One can find there a numerical
simulation of the instability development that is responsible
for the contraction of the current in the leader tip to a thin
filament, thus allowing the plasma heating up to a high
temperature.
In a leader, the ionization-overheating instability builds
up in a somewhat different manner than in the contraction of
a glow discharge. In the latter, the process proceeds for a fixed
voltage, while in a leader for a fixed current. The source of this
current is the streamer zone which possesses an extremely
high resistance. It is as if this region served as a current
generator, and no processes in the leader tip (including
contraction of the currents of many streamers to a thin
pinch) can alter this current.
Progress toward understanding lightning processes is
impossible without prescribing some reasonable dependence
of the leader velocity on external parameters. Having no
theoretical dependence at our disposal, subsequently (see
Section 4) we will invoke an empirical relationship and,
naturally, provide a physical substantiation of which of the
external parameters is the controlling one as regards the
velocity. We note that constructing a good leader theory is a
topical problem for the future, if we are seriously interested in
the processes underlying the development of long sparks and
lightning. Determination of the leader velocity should be one
of the outcomes of this theory.
The situation with the theory of a leader channel is little
better (from the quantitative standpoint). Without this
theory, it is also hard to make advances in the description of
the lightning processes. The voltage drop across the channel
and, hence, the potential of the leader tip responsible for the
leader movement depend on the intensity of the longitudinal
field in the leader channel. The leader channel resembles the
channel of an arc. The quasi-stationary state with a non-
decaying quasi-equilibrium plasma with an electron density
ne  1014 cmÿ3 is sustained in a leader channel and an arc by a
relatively weak field. The state in an arc channel is determined
by the current flowing through the arc. The plasma
temperature and the longitudinal field depend on the
current. For a relatively high current i  100 A, the plasma
is quasi-equilibrium in the sense that the temperature of the
electron gas Te and that of the gas of heavy particles T,
including ions, are close to each other (Te  T  10; 000 K),
and the degree of ionization corresponds to this temperature
according to the laws of thermodynamic equilibrium. For
i  100 A, the plasma of an arc channel is sustained by electric
fields of several volts per centimeter. Indeed, such are the
leader currents in lightning. In a laboratory leader, the
current is lower, i  1 A, and the electric field in the channel
is stronger Ð according to different estimates, several
hundred volts per centimeter ( 1 ± 5 kV cmÿ1 immediately
after the initiation of a new portion of the channel). In an air
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
‡U
‡+
+
+
+
+
+
+
+
+
+
+
Anode
Cover
Channel
Tip
Streamer
zone
Streamer
zone
Channel
Figure 2. Photograph (made in a laboratory) and schematic representation
of a positive leader.
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
703

=== PAGE 4 ===
arc at atmospheric pressure for so low a current, the field is
weaker though also close to 100 V cmÿ1. In low-current arcs,
the gas temperature is distinctly lower than 104 K and the
temperatures are appreciably different, viz. Te > T. It seems
likely that the situation is also the same in the leader channel
of a laboratory spark. Since the theory of the leader channel is
also far from completion Ð and knowing the electric field in
the channel and its dependence on the leader current is
indispensable to an understanding of many lightning pro-
cesses Ð in the subsequent discussion we will take advantage
of the following approximation formula
i  b
E ;
b  300 V A cmÿ1 ;
…2†
which describes in a crude way the calculated and experi-
mental results relating to the volt ± ampere characteristic of
an air arc at atmospheric pressure for moderate currents
i  1ÿ100 A [33]. The leader and arc channels are compared
more fully elsewhere [32].
3. Initiation of descending lightning in a cloud
On the average, about 90% of descending lightning carries a
negative charge to the ground, the start being made from the
lower, negatively charged part of the cloud dipole (Fig. 3).
The initiation of descending lightning in a cloud is literally
shrouded in mist. Nobody ever saw or recorded it. One may
conjecture the initiation mechanism, but one thing is clear. A
cloud is not a conductor and cannot be likened to an electrode
of large radius connected to a high-voltage generator. The
negative charge of the cloud resides in hydrometeors
(droplets, snow flakes) Ð small low-mobile macroscopic
particles separated by a dielectric air medium. In the short
time it takes the lightning leader to propagate to the ground
and the cloud to discharge, the carriers of the cloud charge
have no time, so to say, to move out of the positions.
The average electric field in the cloud cell (of the order of
several kV cmÿ1) is not nearly strong enough to ionize the air,
which requires at least 20 kV cmÿ1 at an altitude of 3 km. The
initial ionization, without which a leader cannot originate,
occurs owing to a chance field strengthening in a small
volume. It is conceivable that a local accumulation (a
vortex) of charged hydrometeors is responsible for this. By
the way, even near uncharged hydrometeors the maximum
field is at least three times stronger than the average, because a
water droplet with a relative permittivity e1 ˆ 80 polarizes
almost like a metal conductor. For a spherical droplet, the
polarization charge suffices to triple the electric field; for
droplets elongated along the field, the effect is even stronger.
It was hypothesized that the initial track of ionization is
produced by a high-energy particle being a constituent of
cosmic rays. Nobody knows this with certainty. It is beyond
question that the lightning leader should originate from some
ionized conducting plasma object extended along the vector
of the cloud field E0. Owing to the polarization of a conductor
of length l 4 r (Fig. 4), the field at its ends strengthens as
Em  E0 ‡ DU
r
 E0

