Re: Streamer formation on the scope...

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Jim wrote:

> I think that quasistatic approximations (the 220K+1pF/ft) kind of
> approximation works nicely for large scale modeling (i.e. fRes
> calculations).  But, for dynamic effects such as streamer growth,
> we need some sort of model for the actual streamer.

Yes, the spikes do seem to be predominantly an RC decay combined with
one or more LC rings.  We would expect the RC time constant to relate
to 220k+1pF/ft.  That would be around 1400nS per foot of streamer, so
on that basis I'd say Terry's 100nS RC spikes are related to around 
1.5" of streamer growth.  

Such a small capacitance doesn't fit with the observed LC ringing with
around 20nS period.  The required inductance comes out much too high.
So I think the 20nS LC signal involves the topload capacitance, perhaps
a topload surface resonance.  If so, then its period will be much the
same on all spikes.  It would remain constant as the power level is
varied.  It would only alter if the topload is altered.  That's
something that could be quickly checked.

We'd expect the fundamental surface resonance of the topload to have
a half-wave length of about half the toroid circumference,
something like 150MHz, but then the proximity of ground and secondary
will slow things down, perhaps by a factor of 2 or so.  So anything
above about 30Mhz or so but below around 150Mhz could be a candidate
signal of this.

I'm left totally awed contemplating the surface modes of a toroid.
Those of a sphere are interesting enough!  Still a 2d surface, but
the hole in the middle splits the modes into those that link the hole
and those that don't.  A rich subject to which some very modern math
could be applied, if only it were comprehensible. :)
--
Paul Nicholson
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