The thing this department exists for is a discharge that looks nothing like a Tesla coil's. Straight, smooth, one channel, growing visibly rather than appearing. A sword instead of lightning.
Why it comes out straight
Not because of anything clever in the geometry. Because of the clock.
A DRSSTC's bang lasts about 300 microseconds and reaches only about ten centimetres. Divided by the cycles in that window at the 50 to 150 kHz such a coil runs, that is 2.2 to 6.7 millimetres per RF cycle [derived], and the metre-and-a-half sword is fifteen such bangs laid end to end on a surviving channel. That much charge arriving that fast means the channel can break out in several directions at once, and it does.
A QCW's ramp lasts 6 to 25 milliseconds and its channel gains 0.13 millimetres per cycle, seventeen to fifty times slower [derived]. At that rate one channel grows, and it grows more or less continuously.
Why the other kinds do not do this
Put every sort of coil on one axis, how often charge arrives at the tip, and the shapes sort themselves out along it:
50 to 150 kHz thick branched lightning
200 to 500 kHz the long straight sword
1 to 4 MHz a thin straight warm flameHigher up that axis the channel is reheated more often, so it stays hot between deliveries and does not need to find a new path. Lower down it cools between them, and a cool channel is a channel looking for somewhere easier to go.
A spark gap coil sits near the bottom and has a second problem on top of the first: it hands over its energy in about eighty microseconds and is then done, so its arc is thrown rather than grown. A DRSSTC fixed that half of it, which is why longer on time buys a DRSSTC length at all, but it still arrives in bursts fast enough for the head to break out sideways. Only when delivery is both slow and continuous does a single channel win the whole way up.
And straighter is not simply better, which is why the useful band is a band. Push the frequency higher and branching keeps falling, but the channel starts to curl instead: a ramped tube coil up at 2 MHz throws loops tens of centimetres across. Branching and curling are two different defects and frequency moves them in opposite directions, so the window sits in the middle rather than as high as the electronics can reach.
The one figure on the record beside the bands is Uspring's, that sword arcs "seem only possible at frequencies of 400kHz or above", and Mads Barnkob on the same thread puts the sword characteristic above 400 kHz too.
The mechanism Uspring offers there, as a hypothesis and stated by him as one: a higher frequency moves the arc's space charges back and forth more often, which gives a higher current and so a higher channel temperature; a hotter channel is more conductive, and a more conductive one needs less voltage for a given length. That puts a high frequency arc in the same category as a slowly ramped one, a low voltage arc, and it is the low voltage rather than the heat that his sideways-breakout hypothesis says suppresses branches.
The ceiling comes from the switches. The bridge commutates at the working frequency, and at megahertz the switching loss plus an IGBT's current tail kills the device. Hundreds of kilohertz is about the limit for IGBTs; above that it is SiC or a valve.
The builds spread across that window rather than sitting at one end of it. Gao Guangyan's QCW 2 is laid out around a 273 against a secondary measured near 308 kHz unloaded, and his QCW 1 ran from 465 kHz down to 434 kHz between the start of the ramp and its peak on first light. About 270 to 465 kHz on one builder's own machines, which is a band and not a threshold.
Another build page (thaumati) states the ramp and the frequency as one thing rather than two: the ramped power cycle, "in combination with a high operating frequency", is what lets the arc grow much longer than a DRSSTC's. Read as frequency buying metres, that contradicts everything above. Read as frequency deciding how many channels the energy is split between, it agrees, because one channel that keeps all of it is longer than several that share it. The second reading is this page's, not the source's.
There are other explanations in circulation
And none of them is a version of this one. Rather than the rate at which charge arrives, one of them points at which half of the cycle the growth happens on, and it has a name on it. It is Steve Ward's, in September 2017 on HVF 117, and he marks it as a guess inside the sentence that makes it: on QCW coils he expects all the streamer growth to happen "during the negative voltage portion of the oscillation", which he calls "my 'theory' for un-branching streamers", while for ordinary DRSSTCs he bets it happens on both. Nothing on file has tested it since: Hydron offers on the same thread to look for it once his own QCW is finished, and no result followed. One argument that was resting on it has already been thrown out, on the overcurrent page: that holding energy in the bridge lengthens an arc by stretching the sustaining half.
Two more sit on HVF 973, a thread that exists to ask for the physics rather than to report it, and they compete with each other as much as with anything above. Uspring's first is sideways breakout: a slowly ramped arc is in effect a low voltage arc, the field across the channel is weaker, and a branch leaving sideways is that much less likely. His second is a random walk: the direction the tip takes next is statistical, and slower growth shrinks the region in which an avalanche can start, so forward is what is left. On the same thread k42 asked a different question, whether the frequency at which the sword appears is a characteristic frequency of the spark plasma itself. Uspring answered it, in the last post on the thread, and the answer is no. The plasma frequency follows the free electron density: 400 kHz corresponds to about one free electron per cubic millimetre, and a Tesla coil arc carries a great deal more than that. The two frequencies are nowhere near each other, so the coincidence the question reached for is not there.