1 ‡ l
2r

:
…3†
The tip of the initiator conductor serves as the source of
streamers in the bundle of which there originates a leader [32].
In this respect, both ends are equivalent, and therefore two
leaders emerge. The twin leaders move in opposite directions.
One, being negative, moves primarily down to the ground (if
the leaders originated in a negatively charged cloud cell, as is
shown in Fig. 5) while the other, the positive one, moves
upwards. The leaders are electrically linked to each other and
are therefore interdependent: as they grow, the charge flows
from one to the other. In this case, the charge cloud remains in
place. During their development, the leaders can bypass the
charged regions altogether if they originated outside the
charged cell. As the descending leader grows, it is supplied
6
km
4
2
0
Rc
‡Qc
ÿQc
D
H
Figure 3. Charge distribution in a cloud and model of the equivalent cloud
dipole. Sometimes beneath the negative-charge domain there resides a
small positive charge, which is disregarded by the dipole model. Typical
geometric and electric scales are: H  D  3 km; Rc  0:5 km; Qc  10 C.
Taking into account the mirror charge reflection by the perfectly
conducting ground, the potential at the center of the negatively charged
cell is U  ÿ290 MV relative to the ground; the potential at the lower edge
of the negatively charged sphere is ±180 MV.
l
x
2r
U…x†
U ˆ ÿE0x
E0
E0
E
E0
Em
Em
t
ÿ
‡
Figure 4. Cause of the field multiplication at the ends of a conducting rod
embedded in and aligned with a uniform electric field E0. The diagram
shows the distributions of the potential U (the dashed line corresponds to
the absence of the rod), the field E, and the charge t of a unit length of the
rod. The potential changes at the rod ends with respect to the external one
are DU  E0l=2.
704
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 5 ===
with negative charge not from the cloud. It takes the charge
away from its twin, leaving it positive. The role of the cloud
charge reduces exclusively to inducing the electric field which
initiates and drives the leader process by supplying it with its
electric energy.
Naturally, the leaders are more likely to originate where
the average cloud field is strongest. When we are dealing with
a negative descending leader, this is the lower edge of the
negatively charged cloud cell. At the center of the cell, the field
is close to zero; outside the charged region, it falls off as we
recede from this region. It is pertinent to note that the
origination of twin leaders is observed in laboratory condi-
tions by placing a polarizable metallic rod in the electric field,
for instance, between plane electrodes (Fig. 6). Concerning
lightning, this idea was apparently first stated by Kazemir
[34]. We came across his forgotten, uncited, and inherently
qualitative paper when we were quantitatively developing a
similar notion in our monograph on lightning [35].
In a similar manner, the twin leaders originate at and grow
from the ends of an extended metallic body insulated from the
ground when its long dimension is aligned with the electric
field vector of a thundercloud, even though it may not be fully
mature. This is the main reason why large-sized aircraft and
rockets are struck by lightning. They suffer from lightning
which they induce themselves rather than from accidental
encounters with descending or intercloud leaders. Running
tip, we note that it is possible, in principle, to provoke the
origination of lightning in exactly the same way with a long
laser spark. It is desirable to produce its conducting channel
as close as possible to the lower cloud edge but within
visibility range and, so far as possible, parallel to the vector
of the local external field. It would then be possible to
observe, with preparations made in advance, the origination
and the subsequent growth of the descending leader. It is
precisely this type of experiment that would hold greatest
interest for lightning science.
4. Build up of the leader of descending lightning
and potential delivered to the ground
The leader velocity vL is determined ultimately by the excess
of the leader tip potential Ut over the external potential U0…x†
at the point of tip location x, DUt ˆ Ut ÿ U0. The quantity vL
may equally be thought of as being dependent on the current
iL which flows to the leader tip and feeds it:
iL ˆ tvL;
t ˆ C1…Ut ÿ U0†;
C1 ˆ
2pe0
ln…L=RL† ;
…4†
where t is the charge, and C1 the capacitance of a unit length
of the leader. The latter obeys the above formula (1), with the
reservation that the channel radius r should be replaced with
the effective cover radius RL that harbors the bulk of the
leader charge. The velocity cannot depend directly on the
external field E0…x† ˆ ÿHU0 at the point of tip location. The
mechanism of leader advance is indeed associated with the
action of overwhelmingly stronger inherent fields induced by
intrinsic charges. In the streamer region of a negative leader,
Es 10 kV cmÿ1. This field determines the radius of the
region and, hence, the radius of the charge cover around the
channel: RL  DUt=Es. In the proximity of the leader tip, the
field is even stronger (Ei  50 kV cmÿ1) to initiate streamers.
In the region of current contraction during the action of the
instability, the field was calculated to be as high as 20 kV cmÿ1
[32]. Meanwhile, the leader quite often propagates in the
external field E0  100 V cmÿ1, which is weaker even than
random variations of the intrinsic one.
Not engaging in speculations as to the vL…DUt† depen-
dence, we take advantage of the empirical relationship
vL  …DUt†1=2 established in laboratory experiments with
positive leaders. Unlike a positive leader which moves in a
near-continuous manner, a negative one propagates (both in
a laboratory and with lightning) in a clearly defined
intermittent, jump-like manner. A leader of this kind is
termed stepped. The nature of the stepping is not completely
understood; it is discussed in Refs [32, 35]. However,
U
U…t†
U0…x†
U…t ˆ 0† ˆ U00
x
Figure 5. Schematic of the initiation and the propagation of twin leaders
which started near the lower edge of the lower cloud charge at the instant
of time t ˆ 0. The potential distribution of the cloud dipole U0…x† (taking
into account the mirror reflection) along the x-coordinate is measured
from the ground upwards. The leader channel is assumed to be perfectly
conducting, so that its potential U is everywhere the same but changes with
time.
ÿU
Streamer zone
Streamer zone of
the descending leader
Metal electrode
Tip of the ascending
leader
Tip of
the descending leader
10
20
30
40 ms
Figure 6. Time scan of the twin leaders which started from a 0.5-m long
metal rod embedded in a uniform field in a 3-m long gap. The interdepen-
dence of their development is evident.
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
705

=== PAGE 6 ===
experiments with sparks hundred meters long exhibited no
fundamental differences between the average velocities of the
positive and negative leaders. The same is also true of positive
(continuous) and negative (stepped) lightning leaders. In the
consideration of the growth of leaders of either sign, in what
follows it is therefore assumed that
vL ˆ a

jUt ÿ U0j
p
;
a ˆ 1500 cm sÿ1 Vÿ1=2 :
…5†
Generally speaking, the potential distribution along the
leader should be calculated in the context of the theory of a
distributed-parameter long line. However, for a typical
current of the lightning leader i  100 A and the field in the
channel estimated using formula (2), the voltage drop across
the channel is found to be relatively low in comparison with
DUt. Hence, the entire channel formed by twin leaders (the
descending and ascending ones) in the first approximation
may be thought of as carrying a common potential U at every
point in time, like a perfect conductor. Then, the growth of
the leaders is described by the elementary equations
dx1
dt ˆ ÿa

