On 5/18/11 6:30 AM, Michael Twieg wrote:
Whoops, forgot about no attachments. I'll try again. Links to pictures are at the bottom. Hi Steve, I was hoping for a reply from you in particular
<giant snip>There's an interesting interplay between the charge on the topload, streamer growth, and the secondary current waveform.
The following is all speculation, so take it with a big grain of salt (and study of Bazelyan and Raizer)..
Streamers grow in jumps, propagating pretty quickly (about 0.01-0.1c, as I recall). Think of the streamer as a wire, with charge moving down it.. as wire gets fully charged, the e field at the end of the streamer/wire gets high enough to exceed the breakdown strength of air, and then it jumps forward, with the jump being fed by charge coming out of the charge stored along the streamer/wire.
All that charge flowing also creates an IR drop, heating the air and keeping the channel alive. But it's sort of a transmission line phenomena, and eventually, the streamer runs out of charge, and stops, waiting while it's filled with charge from the top load.
The top load is pretty low inductance, so it can "fill" the streamer with charge fairly easily. However, if the secondary is pushing charge into the topload faster than the streamer is accepting it (limited by the L of the topload and the L of the streamer, mostly), the voltage on the topload will start to rise, and you'll likely start another streamer.
Eventually, the RF current input into the topload during the positive halfcycle ends, and the charge drains back out of the streamer into the topload, eventually reversing, as the topload goes negative. That's ok, because the charge flowing back down the streamer helps keep it hot, so that when the topload voltage goes positive (relative to the streamer) there's an already ionized channel to follow.
B&R talk about a 2 1/2D model of a streamer, and I've always wanted to fool with a numerical model of streamer growth with a topload and a sinusoidal current source: I'm pretty sure that the primary/secondary can be adequately modeled by a lumped circuit, and to the topload, it looks like a sine current source.
The challenge is modeling the distributed L and C of the topload and the streamer. And the whole thing is very much a transient analysis problem, so it's not like I can just throw it all into a antenna modeling code like NEC and let it grind.
Somewhere back a few years, Terry and I were discussing (on this list) about possibly modeling the streamer as a sort of transmission line with very slow propagation velocity (tricky to do without unrealistic L and C). I think it would have to be a custom simulation code.
The other thing you'd want to take into account is the thermal behavior of the air since it affects the conductivity, which affects the IR drop along the channel. You could probably make some simplifications here, and assume that it's just a tube of variable diameter or something. The conductivity of air has a sort of step function around 7000K, so the tube approximation isn't a bad one, according to the literature.
The radiative and conductive heat loss is reported in the literature as well.
Take home message: Topload size and shape will have a huge effect on spark growth. There's a tradeoff between L and C that will provide the appropriate "impedance transformation" between the growing spark and the current from the secondary.
For the mean time, empiricism is probably your best bet, until someone cranks out a good FEM code.
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