Re: Spheres vs Toroids

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

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

Jim Lux wrote:
 > Actually, the problem's not as complex as all that...

I agree, for the reasons you give.  I was thinking of modelling
the background field of the topload (various shapes) plus the
additional field around the streamer, simulated as a thin curved
wire.  By a somewhat tedious process of iteration this would
approximate the likely streamer path.

 > A more tricky aspect is that you can't just ignore all
 > the dynamic effects, since they greatly affect streamer
 > growth.

Yes, I know I've ignored a heap of stuff.  But I don't want to
work out how far the streamers would develop - but simply
compute the path they would develop along, given the right
conditions.

This could, possibly, give criteria for choice of topload shape
which is independent of Fres, BPS, bang size, coupling, etc.

All we need is sufficient accuracy & realism for topload shape
comparison purposes.

When considering the much more difficult problem of estimating
the actual streamer development taking into account the RF
envelope, Fres, and so on, it seems to me that most of the
various physical models needed are available in the professional
literature, of which there is a great deal out there.  None of
it has been applied to the conditions of TC breakout, AFAIK, but
most of the pieces of the jigsaw appear are there. The most
awkward missing piece concerns quantifying the bang-to-bang
memory effect.

At present, I'm outfaced by the full task - hence this suggested
easy preliminary stuff.  It's a bit weak, I know, but a start
has to made... I don't see how our understanding of TC design
will progress until we come to terms with how the topload
interacts with the breakout.  We seem to be hitting a bit of
a wall at the moment...

Matt wrote:
 > With most real world measuring devices only accurate to 3-5
 > digits, what is the value of 20+digit accuracy in the
 > calculation?

Because the calculation itself is the object of interest.  For
the same reason I spent 3 weeks this summer writing a program to
calculate the group order of an elliptic curve over a finite field
of order 100 digits.  Absolutely no use whatsoever (not even for
crypto), but it was fun trying to get it right!  It's one of
those programs where all 4500 lines have to be exactly right or
you get just random numbers - the SEA algorithm, a tough
programming exercise - very rewarding in its own right.

So compared to that, calculating theoretical toroid capacitances
is highly practical!  You see, when testing finite element models
it's nice to have a high-accuracy target value against which you
can compare your model.  As you increase the number of elements
in the model, the output value should converge towards the target
value.  That's how you know it's all working properly and it
allows you to estimate accuracy as a function of element size.
Then, not only does your model sit well with the mean of measured
values, you can validate to another order of magnitude or so
beyond that.
--
Paul Nicholson
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