From: Paul
Date: Wed, 02 May 2001 04:33:21 +0100
Subject: Re: [TSSP] Time domain modeling
boris petkovic wrote: > This seems to me to be a secondary current waveform > graph display,and not primary one at first sight? Yes! Why didn't I see that? Guess I was just glad to see a beat appear. Somewhere I've inverted the phase of one of the modes, there'll be a - sign dropped somewhere, but just one of the modes and not all... hmm how did I manage that!! > never heard for "Fredholm" equation .. > Seems,extra study have to do. 'Mathematics of Classical and Quantum Physics' Byron and Fuller, Dover 1992, Vols 1 and 2 in ISBN 0-486-67164 The above is an outstandingly good book - IMO the all-time best math/phys book every put together. Amazingly it is low cost too! Also, 'Numerical Mathematics' Froberg, 1985, ISBN 0-8053-2530-1 has a chapter on this subject - mainly concerned with the computational aspects. And also the well known 'Numerical Recipes in C', chapter 18. Malcolm Watts wrote: > I was looking at the large number of oscillations within the > beats. Are we talking about the same beat envelope whose url you > posted (Thor primary current waveform)? Yes, same url. The frequency difference 68.129 - 65.908 = 2.221kHz of the waveform as plotted gives a notch every 450uS. With the revised frequencies of 69.144 and 65.018 there are only around half as many RF cycles per beat. I just found another error in the coupling operator u, so I expect the coupling is now different again. A long weekend coming up, so I'll try to get some more done then. I'm keen to answer the question - 'How much of the bang energy goes into the first two modes?' which translated means 'How well do the spatial distributions of the first two modes cancel out along the solenoid?', with the corollary 'How does the answer vary with k'. My guess is the answer will be 'not much energy at low-ish k', but with more of a spread at higher k. When voltages reach a point where the load becomes non-linear, the opportunity for energy transfer between modes arises. If a significant fraction of the energy of the main two modes spills over into the higher resonances, that could spell trouble for the secondary. This higher-mode energy is largely trapped in the secondary, so maybe if conditions are right it gets 'topped up' on each cycle of the main RF waveform. A question to those who have looked at secondary voltage waveforms on the scope: When arc discharge occurs from the topload to ground, does the breakdown path continue to exist into the next half cycle and beyond, or does the conducting path extinguish at the first zero crossing and have to re-form if it can, on the next half-cycle? Maybe the answer is 'partly', ie some of the ionisation is left over and a temporary lower breakdown voltage is available to the next half-cycle. Can anybody advise? The reason I ask is that, depending on just how long the arc discharge path can be considered to be grounding the top of the coil, it looks like quite a substantial amount of energy can be transfered into one of the higher modes, to be trapped there. Anyone reporting arcs along their secondary - but only when the top is actually discharging? Just some of many question a non-linear time domain model should be able to answer. Cheers All, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.