One thing the slow ramp does is not in dispute. Anders Mikkelsen's reason for ramping is to let the arc form early and clamp the secondary voltage to a low value, which is what lets a short resonator throw long sparks without flashing over and lets the coupling go as high as it does (HVF 3140). That explains the coil. It does not explain the straightness, and the two questions are easy to run together.
Four mechanisms, one observation, and no experiment yet that separates them.
What the ramp has to do
The ideal growth is at a constant speed, and constant speed means a constant voltage at the tip relative to ground. Any jerk in the supply is a jerk at the tip, and the arc answers a jerk with a new branch.
Which is why the bus is ramped rather than switched, why the ramp is made by a converter rather than by skipping pulses, and why a corner anywhere in the curve shows up as a branch. The shape wanted is linear in the bridge's voltage, which gives power rising as the square of time because the load is resistive.
How long it gets
Length goes as the cube root of the energy in the bang. That is the single most important number in the department, because it is what makes upgrades disappointing:
L ~ E^n, n = 0.31 to 0.33Eight times the energy for twice the arc. Raising the bus from 325 to 440 V is 1.35 times the energy and about 18 to 20 centimetres on a 188 cm arc, not the 67 that a linear guess promises.
And the ratio it reaches, arc over the length of the winding that threw it, runs from about 7 to 25 across published builds. That spread is technique, not size, and the records page is arranged to show it. The demonstration worth having is narrower than the whole list, though.
The cleanest case holds size fixed by accident. Gao Guangyan's QCW 1.0 and QCW 1.5 carry near enough the same winding, 14.0 and 14.1 cm, and reach 7.1 and 12.6. Same builder, same size, and 1.8 times apart. Widen it to the seven builds on the wall between 12.4 and 18.0 cm, a size range of only 1.45 times, and the ratios still run 7.1 to 25.0, a spread of 3.5 times, with a correlation against coil length of -0.04 [derived]. Size explains none of it in there.
What limits it
- The overcurrent detector, if the energy piles into the end of the ramp. The bang tears and you hear a pop instead of seeing a sword.
- The frequency. Below about 200 kHz the channel runs cooler and branches; a slow ramp does not compensate for that, which has been tested.
- The channel's own charge. Space charge repulsion in the channel is about 0.01 newtons per cubic centimetre against 10⁻⁵ for the buoyancy of hot air, three orders of magnitude apart, and that is what sets the useful upper limit on ramp time rather than anything in the electronics. Both figures are Uspring's, quoted on the shape page; neither page has relocated the post they came from, so they are named here rather than linked.
What happens when it reaches something
Reach is the point of the thing, and a metre and a half of reach is a metre and a half of things it can touch. This is not the same event as a DRSSTC drawing to an earthed object, and the difference is the clock again.
A DRSSTC throws its arc and the bang is over in about 300 microseconds. Whatever the arc touched, it touched at the end of something that was ending anyway. A QCW's channel is continuous for the whole ramp, so a touch happens in the middle of a burst that has milliseconds left to run, and the rest of that burst is delivered into a load the coil did not choose. What that does to the secondary, the poles and the bridge is its own page, and it is worth reading before running a coil this size anywhere near earthed metal.
The part that belongs here is what the protection should do about it, because the ramp decides that and it decides it the opposite way round from an ordinary coil.
Pulse skip drops a single bridge oscillation and comes straight back. On a DRSSTC that is nearly free: the bus is flat, so the machine returns to the conditions it left. On a ramp there are no such conditions. The buck voltage has moved on, the arc has grown, and the pole structure the driver was tracking is not the one it comes back to. Skipping therefore does not pause the problem, it resumes into a different machine, and it does so repeatedly for the remainder of the ramp.
A latching detector ends the burst instead, and on a ramp that costs exactly one flash, because the next interrupter pulse is the next bang regardless. The arithmetic that makes pulse skip attractive on a long bang inverts here. This is why QCW builders run ordinary overcurrent, and what the detector is actually for is a page of its own.
What the strike then does to the rest of the machine, the feedback, the poles and the mode the coil comes back on, is five consequences on a page of its own.
What the channel is made of, and which clock it runs on
Two questions get asked together on HVF and only one of them has been settled.