jU ÿ U0…x1†j
p
;
dx2
dt ˆ a

jU ÿ U0…x2†j
p
; …6†
where x1 and x2 are the tip coordinates of the descending and
ascending leaders (the leader axis is measured from the
ground upwards). In this case, the instantaneous value of
the channel potential U…t† is determined by the condition that
the total charge distributed along the combined channel of the
leaders with a linear capacitance C1 is equal to zero:
…x2
x1
t dx ˆ 0 ;
t  C1…U ÿ U0…x†† ;
U ˆ
1
x2 ÿ x1
…x2
x1
U0 dx :
…7†
The calculation of the growth of a lightning leader is
exemplified in Fig. 7. The leading role is played by the
descending leader which hardly decelerates as it travels in
the direction of the electric force of the external field and
which feeds the ascending one with its current. Before long,
the latter (leader) begins to decelerate, for it finds itself in the
domain of a steeply rising cloud potential. In this case, the
ascending leader travels in the direction opposite to the
electric force (see Fig. 5) and grows so far as the charge is
delivered to it from the considerably faster descending one.
When the descending leader reaches the ground and stops, the
charge ceases to be delivered to the channel for a moment.
The ascending leader also comes to a halt. Immediately after
this, a wave travels upwards through the channel to carry the
zero ground potential and the highest lightning current, the
wave velocity being only a few times lower than the speed of
light. However, this is an entirely different stage of the
lightning process. This stage is termed the principal, or
return stroke, and we will not enlarge on this subject (it is
considered in detail in the monograph [35]). Formally,
according to Eqns (6), the ascending leader comes to a halt
when the voltage change on a tip U ÿ U0…x2† ˆ 0 but actually
when this difference falls off to a relatively low value
DUt min  0:4 MV 5 U, U0…x2†. Such is the limit below
which the leader cannot grow at all, as shown by laboratory
experiments and calculations [32]. Therefore, the potential Ui
which the descending leader delivers to the ground can be
estimated even without considering the evolution of the
leaders, employing only equalities (7) and putting simulta-
neously U  Ui  U0…x2† and x1 ˆ 0, which corresponds to
cessation of motion of both leaders. Geometrically, this
4
3
2
1
0
5
10
15
x2
x0
x1
Altitude, km
Time, ms
a
2
1
0
ÿ1
ÿ2
ÿ3
1
2
3
4
x, km
t, mC mÿ1
b
2.0
1.5
1.0
0.5
200
180
160
140
120
100
0
5
10
15
Time, ms
Velocity of the descending leader, 105 msÿ1
ÿU, MV
vL
U
c
Figure 7. Simulation of the development of a pair of leaders that start from
the
lower
boundary
of
the
negative
charge
of
a
cloud
dipole
(H  D  3 km, Rc  0:5 km, Qc  12:5 C): (a) positions of the tips of
the negative descending (x1) and twin positive ascending (x2) leaders, and
also of the point of zero potential difference U ÿ U0…x0† ˆ 0; (b) distribu-
tion of the linear charge along the leader axis at t ˆ 16 ms (calculated using
an advanced model); (c) potential and velocity of a descending leader.
706
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 7 ===
corresponds to equality of the two figure areas enclosed by the
U0…x† curve and the U ˆ const straight line in Fig. 8. 1
The potential Ui which the descending leader delivers to
the ground is far lower in magnitude than the cloud potential
U00 at its point of origin. Despite the widespread belief, this is
not owing to the voltage drop across the channel, which is
neglected in the above calculation altogether. The potential of
a perfectly conducting channel which had its origin in a
nonconducting space with an electric field need not necessa-
rily coincide all the time with the potential of this field at the
point of origin. This would be the case if the channel were
connected to a voltage source having zero internal resistance
or with a plate of a charged capacitor of unlimited
capacitance. In the case under consideration, the potential
assumes a value obtained by averaging the U0…x† function
over a length x2 ÿ x1, strongly asymmetric relative to the
point of the channel origin. As the channel grows, jUj
becomes progressively lower in comparison with jU00j. The
reason is that the U0…x† curve is strongly extended towards
the ground from the point of leader origin, whereas it has the
shape of a narrow deep well in the opposite direction (see
Fig. 8). In the case of an unbranched vertical channel, as in
Figs 7 and 8, about half the potential is delivered to the
ground (Ui ˆ ÿ105 MV instead of U00 ˆ ÿ185 MV at the
starting point of the lightning). The numerous branchings and
path curvature usually inherent in lightning significantly
reduce Ui, actually several-fold further.
The magnitude of the potential delivered to the ground is
the most important lightning parameter. The destructive
lightning current upon leader ± ground contact is propor-
tional to the delivered potential: I ˆ Ui=Z, where Z  500 O
is the wave impedance of a long line formed by the leader
channel. It is not inconceivable that record-high lightning
currents of  200 kA correspond to those rare occasions
when the descending leader develops nearly along a vertical
line and without branching rather than to record-high
charged thunderclouds. The magnitude of the potential
delivered to the ground is significant in one more respect.
The `force of attraction' of lightning for a tall grounded object
depends on this potential, as discussed immediately below.
The higher jUtj, the earlier the lightning sets off for the object
and the greater the range of attraction.
5. Attraction of lightning.
Ascending counter leader
It has been known for a long time that lightning exhibits
selectivity, striking primarily tall objects. It is as if the tall
grounded conductors attract it. This underlies the operation
of lightning rods. As a rule, a cloud-to-grounded-object strike
is preceded by the excitation of a counter leader from its
summit. The descending and counter leaders grow, attracting
each other. Their joining connects the descending lightning to
the ground via the conducting object. There may be several
counter leaders in a group of grounded objects (for instance,
they can start from the summits of the lightning rod and the
object under its protection). The earlier the counter leader
originates and the more intense its development, the better
the chance that it intercepts the lightning. The ascending
leader may also originate in the absence of descending
lightning, under the action of the field of the thundercloud
alone (if the object is tall enough and the cloud field is strong).
This is the way so-called triggered lightning is organized
artificially: a small rocket is launched into a cloud, pulling a
thin (0.2 ± 0.3 mm in diameter) grounded wire behind it [37].
The ascending lightning starts when the rocket reaches an
altitude of about 200 m. In experiments [17, 18] on laser
triggering of lightning, the leader was also excited to ascend
from a tall tower.
The cause of the origination of the ascending leader is
simple. If the charges of the descending lightning and (or) the
cloud induce a vertical field E0 in the region of a grounded
conductor of height h, the difference between the zero
potential of the conductor summit and the potential of the
external field at the point of its location is DU ˆ E0h. This
gives rise to a region of local field strengthening near the
summit. This field and DU may turn out to be sufficient to
ionize the air and generate the leader (DU >DUt min 
0:4 MV). However, the lightning is affected only by that
counter leader which is capable of travelling a distance L at
least comparable with the object height, i.e. several tens to a
hundred meters. Only then will the `gain' in an object height
owing to the conducting leader channel become significant.
For this to happen, the potential change near the tip of the
counter leader DUt ˆ …E0 ÿ EL†L ‡ DU0, where EL is the
field strength in its channel, should not lessen in comparison
with DU0 (Fig. 9). The condition for viability of the counter
leader, E0 > EL, proves to be more rigorous than its
origination condition, E0 > DUt min=h.
According to formula (2), the current in the channel of a
viable leader exceeds imin  b=E0, where the current is given
by expression (4). The requirement i > imin imposes condi-
tions on the initial potential change DU ˆ E0h at the object
summit and its height for a given external field or on the
minimal intensity of the external field for an object of a given
height:
DUmin ˆ
 b ln…L=RL†
2pe0a
2=3
1
E 2=3
0
;
…8†
hmin ˆ
 b ln…L=RL†
2pe0a
2=3
1
E 5=3
0
:
Taking the values of b and a from formulas (2) and (5), and
putting L=RL  10 (the dependence on this not-too-well
determined parameter is very weak), we find for E0 ˆ
150 V cmÿ1 that DUmin  3:2 MV and hmin  210 m. Much
Ui ˆ U0…x2†
U0…x†
x
x2
x0
H
U
+
ÿ
Figure 8. Employing the area equality condition to determine the electric
potential delivered to the ground by a negative leader.
1 Curiously, a similar condition for the equality of areas in the correspond-
ing coordinates describes the static equilibrium (co-existence) of a great
diversity of states in physics, e.g., the current and currentless regions in
discharges, the burned and initial mixtures at the moment of a combustion
flame stopping, and many others [36].
July, 2000
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707

=== PAGE 8 ===
the same field at the ground is produced by a cloud dipole
with a lower charge jQcj ˆ 10 C at an altitude H ˆ 3 km.
These parameter values are quite moderate for thunder-
clouds, and the triggering of lightning for a 200-m elevation
of a rocket with a wire is a wholly realistic situation. From
buildings of typical height, say, h ˆ 50 m, the counter leader
is, according to formula (8), excited for an external field
E0  350 V cmÿ1. Over plains, the thunderstorm field from a
cloud charge is rarely, if ever, that strong (in the mountains,
sometimes it is). The leader of the descending lightning should
add about 200 V cmÿ1 by its charge. This may happen, for
instance, when a leader carrying a potential U ˆ 37 MV to the
ground descends along a vertical path to an altitude
H0 ˆ 5h ˆ 250 m at a horizontal distance R ˆ 3h ˆ 150 m
from the object. The main contribution to the leader field at
the ground is made by the charge localized in the portion of
the leader of length H0 immediately behind the tip. Here, the
linear charge density is t  C1U  4:4 mC cmÿ1
for
U ˆ 37 MV. It may be said that the lightning trajectory
deviates `purposefully' from the vertical at a point with
coordinates H0 and R and rushes to the object instead of
striking the ground a distance R away. The calculated figures
given above are in reasonable accord with observations.
6. Physical mechanism for the attraction
of lightning
Clearly the attraction of lightning for a tall building and
most often for its extension Ð a counter leader Ð is
attributable to the electric field produced by the charges
induced in these bodies by the charges of the cloud and the
developing lightning. But this commonplace statement is
void of content unless what this field acts upon is specified
and unless the specific physical mechanism of the interac-
tion of two leaders is elucidated. For, while the leader tips
are hundreds of meters apart, each of them is subject to the
field of the other leader, which is little stronger than the
cloud field. It is as weak as hundreds of volts per centimeter
and they do not exert a noticeable effect on the magnitude
of the leader velocity. This was explained in Section 4 and is
inherent in formula (5). What is the mechanism of mutual
attraction of the leaders?
We allow ourselves to propose a hypothesis. The weak
external field E0, which has no effect on the leader velocity vL
determined by the magnitude of the potential change jDUtj at
its tip, affects the leader acceleration:
dvL
dt ˆ 

