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.