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Re: [TCML] Re: Slo-Mo Videos of Tesla Coil

jimlux wrote:

While faster break rates may permit easier reignition of increasingly smaller current channels, it's not clear that this will contribute much to actually increasing spark length. I suspect that increasing topload capacity and peak output voltage are considerably more important for obtaining maximum spark length. These would indeed increase maximum channel current, but I suspect that maximum spark length would otherwise be be relatively independent of break rate as long as you were significantly higher than ~100 BPS.


I would think that the hot channel cools from outside in (by radiation.. convection isn't going to have appreciable effect in milliseconds). So, as long as the center of the channel doesn't cool below the 7000K or so, then when the next bang occurs, the charge will zoom to the end (heating it up on the way).

Apparently the core cools down very quickly (~1 msec). Although the next leader tends to follow the path of the earlier one, it is not because of residual 7000K air. Instead, the breakdown voltage along the previous leader path is significantly lower than virgin air due to the residual lower density hot air channel. And, the air doesn't have to be very hot. It can be significantly lower than the temperature for thermal ionization >2000K). In a 1958 study, L. L. Alston found that the breakdown voltage of an air gap at 450 degrees C is approximately 50% of the value at room temperature. This is purely due to reduced air density and agrees with Paschen's law.

A series of very interesting studies by Les Renardieres Group (Double Impulse Tests of Long Airgaps, Parts 1 - 4) appears to be relevant to this discussion. In particular in Part 2: Leader Decay and Reactivation, it was found that the high conductivity phase of leaders fully decays in less than 2 msec. Upon reapplication of high voltage, a new leader begins from the HV terminal, and retraces the path of the first leader due to low air density. Specifically:

"For time delay of 1800 usec, the process started from the electrode without any sudden reactivation. However, the channel followed by the new leader was the basic leader path. This indicated that even if the conductivity of the channel was highly reduced, its temperature remained significantly higher, and the gas density significantly lower, than in the surrounding gas".

"The recovery of an airgap in which a leader discharge has been created is governed by three characteristic times: (i) The time characteristic of the decay of the leader channel conductivity. This time is of the order of 1 ms.
(ii) The time characteristic of the cooling of the leader channel.
(iii) The time characteristic of the space-charge dissipation."

So here's the calculation that someone could do.. given a particular hot core diameter, what's the diameter vs time curve look like.

This may not be necessary. The above study implies that the core channel temperature decays significantly below 7000K in 1 msec (or less) after removal of current. Other papers have suggested that the thermal decay of an arc channel is exponential, suggesting a decay constant that is significantly less than 1 msec.

BTW, I just discovered these particular Renardieres Group papers. They look to be potentially quite valuable in providing a better understanding of leader reignition and growth during repetitive discharges (Tesla Coils!).

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