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Spark formation explanation

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Dr. Dark Current

Fri May 18 2012, 11:15AM

Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384

Hi
Does anyone have an idea why sparks from pulsed coils branch a lot, but gradually ramping the power makes them straighter? Why sparks from "QCW"/half wave supplied coils are straight only above a certain frequency? Why does a "spark" at 30 megahertz look like a flame with no defined "channel"?

I don't think there's anyone who would know the ultimate answer, but I was just wondering if someone has an idea how to explain at least one of the above mentioned phenomenons. For me it is really interesting how much "magic" there's behind this...

Steve Conner

Fri May 18 2012, 12:18PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

It is plasma physics, but plasma physicists aren't too interested in researching it because there is no commercial application. If Tesla coil discharges cured hair loss or helped you quit smoking, we would have the answer tomorrow!

As far as I know, it is modelled reasonably well by the same fractal math that models growth of ice crystals, plants, cracks in stressed materials and so on. It's not too much of a stretch to describe the discharge as a crack in a stressed material, just that the stress is electrical, not mechanical.

As a rough generalisation, I would say that the growth pattern is the result of two opposing tendencies. The higher the instantaneous power dissipated at the streamer tip, the more it wants to branch. But on the other hand, the higher the plasma temperature, the less it wants to branch. (You could say that the hotter plasma resists high peak power dissipation because it's more conductive.)

So, high peak-to-average power ratio from the coil means high instantaneous power but a low plasma temperature. Result, purple sparks that branch highly.

A CW coil has low peak-to-average ratio and high plasma temperature, so you get a white or yellow flame.

I expect you could find a formula that relates peak-to-average power ratio to the fractal dimension of the sparks, in the same way that John Freau related power with spark length.

Frequency will also have an influence, in so far as it affects the relation between the streamer surface area, and the displacement current available to heat it. Modelling the streamer capacitance should account for this.

If someone asked me to make a dynamic Tesla coil streamer model, that's what I'd do, anyway. I'd calculate the dissipated energy in the streamer resistance, and use that to make an empirical estimate of the spark length and fractal dimension.

From those two quantities I could estimate the streamer resistance and capacitance to feed back to the circuit simulator at the next timestep, and also feed them into some fractal graphics routine to draw a rough picture of what the spark would look like.

I had some discussions with Roy/Dalus about using cellular automata to do the model and the picture simultaneously, but I'm not sure if he followed it up. I certainly didn't.

There may also be magnetic and electrostatic forces related to the frequency, but I don't understand that part.

plazmatron

Fri May 18 2012, 12:48PM

Registered Member #1134 Joined: Tue Nov 20 2007, 04:39PM
Location: Bonnie Scotland
Posts: 351

The jury seems to still be out on this one!

In standard coils (SGTC's and DRSSTC's) , the discharge seems to straighten out, at higher break rates, as the next discharge conducts through the ionised path of the previous one, allowing the discharge to grow in length.

As for sword like discharges of VTTC's, the characteristics seem to be down to the RF envelope shape. I really don't know the reasons for this.

As for the flame discharges, my best guess is that there is no time at all, for any pre-ionsed channel to even start to disperse, so multiple channels merge into one hot ball of gas, that the RF field is quite happy to sit there and heat.

I will end this comment with a question too. Since arcs from DRSSTC's 'grow', to a length determined by available input power, for the reasons explained in the first paragraph, is arc length a reliable indicator of output voltage?
The reason I ask is that really, ultimate length seems to be determined, by the coils ability to repetitively discharge down a pre-ionised channel. That being the case, measuring spark length for actual output voltage should be determined by measuring the length of a singe 'shot' should it not?

Les

Steve Conner

Fri May 18 2012, 01:44PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

It's well known that spark length from a Tesla coil isn't a reliable indicator of output voltage.

I did a few experiments with single-shot sparks, and I found that the spark length agreed quite well with the output voltage predicted by simulation. However, that was on an OLTC with a short burst length. In a DRSSTC with a longer RF burst, some growth might occur during the burst.

At higher break rates, the spark length goes up, even though the output voltage goes down because of the heavier loading on the DC bus and the heavier streamer loading.

Steve Ward

Sat May 19 2012, 07:41AM

Registered Member #146 Joined: Sun Feb 12 2006, 04:21AM
Location: Austin Tx
Posts: 1055

I think one of the biggest factors if field strength at the streamer tip. Why? well i dont really know exactly why from a plasma physics point of view, but its been observed by other spark researchers that negative corona's occur at a lower voltage than positive ones, and that negative coronas in low field stengths produce "branchless" streamers.

Scott Fusare

Sat May 19 2012, 10:32AM

Registered Member #531 Joined: Sat Feb 17 2007, 10:51AM
Location: Burlington, Vermont
Posts: 125

You may find "Spark Discharge" by Bazelyan and Raizer (ISBN 978-0849328688) to be enlightening. Specifically it is aimed at impulse sparks in "long gaps" (>1m), not RF sparks, but insightful none the less. In particular much attention is paid to spark propagation due to field enhancement at the "leader" tip, as Steve alluded to.

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