plasma-expert/context/qcw-operation.md

id	title	status	source_sections	related_topics	key_equations	key_terms	images	examples	open_questions
qcw-operation	QCW Operation: Driven Leader Growth Through Sustained Energy Injection	established	spark-physics.txt: Part 5 (lines 281-361), Part 9 (lines 666-700); Phase 6 QCW community survey (2026-02-10)	[thermal-physics streamers-and-leaders coupled-resonance power-optimization energy-and-growth capacitive-divider branching-physics field-thresholds empirical-scaling equations-and-bounds open-questions]	[Growth rate: dL/dt = P_stream / epsilon Driven leader step time: step_time ~ step_length / growth_rate Conductance relaxation: dG/dt = (G_st(i) - G) / tau_g Thermal diffusion: tau_thermal = d^2 / (4 * alpha)]	[QCW sword_spark driven_leader burst_ceiling frequency_threshold thermal_ratcheting conductance_relaxation ramp_duration pulse_skip]	[qcw-vs-burst-timeline.png]	[spark-growth-timeline.md]	[No direct arc current measurement on any QCW coil — the actual current flowing through the spark channel during QCW growth is unknown No spectroscopic temperature measurement of QCW sparks — 5000 K is inferred from conductivity, not measured No time-resolved impedance measurement during QCW ramp — the impedance trajectory during growth is unknown No high-speed imaging correlated with electrical waveforms in QCW mode No measurement of energy per unit length (epsilon) for QCW sparks — can only be bounded from total input energy and estimated system efficiency Voltage gradient in TC sparks disputed — Uspring estimates 1.5 kV/cm, Barnkob estimates 3 kV/cm No systematic frequency sweep study — same coil tested at 100, 200, 300, 400 kHz to isolate frequency effect]

QCW Operation: Driven Leader Growth Through Sustained Energy Injection

QCW (Quasi-Continuous Wave) is a Tesla coil operating mode that produces straight "sword" sparks dramatically longer than burst-mode DRSSTCs of comparable size. Where burst mode relies on high instantaneous voltage (200-600 kV) to push streamers outward in a single shot, QCW uses sustained low-voltage energy injection (40-70 kV) over 10-22 ms to grow a thermally persistent leader channel at ~170 m/s. This document consolidates all QCW-specific physics, measurements, and design parameters from the community research survey and framework analysis.

The key insight: QCW sparks grow because the leader channel persists between RF cycles and conducts energy to the tip, not because the voltage is high enough to bridge the gap. This is a fundamentally different growth mechanism from burst mode, and it explains why QCW achieves 7-16x spark:secondary ratios compared to 2-4x for burst DRSSTCs.

1. The QCW Parameter Space

QCW occupies a distinct region in Tesla coil design space, differing from burst-mode DRSSTCs in every major parameter:

Parameter	QCW Range	Burst DRSSTC	Source
Coupling (k)	0.3-0.55+	0.05-0.2	Build survey
Operating frequency	300-600 kHz	50-110 kHz	Build survey
Tank capacitance	5-15 nF	50-300 nF	Build survey
Ramp duration	10-22 ms	N/A (burst ~70-150 us)	Build survey
Peak primary current	50-200 A	200-1000+ A	Build survey
Secondary voltage	40-70 kV	200-600 kV	Ward, davekni
Spark:secondary ratio	7-16x	2-4x	Build survey
Growth rate	~170 m/s	N/A (single-shot)	HVF estimate

1.1 The 15:1 Voltage Ratio

The single most important quantitative comparison in the dataset: davekni measured ~600 kV for 2-3 m burst sparks vs ~40 kV for equivalent QCW sparks at 450 kHz. This 15:1 voltage ratio proves that QCW growth is driven by sustained energy injection, not high instantaneous voltage. Multiple independent builders confirm the low QCW voltage (Steve Ward: 40-55 kV; Loneoceans: 50-70 kV). [Phase 6 QCW community survey]

Physical explanation: The leader formation voltage threshold of 300-400 kV [Bazelyan & Raizer 2000] applies to single-shot impulses where the entire streamer-to-leader transition must occur from one event. In QCW, the thermal ratcheting mechanism (see Section 3) accumulates energy from thousands of RF cycles, crossing the critical temperature thresholds (2000 K -> 4000 K -> 5000 K) without ever requiring high instantaneous voltage. The voltage merely needs to exceed the inception threshold and maintain current flow. See streamers-and-leaders for details.