dvL
djDUtj
 dU
dt ÿ HU0
dx
dt

ˆ 

dvL
djDUtj
 dU
dt ‡ …E0vL†

:
…9†
Here, the upper sign refers to the negative leader, and the
lower sign to the positive one. The first factor in Eqn (9) is
independent of E0 and is always positive, the second consists
of two terms comparable in absolute value. The term dU= dt
related to the charge redistribution along the growing light-
ning channel is most often favorable to the moderation of the
growth of the descending leader. The term …E0vL† charac-
terizes the direct dependence of the leader acceleration on the
external field. The higher E0 and the smaller the angle
between the vectors of the leader velocity and the `electric
force' E0, the higher the acceleration, all other factors being
equal. Hence, the leader will get to the ground or a grounded
conductor sooner if it moves in the direction of the vector of
the electric force.
In reality, the growth of the descending leader involves
inherently statistical factors. As revealed by frame-by-frame
photography of a laboratory leader with an exposure time of
the order of 10ÿ7 s, a growing leader always exhibits several
leader tips. They are connected to the main channel by short,
randomly oriented leader `branches' (Fig. 10). Of all these
tips, the one whose branch grows closest to the direction of
the external electric force has the highest probability of
survival. More often than not the remaining tips soon die
off, because the tip which grows along the E0 vector and
thereby keeps ahead of them hinders the growth of those
lagging behind through the repulsive action of the intrinsic
charge. The infrequent survival of two tips initiates a
U0 ˆ ÿE0x
3
1
2
DU
U
Figure 9. Viability criterion for the leader ascending from a grounded
structure of height h in an external field E0: 1 leader is capable of
developing and accelerating; 2 decelerating nonviable leader; 3 leader on
the verge of viability.
Channel
Tips
10 cm
Figure 10. Photograph of a leader with several tips; the exposure time is
0.3 ms.
708
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 9 ===
`macroscopic' leader branching clearly visible in photographs
of lightning and sometimes of long sparks. The chance
survival of a tip deflected from the direction of the external
field causes the lightning trajectory to bend. However, the
latter event becomes a rarity when the external field builds up
in magnitude along some of the directions of the descending
leader growth. The route to the counter leader is precisely the
one.
An assumption can be made as to the cause of the random
origination of new tips. The surface of the equipotential
plasma channel conductor is unstable. An accidental sharp
spike induces a field enhanced along the spike direction.
Under its action, the spike begins to grow. Growth is possible
in any direction, including that at a significant angle to the
weak external field.
All of the aforesaid, we believe, provides a qualitative
explanation why the leader on the average adheres in its
motion to the external field line but does not necessarily
follow it rigorously. By and large the descending leader is
headed to the ground. But it is more likely to deviate from its
principal direction as the cloud field is combined with a
differently directed field of comparable intensity induced by
some other source, for instance, by the charge carried by the
counter leader. Naturally, the qualitative reasoning outlined
above calls for a more rigorous theoretical substantiation
and, which is desirable, numerical simulations employing,
e.g., the Monte Carlo technique.
7. Adverse effect of the corona on the initiation
of ascending and counter leaders and the
possibilities to overcome it
It is well known, all other factors being the same, that the
ascending leader is far less frequently excited from a
stationary building than from a rocket with a grounded wire
moving fast upwards. The reason lies with accumulation of
the corona space charge nearby the summit of a grounded
building, whereas this charge does not have time to form in
front of a rocket flying with a velocity of 100 m sÿ1. The
electric field near the summit of the building becomes weaker
owing to the space charge, with the effect that a stronger
external field E0, which is induced by the thundercloud alone
or in combination with the leader of the descending lightning,
is required to excite the ascending or counter leaders. We are
dealing now with a `quiet' stationary corona, which is
sometimes termed an ultracorona. It develops for a relatively
slow rise of the voltage across the discharge gap. In the case
under consideration, the field builds up with repeated
accumulation of the charge of the cloud cell after each
lightning discharge or as the thundery front approaches the
location of the grounded building. Hence, times of no shorter
than a second are the case in point.
In a thin layer near the surface of the structure's summit,
where the field is maximum 2, ionization of the air occurs. If
the thundercloud is negative, as is the case in 90% of
instances, the grounded electrode (the grounded structure) is
positively charged. The electrons being produced enter it and
the positive ions drift from the summit to the cloud. In an
ultracorona, the electric field near the summit of the electrode
is sustained close to what is defined by the condition for
discharge self-maintenance, Ecor [33]. For a summit radius of
several centimeters, the latter is nearly coincident with the
ionization threshold, Ecor  Ei  30 kV cmÿ1. The field is
controlled automatically. If for some reason it is enhanced,
the ionization speeds up and more positive charge is
introduced into the space, which induces a negative charge
at the summit to attenuate the field. If the field becomes
weaker than Ecor, the corona is extinguished for some short
time, the previously produced positive ions recede from the
electrode, their action becomes weaker, and the field at the
summit builds up to resume the ionization. Such is the case
only for relatively slow voltage variations, because the
controlling mechanism is based on the ion motion whose
mobility is low. For a sharp rise of the voltage at the summit
of the electrode, the space charge required for the stabiliza-
tion has no time to form and the field rises there significantly
to generate ionization waves Ð streamers. A streamer flash (it
is referred to as a pulsed corona) may trigger the leader
process. This is precisely how the counter leader originates,
when the channel of descending lightning approaches the
object with a velocity of  107 cm sÿ1. Figure 11 gives the
results of numerical simulation of the ultracorona at the
summit of a grounded rod embedded in the external field.
The model, elaborated in cooperation with N L Aleksandrov,
takes full account of the effect of all the charges on the corona
field distribution, including those induced over the whole
length of the rod.
While the corona protects buildings from lightning to
some extent by hindering the origination of a counter leader,
it is detrimental to efficient operation of the lightning rod, for
its task is the opposite Ð to emit the counter leader as early as
possible and to intercept the descending lightning by itself. In
principle, the performance of this function could be promoted
by shooting, in due time, a `harpoon' with a metallic marline
tied to the summit of the lightning rod in order to transport
the conductor tip beyond the ion cloud. It is not improbable
that the main role of a laser-produced spark in the experiment
to trigger the ascending leader from a tower (reported in Refs
[17, 18]) reduced precisely to the transfer of the conductor
outside the corona cloud nearby the tower summit (see
Section 9).
We will consider the simplest corona model to gain an idea
of how far and with what velocity the `extender' of the
lightning rod should be ejected upwards. Let a corona be
displayed by an immobile spherical electrode of radius r0 to
which a voltage U…t† is applied (r0 corresponds to the radius
of the summit of a lightning rod of height h, and U ˆ E0…t†h is
the potential difference of the summit and the growing
external field E0…t† at the point of summit location). Let us
assume, and there are grounds for doing so, that the state of
the ultracorona formed is quasi-stationary in the sense that
the radial distributions of the field E…r† and the space charge
r…r† closely follow the corona current i…t† which varies
relatively slowly in time. At every point in time, they
correspond to the instantaneous value of i…t† as if the current
were invariable. In this case, the current through all the
spherical sections of the charge cloud at a given moment is
the same, i.e. a new portion of charge i dt introduced into the
corona goes exclusively to expand the ion cloud, into an
increment dRf of its front radius Rf…t†. Under this assump-
tion, the electrostatic and charge conservation equations
1
r2
d
dr r2E ˆ r
e0
;
r
e0
ˆ
i
4pr2e0miE
…10†
with a typical boundary condition for an ultracorona,
E…r0† ˆ Ecor ˆ const; are easily integrated (mi is the ion
2 In the absence of a corona, it may be estimated by formula (3).
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
709

=== PAGE 10 ===
mobility). Not writing out the somewhat unwieldy complete
formulas, we give only the compact asymptotic expressions
valid away from the electrode in the stage when the cloud has
strongly expanded and Rf 4 r0, while the space charge in the
gap, Q  4pe0R2
f E…Rf†, is much larger than the electrode
charge qcor ˆ 4pe0r2
0Ecor which does not vary during the
corona discharge:
E…r† 

i
6pe0mir
s
;
r…r†  1
r

3e0i
8pmi
s
:
…11†
More precisely, these formulas are appropriate where the
electric field of the space charge exceeds the field of the
electrode charge, Ecor…r0=r†2.
The electrode potential is calculated employing one of the
equivalent expressions
U ˆ
…Rf
r0
E dr ‡ EfRf ˆ Ecorr0 ‡
…Rf
r0
rr dr
e0
 3EfRf ;
…12†
where Ef  E…Rf†. The radius of the ion cloud and the current
are found by integrating the equation vf  _Rf ˆ miEf with
expression (12) and a given function U…t†. The latter is
governed by the external conditions Ð for an atmospheric
field, by the charge accumulation rate in the thundercloud. In
particular, for U ˆ at, one finds
Rf ˆ t