How hot and how dense. Uspring answers the first from a measurement rather than a guess: "Tesla coil arcs are relatively cold arcs, as e.g. compared to arc lamps", and putting a conductivity measurement against a table gives "about 5000 K". Pressure is ambient, and he notes why it stays that way on a QCW in particular: "These QCW arcs grow slowly and don't compress the air. They don't bang as loud as the non QCW arcs" (HVF 973).
And whether the frequency where the sword appears is a plasma frequency. That was the hypothesis put to him, since "The sword charateristic shows above 400 kHz resonant frequency". His answer is no, and it is arithmetic rather than opinion: "Plasma frequency is related to the free electron density. For e.g. 400kHz that would be about 10^9/m^3 or about one per cubic millimeter. TC arcs generate a _lot_ more free electrons."
That check reproduces. The electron plasma frequency is f_pe = 8980·√n_e with n_e in cm⁻³, so 400 kHz calls for 1984 cm⁻³, or 1.98 × 10⁹ per cubic metre, about two free electrons per cubic millimetre [derived, and it lands on his figure]. Published streamer measurements put the real channel near 10¹⁵ cm⁻³, which is five hundred billion times more [derived]. The plasma frequency of a real arc sits in the hundreds of gigahertz. Nothing a coil does at 400 kHz can be resonating with it.
Which leaves a clock that does fit, and it is a time rather than a frequency
If the plasma's own frequencies are six orders too high, the quantity to compare against a half period is how long the channel stays conductive after the current through it reverses. The pulsed-discharge literature measures exactly that, and the numbers land in the right decade:
half period at 400 kHz 1.25 µs
half period at 350 kHz 1.43 µs
half period at 100 kHz 5.00 µsAgainst those, published work on repetitively pulsed streamers reports that with an interval under a few hundred nanoseconds the next streamer reignites the channel the last one left, while at intervals of several microseconds it does not reuse the old trail and instead starts new channels at the edges of it (review of streamer discharge physics, memory effect in repetitively pulsed discharges).
That boundary falls straight through the band where coils change behaviour. A sword is reported above 400 kHz, which is a half period of 1.25 µs and at the fast end of that transition, and davekni's 100 kHz QCW at 5 µs went zigzagged instead, which is what "new channels at the edges of the old one" looks like from two metres away. The self-repulsion account earlier on this page and this one are not rivals: repulsion says why a fresh channel is pushed sideways, and this says why a fresh channel gets started at all instead of the old one being reused.
So is a lower frequency coil better, which is asked as one question and is two
It gets posted in that form on the Chinese forums, 频率越低越好吗, and the honest answer is that the two halves of it go opposite ways.
On arc character the frequency matters and the direction is known. Everything above says a longer half period gives the channel more time to decay, and the observed consequence is the zigzag at 100 kHz against the sword above 400. Lower is worse on that axis, and it is the axis a QCW is built for.
And on arc length the belief is backwards, which somebody measured in 2011 and almost nobody quotes. Steve Ward, on the Tesla Coil Mailing List:
In my experiments with quasi-CW spark production, i found that my 360khz setup was far superior in converting primary amps to spark length than was a 280khz or 125khz resonator. And not just some 10-15%, but it was better easily by a factor of 2! So basically, same amount of amp-turns in the primary, but huge difference in spark output.
Three resonators, the same amp-turns in the primary, and the highest frequency turns those amps into arc twice as efficiently as the lowest (TCML, 17 May 2011). That is the controlled comparison the folk claim never comes with, and it points the other way.
He also names where the folk claim comes from, and it is not spark length at all. In the same message:
Some day i need to do similar testing with a regular DRSSTC and see if winding low frequency secondaries (to keep the silicon switching slower) is not shooting ourselves in the foot in order to make long sparks. In the QCW case it certainly appeared that way.
Low frequency is wound for the switches, so the silicon has more time per cycle. It gets repeated as if it were for the arc. Ward suspected in 2011 that the two goals pull against each other, said the QCW case certainly looked that way, and flagged the DRSSTC test as undone. This corpus has not found anybody who did it since.
So the answer to the question as asked is: lower frequency costs straightness for certain, costs arc per primary amp by a factor of two on the one QCW comparison on the record, and buys you an easier time in the bridge. Which is a real thing to want, and a different thing from what the question assumed.
And the part nobody can explain
Whether the sword comes out straight or curls over depends on the room more than on the coil: temperature, humidity, atmospheric pressure, and what is standing nearby. Two people with the same machine get different results and go looking for a fault that is not there. Nobody has isolated a single factor, and that is worth its own piece.
The arc on the QCW department page is drawn to this: one channel, grown rather than thrown, with its length following the ramp slider at the cube root of the energy.