1.2 Coupling Requirement: k >= 0.3

All successful QCW sword-spark builds use k >= 0.3:

Builder	k	Spark:secondary ratio	Notes
Loneoceans v1.0	0.32-0.35	7.3:1	Initial
Loneoceans v1.5 (first)	0.306	—	Insufficient — breakthrough came at 0.38
Loneoceans v1.5 (final)	0.38	13:1	Breakthrough
Loneoceans QCW2	0.365	10:1
flyglas	0.391	~12:1
Lucasww	0.44	10:1
Dr. Kilovolt (Jan Martis)	0.55	—	SiC PSFB, 2-2.5 m sparks
davekni	0.71	—	Ferrite-assisted, highest documented
Standard DRSSTC	0.05-0.20	2-4:1	For comparison

Higher coupling enables sufficient power transfer at QCW's lower peak currents (50-200 A vs 200-1000+ A for burst). It also widens pole separation, making frequency tracking more robust (see coupled-resonance). However, Loneoceans' SSTC3 (single-resonant, lower coupling) still produces straight sparks at 380-420 kHz, suggesting k >= 0.3 is an engineering constraint (adequate power delivery) rather than a physics constraint (straightness).

2. The Sword Spark Mechanism

2.1 Frequency Threshold: 300-600 kHz

Six or more independent builders have converged on a frequency range for producing straight sword sparks:

Observer	Observation	Source
Mads Barnkob	"Sword characteristic shows above 400 kHz"	HVF
LabCoatz (Zach Armstrong)	Below 300 kHz: "chaotic and less straight"; above 600 kHz: "more curvy"	Hackaday
Kaizer DRSSTC IV	QCW at ~100 kHz: "swirling" sparks, NOT straight	HVF
Fat Coil builder	"Above 350 kHz, plasma exhibits growth in straight segments"	TCML
Loneoceans SSTC3	Straight sparks at 380-420 kHz	loneoceans.com
Multiple QCW builders	All successful sword-spark builds operate 300-500 kHz	Build survey

2.2 Why Frequency Matters: RF Period vs Thermal Time Constants

The physical mechanism is the ratio between the RF half-period and the streamer thermal diffusion time:

At 400 kHz: RF half-period = 1.25 us
Streamer tau_thermal (d = 100 um) = d^2 / (4*alpha) ~ 125 us

Ratio: tau_thermal / T_RF = 125 / 1.25 = 100x

The channel experiences effectively continuous heating with negligible cooling between RF half-cycles. The conductance relaxation time constant (tau_g = 40 us for heating, see thermal-physics) spans ~16 RF cycles at 400 kHz, ensuring smooth, monotonic conductance increase.

At 50-100 kHz (half-period 5-10 us), thinner streamers (10-50 um, tau ~ 1-30 us) experience significant cooling between cycles. The preferred conductive path diffuses and branches — the channel cannot maintain a single straight track.

At >600 kHz, "curvy" sparks are observed. This may relate to skin effect, displacement current dominance, or switching artifacts at extreme frequencies.

Quantitative prediction: At frequency f, the Joule heating rate scales as ~f (more half-cycles per unit time at the same peak current). A channel at 400 kHz receives ~4x more thermal energy per millisecond than at 100 kHz.

2.3 Pulse-Skip Modulation Does Not Produce Full Sword Sparks

Multiple experimenters (Steve Ward, Steve Conner, others circa 2011) tried pulse-skip approaches to achieve QCW-like behavior and could not produce full sword sparks.

Steve Ward: Sword sparks need "relatively smooth/continuous modulation of the spark power with little ripple." If the coil stores enough energy to smooth out the missing pulses, "it's probably massively overbuilt."