mia
3
r
;
vf ˆ

mia
3
r
;
i ˆ 2pe0at

mia
3
r
:
…13†
For instance, let the cloud field attain a value E0 ˆ 100 V cmÿ1
one second after the commencement of growth, h ˆ 100 m,
and mi ˆ 1:5 cm2 (V s)ÿ1. Then, a ˆ 106 V sÿ1, and at the
point in time t ˆ 1 s we have U ˆ 1 MV, i ˆ 390 mA, Rf ˆ 7:1
m, Ef ˆ 470 V cmÿ1, and vf ˆ 7:1 m sÿ1. These estimative
figures are in reasonable agreement with numerical calcula-
tions.
If the corona-displaying electrode could move fast to
travel through the preformed ion cloud with a velocity v far
higher than vf, in a short time it would be ahead of the
previously produced peripheral ions and the new peripheral
part of the ion cloud formed in the course of motion would
now be unable to be ahead of the electrode. In other words,
the corona charge would cease to accumulate in front of the
electrode.
In
the
radial
distribution
of
ion
velocities
vi ˆ miE…r† given by the first of equalities (11), there exists a
section rc such that vi < v for r > rc, and vi > v for r < rc.
Roughly speaking, the region from rc to Rf is nonexistent in
the new cloud. The contribution of the charge corresponding
to this region to the U potential also vanishes. Since U
remains unchanged, being given by an external source, this
loss should be cancelled out by an increase in the electrode
charge q ˆ 4pe0r2
0E…r0† and the corresponding enhancement
of the field E…r0† at its surface. Formulating these qualitative
notions in the context of the spherical model, we can write a
conditional equality which replaces the second of expressions
(12):
U ˆ E…r0†r0 ‡
…rc
r0
rr dr
e0
:
…14†
Let the electrode velocity ensure the field strengthening
from the previous value Ecor
to half the maximum,
Em ˆ U=r0, which would take place in the absence of the
5
10
15
0
0.2
0.4
0.6
With corona
Without corona
x, m
Electric éeld, kV cmÿ1
a
0
10
20
30
0
10
20
30
40
50
60
With corona
Without corona
x, cm
Electric éeld, kV cmÿ1
b
15
10
5
0
1
2
3
4
Time, s
c
Charge front radius, m
0
5
10
15
103
104
105
106
107
Ion density, cmÿ3
x, m
d
Figure 11. Results of numerical simulations of the corona in proximity to
the hemispherical top of a grounded 30-m tall rod 3 cm in radius embedded
in the external field; the average ion mobility is 1.5 cm2 (V s)ÿ1. The field
builds up linearly with time up to 100 V cmÿ1 for t ˆ 1 s and is thereafter
held constant. (a) Field distributions along the x-axis, reckoned from the
rod upwards, for the instant of time t ˆ 5 s with and without the corona.
(b) The same on an enlarged scale in proximity to the top. (c) Radius of the
front of the ion cloud. (d) Ion density distribution at the moment t ˆ 5 s.
710
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 11 ===
corona. In the numerical example given above for r0 ˆ 3 cm,
Em ˆ 333 kV cmÿ1 and a field half as strong would suffice to
excite the leader. Bearing in mind that E…r0† ˆ Em=2 4 Ecor
and U 4 Ecorr0, we estimate rc from the condition which
follows from expression (14):
…rc
r0
rr
e0
dr  U
2  1
2
…Rf
r0
rr
e0
dr :
…15†
Employing formulas (11), we find that rc=Rf  1=4,
rc  1:8 m, and vc  vi…rc† ˆ 2vf  14:2 m sÿ1. These
figures give an idea of the scale of the quantities. To
eliminate the action of the corona, a conductor connected
to the lightning rod is to be fired upwards from its top to a
distance l of several meters (l > rc) with a velocity of several
tens of meters per second (v > vc). Solving the two-
dimensional axially symmetric problem of the field and
space-charge-density distributions in the discharge of a
spherical electrode in a gas flow would aid to refine these
results. For a flow velocity v exceeding some value vc, the
solution with Ecor ˆ const would cease to exist. The flow
with a velocity v ˆ miEcor  450 m sÿ1 would indeed blow
away all the ions completely. In this case, the potential
U 4 Ecorr0 is to be induced only by the increased electrode
charge. The critical value vc arrived at will indicate the
lower velocity bound for firing the extender of the lightning
rod. Also note that the numerical solution of the problem
on corona discharge of a rapidly growing electrode
encounters no difficulties.
8. Demands for, capabilities of, and modern
trends in lightning protection
Half a century ago, the main goal of lightning protection was
to eliminate fire arising from the contact of the lightning
channel with combustible materials and to guard power
transmission lines against storm overvoltages induced by
the current and the strong electromagnetic field of lightning.
Lightning rods cope with this `coarse task' easily. To solve
this problem, it will suffice to divert lightning from a fire
hazardous or dangerously explosive area. Power transmis-
sion lines are safely protected by lightning protection wires.
Suspended above the lines, they serve the function of an
extended lightning rod by intercepting the lightning channel.
So-called induced overvoltages turned out to be the first
truly serious indication that the lightning protection is
inadequate. Induced by the lightning current from a
distance of several hundred meters, they bring a threat to
relatively low-voltage power distribution networks (up to 10
kV). It was recognized that the lightning hazard becomes
more severe as the operating voltage in electric devices is
lowered. Regrettably, this prediction was amply borne out
with the advent of the microelectronic era, when electronic
devices with operating voltages of tens-to-several volts came
into being and became indispensable. Aeroplanes, space
vehicles, communication and information processing facil-
ities are literally stuffed with microelectronics. Here, the
`long-range action' of lightning reveals itself in full measure.
Damage may be caused not only by a direct lightning strike
to an object, but also by quite remote discharges. Their
electromagnetic fields may be extremely strong, for the
lightning current build-up rate may exceed 1011 A sÿ1. We
are forced to provide screening devices, quite often heavy
and bulky, or to protect the object from any lightning,
including remote lightning.
No better is the situation concerning highly inflammable
fuels, explosives, and gaseous exhaust into the atmosphere,
produced in the operation of some technical facilities. All of
these are an integral part of many present-day devices.
Explosives have long ceased to be exclusively a means of
destruction. Many compact one-time actuating mechanisms
employ explosives. The explosion does not destroy but
performs a specific, previously planned action. Lightning-
induced actuation of such a pyrotechnic device cannot be
tolerated, which it can well do by remotely exciting current in
the electric ignition circuit. Nor need the lightning channel
necessarily strike an inflammable gas mixture to set it on fire.
Counter discharges discussed in the foregoing and all kinds of
sparking due to electromagnetic noise can easily do the job. A
home piezoelectric igniter sets fire to the gas in the kitchen
with an incommensurably weaker electric spark.
Experts in lightning protection have never abandoned the
dream of diverting lightning to a safe place, far from the
critical object. Nor have they abandoned the idea of finding a
means for provoking lightning to discharge thunderclouds in
uninhabited vacant areas, where the lightning would cause no
damage. There is no question that this is basically possible.
But when the question is raised as to the use of new means in
lightning protection, issues of technical substantiation,
reliability, and cost come to the forefront. These factors are
intimately related. For instance, it is beyond reason to
increase the power or the energy capacity of a complex and
therefore expensive device in an attempt to attain a 100%
efficiency of lightning interception with the use of this device
if the device itself cannot ensure the controlling action with a
reliability of over 0.9. A primitive and inexpensive metal
lightning rod would easily ensure at least one more nine after
the decimal point in a reliability index.
Of course, there may be circumstances in which tradi-
tional lightning rods are basically incompatible with the
technological functions of an object. A lightning rod cannot
be mounted within the field of vision of a large-scale radar
antenna. A lightning rod of many meters high should not
tower on the launching site of a space vehicle. It constitutes a
real life hazard in the actuation of the astronauts rescue
system, for an ejected capsule may collide with the metal
frame of the lightning rod. Present-day technology rapidly
multiplies the list of these examples, sending us in search for
unconventional protection devices.
It is not always possible to devise an electronic unit
capable of withstanding the electromagnetic field of light-
ning by the application of metal screens or pulsed overvoltage
limiters. For the most critical and easily vulnerable objects, it
is desirable to arrange protection in such a way as to prevent
the lightning discharges from occurring anywhere near the
object whatsoever. But it is hardly realistic to construct a
fencing of lightning rods at the distant approaches to the
object, the more so as this does not ensure that lightning will
not break through. In principle, the problem could be solved
by a mobile laser facility capable of discharging a thunder-
cloud in a safe place. To do this, the laser should `shoot'
kilometers upwards to provoke descending lightning by a
plasma trace appropriate in length and other characteristics
(see below). This would be an inestimable aid to investigators
pursuing descending-lightning research. They would not have
to set hopes upon good fortune and wait for a successful
discharge within the field of sight of the short-run recording
instruments. During a thunderstorm, it would be possible to
excite lightning in the required place and ensure timing down
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
711

