From: Paul
Date: Thu, 07 Dec 2000 09:37:38 +0000
Subject: Re: [TSSP] E-Tesla6.11
I wrote:
> > Terry, you recall I expressed some doubts about the method
> > applied in E-Tesla6 - I felt that it might not be representing
> > the energy stored in the internal capacitance. Computers here
> > have been churning through telescope data, so I've had time to
> > sit back and work through the math and I'm quite certain now that
> > your method is correct, providing that is, you calculate Fres by
> > resonating your C with the right inductance. The required
> > inductance is the equivalent series inductance (Les), formed by
> > integrating the EMF induced along the coil,
> > Les = integral{ x,y = base to top, M(x,y) * I(y) * dx * dy}/Ibase.
Terry wrote:
> Oh good! The capacitance should have been right.
> You had me worried ;-))
Yes, sorry about that! Some time ago now, when I first came across
E-Tesla, I wrote saying that I thought you should be calculating
the V profile rather than just assuming it. Having since gone to
the trouble of doing just that, I can appreciate now that assuming
the profile is a reasonable thing to do in order to arrive at a
practical program. I also thought that you would not be able to
fully capture the effect of the coil capacitance with just a single
surrounding gaussian surface, thus ignoring internal stresses.
Having learnt a few things since then, and thought it through more
deeply, I'm beginning to think that you've got a nice compromise
with E-Tesla. OK, you're also having to 'guess' the effect of the
current profile by introducing an Lfac, which includes a hidden
guestimate of the internal capacitance by way of its effect on the
current profile. Thus, on the face of it, you're still having to
guess two out of three reactance distributions. Having said that,
the one which you are calculating - the external C, is surely the
one to go for, since this is the one most affected by the coil
surroundings. The other two - internal C and mutual inductance -
are related to the coil size, turns, and h/d, but less dependent
on the exterior geometry and so these ought to lend themselves to
being determined by some formula mapping h/d to an Lfac. For that
reason I'm beginning to think that E-Tesla is applying the right
kind of effort in the right place to achieve a practical result.
I wrote:
> > I'll endeavour to produce a document which defines all these
> > 'equivalent self capacitances' and shows how each is related
> > to the physical capacitance distribution, and to each other.
It's well on the way - the first 18 pages are done. This is a new
doc which will replace the hurriedly written pn1310 and pn1710 and
which goes into things in much more detail, but hopefully with a
more accessible exposition.
Cheers,
--
Paul Nicholson,
Manchester, UK.
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.