What pulse-skip actually does: In a DRSSTC, pulse-skip is a bridge current-limiting method. During "skip" cycles, one GDT (gate drive transformer) is inverted so the H-bridge effectively shorts the primary tank (single-leg inhibit / "freewheeling"), or both bridge halves shut down and energy returns to the bus caps. The IGBTs continue switching synchronized to secondary current feedback — phase coherence is maintained and there is no phase discontinuity when active drive resumes. Primary current does not drop to zero; it decays gradually through the loaded Q of the resonant system. The resulting current envelope is a sawtooth bounded by the OCD (overcurrent detection) threshold — current rises to the limit, bridge freewheels until current decays, then drive resumes. [Steve Ward DRSSTC design guide; UD+ documentation (P. Slawinski); UD3 (Netzpfuscher)]

Why it doesn't produce full swords — envelope quality: The sawtooth current envelope at a fixed OCD threshold delivers approximately constant average power, not the smoothly ramping power profile that QCW requires. True QCW uses a linear voltage ramp, which produces a quadratic power envelope (P ~ V^2) — the natural profile for growing a spark against increasing capacitive loading. Pulse-skip cannot easily produce this quadratic profile. The per-cycle current jitter from the on-off-on switching pattern, even with optimal distribution of skip events, creates enough power envelope ripple to prevent clean single-channel dominance. [Loneoceans QCW documentation; HVF topic 292]

It's a continuum, not binary: The effect of envelope quality on spark straightness is progressive. Coarse pulse-skip at a fixed OCD threshold produces standard branchy DRSSTC sparks. A more sophisticated Bresenham-algorithm pulse-density modulation creating a linear ramp envelope produces sparks that are noticeably more sword-like but still branch — an intermediate result. True analog QCW with a smooth quadratic power envelope produces full swords. The evidence suggests that spark straightness improves continuously with envelope smoothness, with no sharp threshold.

Smooth topologies that work: Steve Ward's original linear voltage ramp (giving quadratic power), Dr. Kilovolt's SiC Phase-Shifted Full Bridge (inherently smooth with a "1-cosine" transfer function), and Loneoceans' SSTC3 staccato approach (using the rising AC mains waveform as a natural voltage ramp) all produce straight sparks because they deliver smooth, continuously ramping power without per-cycle jitter.

Note: Pulse-skip (bridge current control) is distinct from staccato (interrupter timing synchronized to AC mains). They serve different functions and can be combined. Staccato provides a natural voltage ramp over ~4-5 ms per mains half-cycle; pulse-skip manages current limits within each burst.

3. The Driven Leader Growth Model

3.1 Growth Rate: ~170 m/s

QCW sparks grow at approximately half the speed of sound. This is estimated from community observations of spark growth during QCW ramps. [Phase 6 QCW survey, HVF topic 973]

Self-consistency check: At 170 m/s over a 10 ms ramp, the spark grows 1.7 m. Over a 20 ms ramp, 3.4 m. These match observed QCW spark lengths (1-2 m for standard builds, 3.35 m for the Fat Coil).

This velocity is intermediate between free streamers (~10^6 m/s) and natural lightning leaders (~10^4 m/s for stepped leaders, averaged). It represents a driven leader propagation mode unique to QCW: the leader advances continuously, fed by the circuit, at a rate limited by the thermal conversion of streamer-to-leader at the tip.

3.2 Step Time Derivation from tau_g

From the growth rate and Bazelyan's typical leader step length (~1 cm):

step_time = step_length / growth_rate = 0.01 m / 170 m/s ~ 60 us

This 60 us step time is close to the conductance relaxation heating time constant (tau_g = 40 us from Bazelyan). The channel needs approximately one tau_g to heat each new segment to leader temperature. The 1.5x ratio (60 us vs 40 us) is reasonable given that the transition also requires crossing the eta_T efficiency bottleneck (10% heating efficiency at ambient → 100% above 2000 K). See thermal-physics for the full conductance relaxation model.

3.3 Contrast with Bazelyan Leader Velocity

The Bazelyan formula v_L = 1500*sqrt(|Delta_U_t|) gives ~4.7-8.2 km/s at 100-300 kV — 25-50x faster than the observed 170 m/s QCW growth rate. The discrepancy is explained by the fundamental difference between:

• Bazelyan's v_L: Instantaneous leader step velocity (the speed of thermal instability contraction within a single step)
• QCW 170 m/s: Net growth rate averaged over many steps including the time to heat each new streamer segment

The QCW leader advances in rapid micro-steps at ~km/s but spends most of its time waiting for each new segment to thermalize. See streamers-and-leaders for details.

