Re: Breakdown voltages of toroids

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

Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk> 

Hi Antonio,

I see you've been pretty busy putting out some very useful
software.  Wish I could run the stuff but no windows here...

I agree, the thing with the self potential calculations can
get a bit messy.  There are whole books devoted to this problem,
so we should be relieved that the methods we're using work as
well as they do - it could have been a lot worse!

For bulk C values, the distortion of the charge distribution is
negligible, and only really becomes a problem when we want accurate
values for surface field.  Even then, other factors make this
problem relatively minor, I think.

 > I will eventually code a simulator like yours, since I have how
 > to calculate inductances and capacitances from coils.

Yes, I think you have done the hardest parts already.  Now you just
have to model a suitably detailed equivalent network.  When doing
this, to get reasonable accuracy and to reproduce all the
qualitative features of the V/I distributions, you have to include
the effect of C between each pair of N secondary coil rings, ie
N*(N-1)/2 capacitances.  This is what I call the 'internal'
capacitance in my notes.  Other coil models that I've seen fail to
do this, or only include capacitances for immediate neighbour rings.
Then their authors wave hands rapidly to explain why the results are
a few percent out at the fundamental, and proportionally more error
at the higher modes.  For the higher order resonances to work out
right, the internal C must be reasonably well approximated.  I also
include C terms for distributed capacitance between topload and
secondary, which is another kind of 'internal' capacitance.  All
this requires meticulous book keeping of the many internal C terms
involved, but is well worth the extra effort.

 > I don't like those formulas where the breakdown voltage depends
 > on the gap distance. This doesn't look physical.

Right, it isn't.  Those figures appear to take into account the
overall geometry, ie they represent the average field across a
large gap.  But the local breakdown field remains some 26-30kV/cm
(depending on risetime).
--
Paul Nicholson,
Manchester, UK.
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