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

[jimlux <jimlux@xxxxxxxxxxxxx>]

Bert Hickman wrote:
> 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.
> > >
> > > Bert
> >
> > 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
PV=nRT
since P and V are constant, nT has to be constant, so as T goes up, n 
goes down.

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.
> Also:
> "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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