=== PAGE 12 ===
to a microsecond. In the same way it would be possible to
solve the problem of modelling situations characteristic for
the initiation of lightning from bulky aircraft. This would
hold the great interest for both lightning science and practical
lightning protection.
The laser technique of exciting ascending lightning is
much simpler but less expedient from the practical stand-
point. First, a tall structure (`extended' by a laser) is required,
because producing a very long laser spark (of the order of
200 m, for the electric field at the ground is too weak) with
appropriate conductive properties would require prodigious
laser energy and power. Second, this technique nevertheless
does not ensure perfect protection. Ascending leaders are
quite often excited from the summit of the 540-m high
Ostankino television tower in Moscow. However, they do
not discharge the clouds completely. Though the density of
descending lightning in the neighborhood of the tower is
lower than usual, it is far from zero, and not all of the
lightning strikes the tower. Furthermore, it is well known
that subsequent lightning components do not always follow
the same path. Nearly half of them do not take the path of the
primary channel [38]. Hence, there persists a real danger that
one of the components of the lightning provoked would strike
the nearby protected object rather than the construction
intended for the purpose. Of course, this does not diminish
the significance of the experiment performed, which is the first
real step toward laser control over lightning.
It should be admitted that alternate, non-laser-based
techniques of initiating and controlling lightning are also
possible, some of them being technically simpler. The
excitation
of
artificially
triggered
ascending
lightning
referred to in the foregoing text has been practiced since the
70s, though for the purposes of research. A well-heated gas jet
ejected from the top of a stationary lightning rod can be used
to `extend' it and improve its efficiency. The lowering of gas
density arising from the heating lowers the counter-discharge
ionization and excitation thresholds. It is well known that the
long wake of hot gas jets from aircraft and rocket engines
facilitates the initiation of lightning from them. It is not
unusual that combustion products are partly ionized; there
also exist special techniques to produce plasma jets, which
may, in principle, have an effect similar to that of a laser-
produced spark.
Controlling lightning is also possible by applying a high
voltage to an object. In this case, there are several options.
With a voltage of the same polarity as the descending
lightning, the latter should be repelled from the object (in
principle, this is a way to protect a structure). For an opposite
polarity, the lightning is attracted, and this is a way to
improve the efficiency of a lightning rod. However, from the
technical standpoint it is clear that applying megavolt
voltages at the necessary times with the required repetition
rate is a complicated task. Lower voltages are out of the
question, which was shown in the estimation of the excitation
conditions for counter and ascending leaders. The problem of
action of high voltage on lightning arose inevitably in the
construction a 1150-kV power transmission line. The ampli-
tude of the alternating voltage at its conductors relative to the
ground is close to 1 MV, which is commensurable with the
potential of the lightning leader. This gives rise to quite
tangible difficulties in the design of a reliable lightning
protection for the power transmission line. The feasibility of
overcomingtheactionofthecoronawasdiscussedinSection7.
The same effect may be attained if a voltage of polarity
opposite to that of the cloud is applied to the electrode. The
case in point are quite moderate voltages of the order of E0h,
where h is the electrode height, and E0  100 V cmÿ1.
There is no question that the above-listed methods of
affecting lightning and similar methods are the right subject
of discussion from the viewpoint of investigations, but they
do not attract considerable attention when it comes to
practical lightning protection. Pragmatic considerations
underlie the skepticism of engineers Ð is the game worth
the candle? We repeat: the reliability of lightning protection
is primarily determined by the reliability of actuation of the
entire sequence of complex technical devices that form the
controlling action on the lightning rather than by the
efficiency of the controlling action itself. One is forced to
take into account the possibility of interruption of the
power supply to the controlling devices caused by a
thunderstorm, the operational lifetime, maintenance expen-
diture, etc. The use of conventional lightning rods is not
associated with these problems, and therefore dilettante
inventors, and sometimes even solid companies, address
themselves to precisely these rods, proposing inexpensive
and allegedly efficient means to improve the reliability and
extend the protection radius. As an example we refer to
radioactive and piezoelectric attachments. In the view of
their manufacturers, both ionize the air to prepare the
easiest route for the lightning channel. In reality their effect
is akin to the action of an ultracorona. The effect, if any, is
the opposite of that expected. But even that is in fact
nonexistent. A weak radioactive source, the more so a
piezoelectric cell, cannot compete with a corona. The
action of radioactive sources of safe intensity has been
repeatedly verified in the laboratories. They have no effect
on the origination and development of a long spark.
9. Laser triggering of lightning
Two schemes of producing a laser plasma for controlling
lightning are now under development. One of them has roots
stretching back 30 years, when a long laser spark was
produced [7, 39 ± 43]. It is produced employing neodymium
or CO2 lasers, in record-breaking versions with an energy of
2 kJ or even 5 kJ [31] and a duration of the main part of the
pulse of 50 ns. The respective threshold intensities for the
breakdown of the pure and aerosol-containing air are
109 W cmÿ2 and 107 ± 108 W cmÿ2, respectively. The virtue
of this scheme involving a CO2 laser is that the channel can be
heated to several thousands of degrees. Reducing the gas
density N by an order of magnitude promotes the collisional
ionization by electrons, whose rate constant is determined by
the reduced field E=N. For a temperature above 4000 K, the
associative ionization N ‡ O ! e ‡ NO‡, which does not
depend on the field at all, becomes appreciable. Heating also
strongly suppresses the electron losses due to their attachment
and recombination. But the laser spark proves to be
continuous only when it is not too long, no longer than
several meters for the energy specified above. When the
radiation is focused to a distance of tens or hundreds of
meters, spark production does occur, but the resultant spark
consists of separate plasma centers. The longer the focal
distance, the greater their spacing. The discontinuity of the
conductor hinders its polarization as of an entity in the
external field and does not permit using it as an efficient
`extender' of the lightning rod or for the triggering of
lightning in the open atmosphere.
712
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 13 ===
The other scheme pursued in Refs [14, 16, 20, 22] is free
from this drawback. It is suggested that a short and extremely
intense pulse of ultraviolet radiation be employed to accom-
plish the three-photon ionization of the O2 molecules and the
four-photon ionization of N2. A longer pulse of visible
radiation complements the short one to release the electrons
from negative ions. In this case, far less energy goes to ionize
the air as compared with the breakdown by a CO2 laser,
because the energy is in fact not expended on anything else.
The objective is to produce a long thin ionized channel in the
open atmosphere. It will be polarized under the cloud field,
and leaders will be excited from its ends.
In laboratory experiments involving these laser pulses, the
gap exhibited a lowering of the breakdown voltage and the
spark discharge was observed to make its way through the
laser-produced channel [14, 20]. A multistage laser system
produced ultraviolet radiation with a wavelength l ˆ 248 nm
starting from the fourth harmonic of a neodymium laser, with
final amplification by an excimer KrF laser. The output was a
10-ps long pulse with an energy of 10 mJ (1 GW in power).
This pulse was superimposed on an alexandrite-laser pulse
with a wavelength l ˆ 750 nm, an energy of 0.21 J, and a
length of 2 ms. The authors are designing a system to provide a
l ˆ 248-nm pulse with an energy of 50 mJ and a length of
200 fs (250 GW in power), and also a l ˆ 750-nm pulse
several joules in energy and tens of microseconds in length.
They carried out a numerical simulation of the initial stage of
the evolution of a thin channel several tens of meters long
ionized by the laser radiation at a small altitude in the open
atmosphere. A gradual field multiplication was seen at the
ends (the calculations indicated a two-fold multiplication).
However, the controlling parameter Ð the external field
E0 ˆ 6:5 kV cmÿ1 Ð adopted in the calculations seems to be
unrealistically overrated. This supposedly led the authors to
make an unjustifiably optimistic prediction that low-energy
laser pulses would be sufficient. Real storm fields at the
ground are weaker by a factor of several tens; even at an
altitude of 2 km they are still 2 ± 3 times weaker than those
adopted in the model.
Experiments [17, 18] were carried out to model lightning
with a laser on the shore of the Sea of Japan in the period of
intense winter low-cloudage thunderstorms typical of this
region (Fig. 12). In this case, the electric field at sea level is
usually close to 100 V cmÿ1. To trigger the ascending leader, a
tower with a height h ˆ 50 m (the authors do not give the
magnitude of the h parameter most critical for the analysis;
the figure was borrowed from an entirely different source [23])
was constructed on a 200-m high hill. Data on the electric field
profile in the neighborhood of the tower are not given, either.
However, there are grounds to believe that the field was
significantly more intense (in the classical problem of a
conductive hemisphere on a grounded plane in a uniform
field cited in textbooks of physics, the maximum field at the
top of the hemisphere is three times stronger than the external
one).
Stationed on the ground were two CO2 lasers delivering
50-ns pulses with an energy of 1 kJ. One laser beam was
focused with a mirror on a dielectric target at the tower
summit to produce the initial plasma. The other beam, also
focused with a mirror, produced a two-meter-long laser spark
from the tower summit. In addition, an ultraviolet laser was
employed (like in the second scheme outlined above) for
producing a weakly ionized channel to direct the leader to
the cloud, which was slightly offset from the tower.
The experimenters believed that the selection of the
instant of laser actuation was one of the most critical
elements of the operation. Should it be done too early,
nothing would be accomplished owing to the smallness of
E0. Should it be done too late, spontaneous descending
lightning might originate in the cloud to strike the structure
beneath. Special-purpose microwave instrumentation traced
the state of the cloud, and the lasers were actuated at the
instant of the onset of the cloud discharge, which may be
considered as the precursor of the descending lightning. In the
authors' opinion, among the many attempts made two were
successful; the lightning thus provoked was synchronized
with the laser pulses. The authors state that an ascending
leader went off the tower upwards. As a consequence, the
nearby cloud region measuring about 2 km discharged 3 C
into the tower with a current of 35 kA typical of lightning.
It is safe to assume that the cloud field E0 near the tower
was so strong that the natural potential change DU ˆ E0h was
on the verge of provoking an ascending leader, were it not for
the screening corona action. Of course, we cannot expect the
numerical value of DU to literally satisfy the estimative
formula (8), which relies on the not-too-dependable relation-
ships (2) and (5). Furthermore, it is highly improbable that
condition (8) was not satisfied without a laser spark and came
to be satisfied when the 50-m high tower became two meters
longer. The entire experience of experimental investigation of
long spark discharges suggests that the statistical scatter of
their threshold values is much larger. It may well be that the
function of the lasers was as follows: a moderately long and
therefore continuous laser spark `shot through' (perforated)
the corona to instantly bring the conductor summit beyond
some portion of the ion cloud, which was responsible for the
origination of the ascending leader. Upon its penetration into
the thundercloud or in consequence of the interception of a
travelling descending leader, there followed a completion of
the lightning discharge. It is conceivable that the discharge
was multicomponent and comprised its return strokes, for
which the current with an amplitude of 35 kA measured is
Ascending leader
Structure under
a cloud
Laser
Laser
spark
Mirror
Tower
h ˆ 50 m
Hill
Figure 12. Schematic diagram of the experiment on the laser triggering of
lightning [17, 18].
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
713

