From: Paul
Date: Thu, 03 May 2001 20:22:53 +0100
Subject: Re: [TSSP] Time domain modeling
Malcolm Watts wrote: > Some questions, some information and some comments: > > Firstly, I have enjoyed immensely reading through the notes you > have been producing and it has been a great little exercise to > stretch myself to follow them (which I am mostly doing although it > has been some years since I actively applied calculus to electronic > modelling). I am getting up to speed once more :) Yes, hope it makes a good read - have to go back and rework the text quite a bit because it has the bare minimum of explanation right now. > On 2 May 01, at 4:33, Paul wrote: > > When voltages reach a point where the load becomes non-linear, > > the opportunity for energy transfer between modes arises. > Are you meaning spurious and transient loads of various kinds caused > by sparks being formed at the terminal? I'm separately considering a smooth, roughly continuous, time varying load conductance, to represent ionisation around the coil, corona, and brush discharges into the air, as against the short temporary arc discharges to ground. The former I'm handling by a piecewise linear interpolation of a set of normal modes, and the latter I'm treating as a step change in the boundary conditions. Starting and stopping of the primary gap arc also goes into the second category, but the gap resistance contributes to the first category. Remains to be seen whether this distinction proves worthwhile. Either way, the normal modes are constantly changing, which implies that energy must be exchanged between the modes. I feel that a great deal of interesting and enlightening information will emerge from a careful study of just how the bang energy spreads out through the modes, entropy-wise, as the system decays, and in the investigation of the effects of the higher modes on quenchability and secondary breakdown. > There is an optimum terminating spark which can drain the secondary > in just a couple of cycles. Trying to define it is not simple as the > impedance is time-varying with current which is constantly changing > (OK - that sounds like a tautology of sorts). But I know what you mean. Its this time varying 'instantaneous impedance' that we need to know. An instantaneous impedance is not a valid concept, although an 'instantaneous resistance' is. Taking proper account of the reactive part will need careful definition of the quantities involved. > You might consider > that there is an optimum rate of energy drain which could be equated > to some equivalent purely resistive termination (at a guess matching > Zft). Yes, I'd put my money on Zft for critical damping. It seems to be the point of lowest Q. As the load is brought down to Zft, the Q plummets to a minumum at around Zft, and then starts to rise again as the top load resistance drops from Zft down to zero. It's in this regime of load resistance below Zft that the normal modes change shape considerably, the lowest mode looking more like a 1/2 wave. This is just the region the coil would be pulled into with an arc discharge from the top, given the kind of resistances Boris mentioned. I'm looking forward to figuring out just what happens to the energy left in the coil - that which isn't dumped immediately in the discharge. Cheers All, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.