TSSP: List Archives

From: Paul
Date: Tue, 05 Jun 2001 10:48:10 +0100
Subject: Re: [TSSP] Interesting article on Medhurst, Wheeler, modeling,

Hi Terry, All

Terrell W. Fritz wrote:

> As I look at it more and more, you are indeed correct.  He got the
> program to do the mutual coupling and the capacitances and got the
> values pretty close but he really did not see the "light"...

Yup, by using a naive handwaved argument to dismiss Cint, he has thrown
out the most interesting physics and reduced the thing to a bog standard
transmission line.  The filters he describes aren't exactly novel. At
age 20 I was being paid to design transmission line filters using just
the same techniques.  All he's done is to take a solenoid and discard
the bits that make a solenoid different and interesting. What remains is
just a regular, albeit non-uniform, transmission line, to which he
applies some standard RF engineering to produce filters and oscillators.

When I decided one day to build a big CW coil a year or two ago, I just
assumed the spectrum of resonances would be reasonably easy to predict.
Straight away I applied the usual theory, just as Rhea does, but the
first decent measurements I made were enough to convince me that there
was something slightly more involved happening. Simply - I could not
predict the frequencies - even approximately.  It was obvious to me
that mutual inductance and longitudinal capacitance were candidate
explanations, so I set about calculating their distributions, and
calculating their effect on the spectrum.  I put in a mutual inductance
model, crude at first, until Mark told be about Grover.  But that didn't
fix the frequencies.  So I calculated roughly the Cint matrix, put that
in, and immediately, without any tweaking, the resonances started to
come out right.

Well, that's history now.  We're not the first to talk about internal or
longitudinal cap, call it what you will.  Others, eg Breit,  have
mentioned it and included approximations to it in their calculations.
So far as I can tell, we are the only bunch who have approached the
problem quantitatively.  You'll appreciate now why I always ask for f3,
f5, etc.

In the concluding remarks, Rhea blames non-uniform external C for the
dispersion. I've never been able to achieve dispersion with just Cext,
not by any distribution - with a non-uniform Cext, the velocity factor
and phase 'constant' become functions of position, but not of frequency.
Dispersion seems to originate entirely with Cint and M, with Cint
pulling the higher modes one way, and M the other.  There is some nice
math still to be worked out there, to actually prove this formally.

His final comments are revealing: 'Dispersion is low for ... solenoids
that are mounted close to a ground plane.'  Yup, that pushes up Cext
to disguise Cint.   And: 'Dispersion is most severe in large solenoids
with few turns..'. Yup, I think he means small h/d,  where Cint takes
over with a vengeance.  And of course, the picture changes significantly
if the solenoid is no longer small compared with the free space
wavelength - then, the quasi-static approximation (potential at A
influences field at B instantly, ie no retardation) breaks down and
you have to go to Maxwell's equations, but that's just antenna theory,
as applied to helical radiators - itself an ongoing field of research,
and a very important one.

As always, there is a decisive question that you can ask which blows
the thing open.  In this case:  "What is the capacitance of the solenoid
when it is floating in free space, and what are its resonant modes".

Pondering the answer to that forces you to take Cint seriously.

The original intent of this project was to find some academic
institution or journal that would apply some proper peer review. That
hasn't happened, I'm afraid.  Posted up on the web like it is, our work
is just another cranky Tesla theory, of which there have been more than
enough over the years.  What should we do about that?  Anyone know of a
department anywhere that does this kind of thing - I don't.

> Forgive if you have talked about this before (I get a LOT of mail and
> loose track...) but are their any areas in your present models that
> seem weak to you or are giving odd results?

Yes, indeed.   On the whole, the project is lacking in experimental
evidence.  We have, thanks to you and a few others, a number of
measurements of higher mode frequencies, most of which agree nicely.
Many do not, these are the small radius and high elevation coils.  To
add experimental weight to the Cint issue, we need some of those
'unequivocal' results applied to the higher mode frequencies. We need
to be able to show, without a shadow of a doubt, that the correct
dispersion cannot be reproduced without Cint, and that when Cint is
introduced, the correct mode frequencies come out.  This should be done
for a short coil, say h/d = 1 or less, so that the effect is largest.
As it happens, these are the hardest to model, and I need to smarten up
the Cint calculation in order to tackle it. I plan to introduce a short
range approximation using pieces of an elliptic integral, stitched
together and normalised to match the longer range Cint as presently
calculated using the boundary element method.  This will give us a
reliable and justifiable short range interpolation to improve the
accuracy at small h/d, but it's at least a month or two's work.

What this project **really** needs is the kind of stiff peer review that
it would get in an academic environ.  I'm not in touch with any such
organisation, so I'm open to suggestions.  I wish we could find someone
who could publish a proper paper on longitudinal coupling in solenoids.
In fact, the work that we have covered could inspire a couple of papers,
eg  'Effect of long range mutual capacitance in solenoids',  and
'Solenoids described by Fredholm integral operators', would be a couple
of good titles.  Someone should write these papers and get them
published.  I'm probably not the best person to do that.

Finally, Rhea's paper serves to remind us that we may even be leading
the field, in this aspect at least.  We can be justifiably pleased with
this, but in amongst all the excitement about time domain modeling of
Tesla coils, we *must* try to consolidate more firmly our earlier work,
and we have to try to get the project under the wing of an academic
department somehow.  Without critical review, and without a solid body
of experimental evidence, our work is just baloney, not science.

Cheers All,
--
Paul Nicholson,
Manchester, UK.
--


Maintainer Paul Nicholson, paul@abelian.demon.co.uk.