3.4 Thermal Ratcheting Mechanism

The 5:1 asymmetry in conductance relaxation time constants creates a one-way thermal ratchet:

tau_g = 40 us   (channel heating — current rising)
tau_g = 200 us  (channel cooling — current falling)

[Bazelyan & Raizer 2000, Ch 4, pp. 194-195]

Over many RF cycles:

1. During the high-current half-cycle: conductance increases toward G_st(i_peak) with tau_g = 40 us
2. During the low-current half-cycle: conductance decreases toward G_st(0) = 0 with tau_g = 200 us
3. Net effect: Conductance ratchets upward over ~10-50 RF cycles (50-250 us at 200 kHz)

This is the microsecond-timescale mechanism underlying the millisecond-timescale streamer-to-leader transition. Each RF cycle deposits a net conductance increment, accumulating over thousands of cycles during the QCW ramp.

4. Three Ramp Regimes

Loneoceans documented three distinct outcomes through controlled variation of ramp duration (QCW v1.5):

Ramp Duration	Visual Result	Physics Interpretation
Too short (<5 ms)	"Gnarly, segmented sparks"	Insufficient time for leader transition; disconnected leader segments don't merge
Optimal (~10-20 ms)	Straight sword sparks	Leader forms within first few ms; grows continuously for remainder
Too long (>25 ms)	"Really hot and fat but bushy"	Leader reaches voltage-limited L_max; excess energy drives branching

4.1 The "Too Long" Regime

Once the leader reaches its maximum length (set by the capacitive-divider), additional energy cannot extend it further. The leader channel becomes very hot and thick, increasing C_sh and worsening voltage division. The excess power must dissipate somewhere — lateral breakouts from the superheated leader trunk become the path of least resistance.

4.2 The "Too Short" Regime

Ramps shorter than ~5 ms don't allow the full streamer-to-leader transition (which requires ~0.5-2 ms from streamers-and-leaders). The "segmented" appearance suggests the spark advances as disconnected leader segments that don't merge into a continuous trunk. This is consistent with the thermal ratcheting model requiring multiple dark period cycles — see thermal-physics.

4.3 QCW Timing Analysis

Typical optimal QCW ramp: 12 ms at 400 kHz

• 0-2 ms: Voltage builds toward inception. Possible aborted leader attempts. High epsilon.
• 2-4 ms: Streamers form and begin heating. Transition zone. Temperature crosses critical thresholds at base.
• 4-8 ms: Leader trunk established. Low-resistance channel conducts energy to tip. Epsilon falling as thermal accumulation helps.
• 8-12 ms: Leader-dominated growth. Streamer crown at tip continuously fed by leader current. Best epsilon (5-8 J/m). Growth slowing as capacitive-divider attenuates V_tip.

5. The Burst Ceiling: Why QCW Is Necessary

5.1 Steve Ward's 80 us Measurement

Steve Ward's DRSSTC-0.5 provides a clean measurement of burst-mode growth saturation:

ON Time	Spark Length	Input Power
~70 us	10-18 inches	33-180 W
>80 us	No additional length	Diminishing returns

"Gained almost no spark length after about 80 us of ON period." [Steve Ward, stevehv.4hv.org/DRSSTC.5.htm]

5.2 Thermal Physics Explanation

The 80 us ceiling is strikingly consistent with the thermal time constant for 100 um streamers:

tau_thermal = d^2 / (4*alpha) = (100e-6)^2 / (4*2e-5) ~ 125 us

After approximately one thermal time constant, channels are cooling as fast as they are being heated. Additional energy goes into re-heating decaying channels rather than new forward growth. This is the fundamental wall that QCW overcomes by sustaining drive beyond this timescale.

5.3 Steve Conner's Burst Efficiency Finding

Short bursts of high peak power grow sparks more efficiently than long bursts of low peak power. A 100 us burst works better than 150 us at the same total energy. Higher peak power pushes the initial streamer further before the 80 us ceiling hits. See power-optimization.

