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Re: [TCML] Re: Slo-Mo Videos of Tesla Coil
Bert Hickman 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.
Hmmm, all that air is at the same pressure, so by
since P and V are constant, nT has to be constant, so as T goes up, n
I'll buy it.. so how cold does it get.. the same T^4 cooling stops
working as well as it gets colder.
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".
OK.. so they're talking time constants in the millisecond sort of scale.
"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.
Why it's simple.. all we have to do is integrate dT/dt = -k(T^4) or
something along those lines..(left as an exercise for the reader)
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