=== PAGE 14 ===
quite typical. As regards the interpretation of the experi-
mental results, there are some indications that preference
should be given to the interception of the descending leader.
Be it as it may, the current oscilloscope trace given in the
paper does not exhibit a long-duration build-up of the current
pulse up to several hundreds of amperes typical for ascending
lightning.
10. Requirements on a laser-produced channel
In our opinion, the capability of triggering lightning high in
the sky would hold the greatest interest for lightning science
and lightning protection, in particular, for modelling the
origination of lightning from aircraft. Let us see what the
parameters of a channel between the cloud and the ground
should be to permit the excitation of viable leaders from its
ends. The channel should work as a good conductor. Hence,
the electric field should be largely suppressed inside it but
multiplied at the ends. Given this, a unit length will harbor a
charge t  2pe0E0x= ln…L=r†, where E0 is the external field
parallel to the channel, L is its length, r its radius, and x the
coordinate reckoned from the middle. This is explained by
Fig. 4 and formula (1). The potential difference DU ˆ E0L=2
originating at the ends of the initial conductor should ensure
viability of the leaders. The requisite length L is defined by
formula (8):
Lmin  2
 b ln…L=RL†
2pe0a
2=3
1
E 5=3
0
:
For instance, in order to excite lightning for E0 ˆ 1 kV cmÿ1
(say, at an altitude of 2 km, 1 km below the center of a cloud
charge of 10 C), a length Lmin ˆ 20 m (DU ˆ 1 MV) is
required. To polarize the plasma conductor, a charge
Q  pe0
E0L2
4 ln…L=r†  90 m C
should flow from its one half to the other. On the verge of
possibility, it is afforded by a length-averaged ionization
Ne min ˆ 2Q=…eL† ˆ 5:5  1011 electrons cmÿ1. For the elec-
trons to flow from one half of the conductor to the other
before they recombine, the current i should be provided with a
sufficiently large section. The magnitude of the electron
density ne ˆ Ne=…pr2† has only a small effect on this, because
the charge transfer time tp  Q=i  nÿ1
e
and the characteristic
recombination time trec ˆ …bne†ÿ1 vary similarly in propor-
tion to nÿ1
e
(b is the recombination coefficient). The time of
charge transfer and significant attenuation of the electric field
inside the plasma conductor is approximately
tp 
Q
pr2emeneE0

1
ln…L=r†
 L
2r
2
tM ;
where
tM ˆ e0=…emene† is
the
Maxwellian
time,
and
me  600 cm2 (V s)ÿ1 the electron mobility. Unlike a plasma
volume equally extended in all directions (L=2r  1) where
the times of space-charge relaxation and field attenuation are
close (tp  tM), for an extended thin conductor tp 4 tM.
The requirement tp < trec defines the lower permissible
bound for the radius of the initial plasma channel
rmin  L
2

e0b
eme ln…L=r†
s
 3:8 cm :
The numerical value of rmin corresponds to the value
b ˆ 10ÿ7 cm3 sÿ1 inherent in cold air. It is impossible to get
by with a smaller radius in a scheme involving multiphoton
ionization. However, it may be that a longer channel will
prove to be hard to produce as far as radiation focusing is
concerned, but this is quite a different matter. A long CO2-
laser-produced spark, if it is continuous, usually proves to be
heated. This circumstance is beneficial because a high
temperature significantly suppresses both electron recombi-
nation and attachment. However, considerably higher expen-
ditures of laser energy are the price that has to be paid.
We revert to the scheme involving multiphoton ioniza-
tion. To induce the needed voltage change DU provided by the
transfer of a charge Q, a very low ionization would suffice:
ne min ˆ Ne min=…pr2
min†  1:2  1010 cmÿ3. But for so low an
electron density the current would be too weak, i  0:1 A
(even for an electric field still retaining the initial level,  1 kV
cmÿ1), and the charge transfer time would be tp  1000 ms.
For at least this time, electrons would have to be released
from negative ions with the aid of a laser. The case in point
now is a real laser with a pulse length t  10 ms. For the
charge transfer to be accomplished during this time, a current
i  10 A and an initial electron density ne  1012 cmÿ3 are
required (for a field of the order of the initial one). There is
little point in producing orders of magnitude higher electron
densities employing an ultraviolet laser, because the density
will inevitably lower to the 1012 cmÿ3 level owing to
recombination
during
the
same
period
of
time
trec ˆ …10ÿ7ne†ÿ1  10 ms. To ionize a column of air of length
L ˆ 20 m and radius r ˆ 3:8 cm to a level ne ˆ 1012 cmÿ3
takes an ultraviolet radiation energy W  pr2LneI  200 mJ
(I  15 eV is the ionization potential).
However, the above list of difficulties is not exhaustive.
Until now, we have been dealing with the preparation of
conditions for forming a potential change and a strong field
multiplication at the ends of a long artificial conductor.
However, it also takes time for the leaders to develop. This
time is hard to estimate but, according to laboratory
experiments, it runs into the tens of microseconds. Hence,
negative ions will have to be destroyed for a longer period of
time, though this will not exclude recombination. But most
important of all, the leader process, namely, the propagation
of two leaders in opposite directions, will require an
uninterrupted charge transfer from one channel to the other,
i.e. characteristic leader currents of 1 ± 100 A flowing through
a conductor initially produced by artificial means. For the
leader to commence unimpeded propagation and provoke
real lightning, the laser-produced channel should acquire the
properties of a true leader channel, i.e. become thin and
strongly heated, like an arc, and additional ionization should
proceed in it. In the leader tip, all this takes place through the
action of the ionization-overheating instability. However,
this process in the leader tip begins with a far thinner channel
in a stronger electric field and for a higher electron density
ne  1014 cmÿ3, which cannot persist in our case without
heating for more than trec  10ÿ7 s. In essence, the question
which we now are dealing with is the same as the glow-to-arc
discharge transformation, the question of contraction or
arcing in a weakly ionized cold plasma (the terms are many),
which is still a long way from being solved [33].
An alternate scenario for the course of events is also
possible. If the conductivity in the cold laser-produced
channel is somehow maintained for a time period such that
the leader develops and travels a distance L, at least one (if the
714
EÂ M Bazelyan, Yu P Ra|¯zer
Physics ± Uspekhi 43 (7)