6. QCW Energy Budget

6.1 Measured Energy Data

Quantity	Value	Source
QCW energy per pulse	275 J (for 1.78 m)	Loneoceans v1.5
Apparent epsilon (total input / length)	155 J/m	Derived
Estimated system efficiency	30-50%	Community consensus
Estimated spark epsilon	45-75 J/m	Derived (155 * 0.3-0.5)
Burst DRSSTC energy per bang	5-12 J	Steve Ward
Burst DRSSTC average power	33-180 W for 25-46 cm	Steve Ward DRSSTC-0.5

The apparent epsilon of 155 J/m includes system losses (primary resistance, secondary losses, corona, radiation). The spark epsilon of 45-75 J/m includes the early inefficient growth phase (first ~2-4 ms at high epsilon). The leader-dominated late-stage epsilon is significantly lower (estimated 5-15 J/m), consistent with the framework's QCW range.

6.2 Frequency Tracking During QCW Ramp

Loneoceans measured frequency shifts during QCW operation:

Condition	Frequency	Shift
Unloaded secondary	406-409 kHz	baseline
With 50 cm simulated streamer	349 kHz	-14%
With 1 m simulated streamer	310 kHz	-24%
QCW v1.5 during actual spark	413 → 377 kHz	-8.7%

The 8.7% shift during actual QCW operation is less than the simulated 1 m streamer (-24%), suggesting a real 1.78 m spark has lower effective capacitance than a solid wire — consistent with the branched, non-solid nature of real sparks. Frequency tracking (PLL or programmed) is essential during QCW ramps; a 5% detuning costs ~50% of delivered power (see coupled-resonance).

7. Environmental and Design Factors

7.1 Environmental Sensitivity

davekni observed straighter arcs in warm, dry conditions; curved/branchy arcs more common outdoors (cooler, more humid). Dr. Kilovolt reported "looping" or "curving" streamers under humid or cool outdoor conditions.

Physics: Higher humidity → faster complex-ion recombination (25x for hydrated ions, see streamers-and-leaders) → shorter plasma lifetime → less thermal persistence → more branching. Lower temperature → higher gas density → higher E_propagation → harder to sustain growth in single channel.

7.2 Smooth Power Delivery Topologies

Successful QCW implementations use inherently smooth power delivery:

• Steve Ward's quadratic ramp: Voltage rises linearly → power rises as V^2 → smoothly increasing energy delivery
• Phase-Shifted Full Bridge (PSFB): Dr. Kilovolt's SiC PSFB provides a "1-cosine" transfer function with no pulse-skip artifacts
• UD3 controller: Netzpfuscher's phase-shift modulation design provides smooth QCW control
• Analog ramp generators: Finn Hammer's reference design for linear voltage ramp

Pulse-skip modulation produces more sword-like sparks than standard burst but falls short of true swords due to envelope jitter (Section 2.3).

8. Spark-to-Secondary Ratios: The Efficiency Measure

The spark:secondary ratio (spark length divided by secondary winding length) is the clearest measure of QCW's advantage:

Builder	Mode	Spark	Secondary	Ratio
Steve Ward	Burst	80"	22"	3.6:1
Loneoceans DRSSTC3	Burst	70"	27.5"	2.5:1
Loneoceans QCW v1.0	QCW	40"	5.5"	7.3:1
Lucasww	QCW	51"	5"	10.2:1
Loneoceans QCW2	QCW	24"	2.4"	10:1
Loneoceans QCW v1.5	QCW	70+"	5.55"	12.6:1
Mathieu thm	QCW	76"	5.6" dia	13.6:1
Fat Coil	QCW	132"	8"	16.5:1

The 3-5x improvement from burst to QCW is a direct measure of the leader-dominated growth advantage. Leaders extend the effective electrode continuously, so the secondary length (which constrains maximum voltage) becomes less important relative to sustained power delivery.

9. Critical Time Comparisons

Timescale	Value	Significance
RF half-period at 400 kHz	1.25 us	Channel heating between cycles
RF half-period at 100 kHz	5 us	Channel heating between cycles
Streamer tau_thermal (100 um)	~125 us	100x longer than RF period at 400 kHz
Conductance tau_g (heating)	40 us	Time to heat one "step"
Conductance tau_g (cooling)	200 us	5x longer than heating → ratcheting
Driven leader step time	~60 us	Close to tau_g; sets growth rate
Burst pulse duration	70-150 us	Comparable to streamer tau → saturation
Burst ceiling (Ward)	~80 us	Streamer growth saturates
Leader transition time	0.5-2 ms	Within QCW ramp; exceeds burst pulse
Streamer persistence	1-5 ms	Exceeded by QCW ramp
Dark period cycle	1-5 ms	Multiple cycles fit within QCW ramp
QCW ramp duration	10-22 ms	100x longer than tau_g

10. Community Hypotheses (Unproven)

10.1 Uspring's Sideways Breakout Suppression

QCW's slowly ramped voltage keeps tip voltage low, reducing the transverse field component. The field is only strong enough for forward propagation along the existing hot channel.

