A spark propagates at two to three metres a microsecond. A DRSSTC's bang lasts about three hundred microseconds. At the spark's own speed that is seven hundred and fifty metres of arc, and what you get is a metre and a half.
The arc grows about five hundred times slower than its own limit, and the thing holding it back is the supply of charge. That one fact explains the branching, the thickness, the speed, and why a DRSSTC looks like lightning while a QCW looks like a sword.
How it grows
Charge runs up the channel and collects on the leader's head. The head behaves roughly like a one centimetre ball. When the field on it passes 30 kV/cm the channel jumps to a new segment, and the current flowing through the channel keeps it hot enough to stay conductive.
A one centimetre ball is 1.11 pF and needs 30 kV to reach that field, so each jump costs about 33 nC.
Step length is just voltage over breakdown
one step = topload voltage / 30 kV per cm200 kV gives 6.7 cm, 250 kV gives 8.3, 300 kV gives 10. Extreme Electronics puts it exactly that way: each burst of RF makes a 10 cm leader from the available 300 kV.
Between bursts, if the channel has not had time to disperse, the energy of the next burst rushes to the end of the ionised channel and makes another leader there, each one slightly diminished by losses. That diminishing is where the sublinearity comes from: L goes as E^(1/3), not as E. And it is why the length breathes from bang to bang, because a channel that did disperse starts again from ten centimetres.
Against a QCW
Same metre and a half, different clock:
- DRSSTC, 300 µs at 250 kHz: 5.0 mm/µs, and 20 mm per RF cycle.
- QCW, 20 ms at 460 kHz: 0.075 mm/µs, and 0.16 mm per cycle.
A hundred and twenty five times faster. That is the whole difference in appearance. The DRSSTC's channel takes so much charge per cycle that it can break out in several directions at once; the QCW's gains a hundredth of a millimetre a cycle and grows one channel.
What it is, electrically
Two independent estimates twenty years apart, agreeing to five per cent: Terry Fritz fitted about 220 kΩ in SPICE around 2001, and Hydron measured about 210 kΩ with roughly 29 pF at the peak in the 2020s. Along the channel, a few pF and about a microhenry per metre.
The capacitance, being comparable with the topload's, pulls the secondary's resonance down. That is the detuning. The resistance drops the secondary's Q from around 200 to about four, which is not a typo: the arc loads it by a factor of fifty, which is why tuning is far more forgiving under load than on an idle bench.
Inside one bang
The bridge turns on, the current rises for five to seven cycles, the secondary voltage climbs until the breakout fires, the channel goes, it grows and branches and adds capacitance, the secondary slides down in frequency and loses Q, the reflected resistance changes and takes the primary current with it, and then the bridge turns off and most of the primary's energy goes back into the bus capacitors.
A bang cut short is energy that never reached the arc, because a DRSSTC is not a spark gap coil: the energy does not leave in one transfer time, it is pumped in for the whole bang. So a longer ontime gives a longer spark, most visibly at modest peak currents.
Between bangs, the channel remembers
Successive bangs go into air that is already hot, which is thinner and breaks down at a lower voltage, so the current starts rising earlier and the voltage peak comes out slightly lower. The first bang after a pause does not behave like the tenth, which shows up in captures as a drift that is not really there.
This only works if the next discharge takes the same channel. A wandering root kills it, which is a practical argument for a fixed breakout point.
Roughly: below about 30 bangs a second each one starts from nothing and the spread is wide; between 100 and 300 there is partial memory and the arc hangs in one corridor; above 500 the channels barely cool and it reads as continuous light.
Why it branches
The zigzags and the branches are the same defect. A dip in current raises the losses in the channel, the channel loses conductivity, and it breaks out in a new direction.
Higher frequency runs the channel hotter and gives straighter arcs with fewer branches. Power delivered abruptly branches; delivered smoothly it makes one channel. Residual voltage left on the bus branches the start of the bang. A smooth breakout surface gives one large channel and a rough one gives several short ones. And a toroid that is too small gives many weak streamers instead of one strong one.
And do not confuse branching with the whole channel bending. Frequency moves those two in opposite directions, and the bending has its own article.
The shape, for anyone drawing it
A tree with a definite trunk, not a bush. Branches leave from where the channel lost conductivity, which is behind the head, not from the base: a fan out of one point is wrong.
Branching angle, measured on streamers in air: 43° ± 12° in the plane of the image, 49° ± 6° in three dimensions. Fractal dimension 2.16 ± 0.05, so a heavily branched tree, denser than flat and nowhere near filled.
Thickness is a cone, not a cylinder. The section nearest the topload carries the current of every branch above it and runs hottest. Jan puts the growth side of it well: the outer half costs as much as the whole original arc, while the inner half thickens and heats.
Strike to ground
The topload voltage collapses in 100 to 250 nanoseconds. The ground arc is 25 to 50 kΩ. The arc takes the load off the secondary so the primary rings up, which means the overcurrent protection usually fires after the event rather than at it.
On an ordinary DRSSTC the current rises on a ground strike. On a QCW it falls. Under heavy ground strikes a freewheeling driver skips about 80 per cent of its pulses, because the strike is a low resistance short across the secondary and the primary current hits its limit immediately.
What the models still cannot do
Uspring built an LTspice model of the arc and ran it against a real coil. The starting current matched, 35 A at one or two kilowatts. The peak matched, 115 A modelled against 100 measured at the overcurrent limit. The constant growth rate was confirmed. The length came out at half of reality.
The reason is that the model has no wander and no branching, and a smoothed arc is longer: a real channel meanders, so measured straight it reaches further than the straight model does.
For anybody simulating one, the practical consequence is small and annoying: if you draw a straight channel, take a longer length than the calculation gives. If you draw a meandering one, take the calculated length. Otherwise the picture and the number disagree by a factor of two.
The discharge on the DRSSTC department page is drawn to this: segments of a fixed step, branches at forty odd degrees behind the head, thickness as a cone. Sources are Bazelyan and Raizer, Jim Lux's exposition of them, Terry Fritz, Hydron's dataset, and Extreme Electronics.