=== PAGE 15 ===
leaders of opposite polarity behave in a different way) viable
conductor of the same length L will result. Subsequently, if
the laser-produced channel decays, this new conductor will be
polarized in the external field and the development of leaders
from
its
ends
will
continue.
For
a
leader
velocity
vL  2  106 cm sÿ1 and L ˆ 20 m, the time taken for this is
about L=vL ˆ 100 ms. The time it takes the contraction to
develop also runs into the tens of microseconds (according to
our calculations [32] referring to the formation of the leader
channel in the leader tip, where the conditions are, we repeat,
more favorable, this proceeds faster Ð in a time t  1 ms).
That is why the ionized state of the cold laser-produced
channel will have to be artificially maintained for at least
tens of microseconds. Which of the scenarios outlined above
will be realized, if at all, will be revealed by a close theoretical
treatment and numerical computations probably supported
by a dedicated experiment Ð which presents a real challenge.
It is conceivable that it will not be possible to dispense
with the initial artificial heating of the primary channel
altogether, and then preference will be given to the long
laser spark produced by a CO2 laser. This will require a
higher laser energy because the same 20-m long channel (for
an external field of 1 kV cmÿ1) is to be made continuous. To
make it clear what kind of energy expenditure will be dealt
with, we point out that a 20-m long column of cool air 1 cm in
diameter harbors, when heated to 4000 K at pressure 1 atm
(to which there corresponds an equilibrium electron density
ne  7  1012 cmÿ3), 16 kJ of energy. At present, CO2-laser
pulses with an energy of 2 ± 5 kJ have been realized.
In brief, it seems likely that the problem of lightning
triggering at high altitudes is still a long way from receiving a
final solution, despite the fact that there appear to be no
fundamental obstacles. The reason is that the natural source
for the origination of lightning is, we believe, the same kind of
cool plasma object that we are dealing with. Here, we do not
discuss the problem of focusing and transportation of high-
power laser radiation to a high altitude provided that it does
not induce air breakdown and is not absorbed on its path.
When it comes to moderate altitudes, this problem does not
generate skepticism among enthusiasts of laser triggering of
lightning [16]. But, as the altitude decreases, the requirements
on the length of the initial channel L and the laser energy
become more stringent owing to weakening of the cloud field:
L  E ÿ5=3
0
. Conversely, the difficulties associated with trans-
portation and focusing of the radiation become more severe
with increasing altitude. One can see that the conditions for
selecting the appropriate altitude are contradictory. There-
fore, future work should proceed not only on the develop-
ment of laser pulses of higher energy and power. It should
search for ways of unimpeded transportation of the radiation
to as high an altitude as possible.
We emphasize once again that the very possibility of
exciting twin leaders from an isolated conductor embedded
in an external field is beyond question. This is precisely how
lightning originates from airplanes, and experiments of this
kind on metal rods of moderate length have been repeatedly
staged in laboratories (see Fig. 6). The question arises of how
to gain the `right' behavior of a plasma conductor, which
possesses a far lower initial conductivity and is prone to lose
it. This issue may and should be purposefully studied in a
laboratory, as applied to the problem of triggering lightning.
In doing this, emphasis should not be placed on lowering the
breakdown voltage in a long gap or the use of a laser spark to
direct the high-voltage spark, as have primarily been done
until now. For simplicity, solid rods with a conduction well
below that of metals are perhaps worth trying as the initiators.
We point to the experimental fact which may be pertinent
to the behavior of a discontinuous (broken) long spark. It is
well known that a high-voltage discharge can propagate
along a path in which small metal rods are placed at
intervals. As the leader approaches, each of the small rods is
polarized in the enhanced external field supposedly to emit a
pair of leaders: one toward and the other in the same direction
as the principal leader, and that is the way the spark
propagates. It is significant that only a negative spark, and
not a positive one, propagates in this way, which is clearly
associated with the fact that the leader process is inherently
stepwise in the former and void of steps in the latter.
11. Conclusions
So, in the foregoing we showed how and why lightning that
propagates from a cloud to the earth opts to strike a tall
structure, even though it may have to depart from its initial
path. Under the action of the electric field induced by the
charges of the lightning leader, electric charges are induced on
the grounded structure and the electric field is multiplied at its
summit; and the higher the structure, the greater the multi-
plication. This is responsible for the origination of a leader
ascending from the summit, the leader behaving like a high-
voltage electrode. The criterion for viability of the counter
leader imposes a constraint on the minimal structure height or
the combined field of the charges of the lightning and the
cloud acting on the structure. The mutual attraction of the
descending and counter leaders, when they are widely
separated (by over a hundred meters) and interact via weak
fields, is determined by a subtle nontrivial mechanism which
affects the acceleration. In this case, the absolute values of the
leader velocities, which are determined by intrinsic fields in
the proximity of the tips that are several orders of magnitude
stronger, are virtually invariable.
The joining of the leaders attracted to one another results
in the closing of the electric cloud ± ground circuit. During the
subsequent (not discussed in this paper) return stroke, the
plasma channel between the structure summit and the cloud
recharges acquiring the potential of the ground, with the
result that an extremely high current flows through the
structure. To protect buildings, recourse is made to lightning
rods which are raised in the neighborhood of the object under
protection but are made even higher in order for the counter
leader to be excited from the lightning rod rather than from
the object.
In the quest to improve the reliability of protection of
especially
vulnerable
and
critical
objects,
different
approaches to controlling lightning are basically possible.
Attempts are being made to use lasers for this purpose as well.
The laser triggering of lightning involves the production of an
ionized air channel by employing laser radiation. Two major
schemes are conceivable on this route. In one of them, the
plasma channel is produced by a laser at the summit of a tall
tower to promote the earlier excitation of an ascending leader,
which intercepts the lightning. It is precisely this effect that
was recently observed in Japan as a result of extensive
preparatory work and after many unsuccessful attempts. It
is conceivable that the role of the laser-produced plasma
reduced to the extension of the top of the grounded conductor
beyond the corona charge layer which was prohibitive to
leader excitation.
July, 2000
The mechanism of lightning attraction and the problem of lightning initiation by lasers
715

=== PAGE 16 ===
The other scheme under development involves laser-
assisted production of a plasma channel in the open atmo-
sphere so as to have lightning-provoking leaders excited at its
ends, much as large airplanes do. The condition for the
excitation of viable leaders from a plasma conductor is the
same as for a grounded structure. It also defines the minimal
conductor length. This approach to laser triggering of
lightning is much more complicated but is of greater interest
for both lightning science and, potentially, lightning protec-
tion. That would be the way to excite descending lightning in
the required place and time, timing the recording instruments
to a fraction of a millisecond and, on the other hand, to
discharge the cloud in a safe place. Many basic and practical
difficulties will be encountered in reaching this goal, but a
start has been made on this research and the scope of work
will most likely expand. One of the major problems is to focus
the laser radiation at as high an altitude as possible and in
doing this to eliminate the breakdown of air over the path of
radiation transportation. The higher the altitude of the
plasma channel produced to excite the leaders, the shorter it
may be, because the cloud field at a high altitude is stronger. A
shorter laser-produced spark would require less laser energy.
The laser radiation is easier to focus near to the earth, but in
this case the requisite length of the initial laser-produced
channel and the laser energy rise steeply.
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Wili S R, Tidman D A Appl. Phys. Lett. 17 20 (1970)
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Norinski|¯ L V Kvantovaya Elektron. 5 108 (1971) [Sov. J. Quantum
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Koopman D W, Wilkerson T D J. Phys. D 42 1883 (1971)
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