Assessment: Physically plausible. The hot leader channel has much lower impedance than virgin air to the side, so a weak field preferentially drives current forward.

10.2 Channel Temperature: ~5000 K

Uspring estimated ~5000 K from conductivity analysis. Not spectroscopically measured. Consistent with Bazelyan's leader temperature range (4000-6000 K) and the white/yellow visual appearance of QCW sword sparks (blackbody peak near 5000 K).

10.3 Steve Ward's "2000 Small Sparks" Model

At 400 kHz over 5 ms, there are ~2000 RF half-cycles, each depositing a small amount of energy. This is a simplified but correct description of the driven-leader mechanism as viewed through the conductance relaxation model.

11. Framework Validation Summary

Prediction	Community Data	Agreement
Thermal persistence is key to QCW advantage	Confirmed by all data	Excellent
Streamer-to-leader transition requires sustained drive	Confirmed	Excellent
Capacitive voltage division limits length	Confirmed by frequency shift data	Excellent
Hungry streamer self-optimization	Confirmed by Burnett causality insight	Excellent
Burst mode limited by streamer cooling	Ward: 80 us ceiling (cf. tau ~ 125 us)	Good (within 1.5x)
Optimal QCW ramp: >5x tau_thermal	10-20 ms (well above minimum)	Consistent

What the Framework Missed

1. Frequency threshold for sword sparks (300-600 kHz) — derivable from existing thermal physics (RF period << tau_thermal) but was not explicitly predicted
2. QCW secondary voltage is low (40-70 kV) — framework implicitly assumed higher voltages for longer sparks
3. Power envelope quality matters — growth model dL/dt = P/epsilon does not capture the effect of envelope smoothness on channel selection; spark straightness improves progressively from pulse-skip (sawtooth) through Bresenham PDM (linear ramp) to true QCW (quadratic ramp)
4. Three ramp regimes — the "too long" bushy regime was not predicted (arises from capacitive divider saturation + excess power branching)
5. QCW growth rate (~170 m/s) — not previously predicted but derivable from tau_g and step length

12. Key Persons

Person	Contribution
Steve Ward	QCW inventor; quadratic power profile; 40-55 kV measurement; 80 us burst ceiling
Gao Guangyan (Loneoceans)	Most detailed QCW measurements (4 builds); frequency tracking data; three ramp regimes
David Knierim (davekni)	Critical 15:1 voltage comparison; oversized QCW; fiber probe
Richie Burnett	Causality reversal; pole splitting theory
Steve Conner	Burst efficiency finding; hungry streamer principle
Uspring	Temperature estimates (~5000 K); voltage gradient analysis
Jan Martis (Dr. Kilovolt)	SiC PSFB QCW; k=0.55; 2-2.5 m sparks; environmental sensitivity
Mads Barnkob	Frequency threshold observation (>400 kHz)
Zach Armstrong (LabCoatz)	Frequency window (300-600 kHz)

Key Relationships

• Derives from: thermal-physics (thermal persistence, conductance relaxation, tau_g asymmetry are the physical foundation)
• Derives from: streamers-and-leaders (driven leader growth is a special case of the streamer-to-leader transition)
• Interacts with: coupled-resonance (frequency tracking during QCW ramp is essential; pole shifts 5-25%)
• Interacts with: power-optimization (R_opt_power shifts continuously during ramp; match at 50-70% of target length)
• Interacts with: capacitive-divider (voltage division limits maximum length; causes "too long" regime)
• Interacts with: energy-and-growth (epsilon varies during ramp from ~15 J/m early to ~5-8 J/m late)
• Constrained by: field-thresholds (inception threshold must be exceeded; propagation threshold sustains growth)
• Measured via: Phase 6 QCW community survey (primary data source)