From: Paul
Date: Thu, 16 May 2002 23:35:46 +0100
Subject: Re: [TSSP] Topload breakout potentials
OK, I'll have to scrap that hypothesis about ratios of surface propagation rates and risetimes. It doesn't work as I thought it might (: But I have the next idea lined up...sorry for thinking out loud like this! First, a questions: Do streamers form at a fixed speed, ie advancing at so many metres/sec, regardless of the size of charge reservoir or potential behind it? If so, then charge pouring into the topload from the coil at a rate determined by the RF risetime would give rise to streamers as the surface reached 26kV/cm, but if those streamers weren't enough in number to absorb the arriving charge, then the topload potential would rise a little, more streamers would form, thereby setting up a sort of dynamic equilibrium. Suppose a coil delivers a surplus charge of say 12 streamer-feet, then we can divide by the RF risetime to obtain a formation rate, a number of feet per uS, and this is the rate the equilibrium will try to achieve. If the 12 streamer-feet were delivered in say 0.5uS, then it would have to form streamers at a rate of 24 feet per uS. If that's too quick for one streamer, then the topvolts will be able to rise and further streamers would form. Well, that's just another hypothesis. What I'm after is some rule that will tell me how 'stiff' the breakout barrier is to further rise of topvolts. This could easily be determined from scope traces of topvolts during streamer formation - but a non-trivial measurement. Basically, if Q is the topload+streamer stored charge then we need to find a function f that gives the associated topvolts, in a form such as Vtop = f(Q, dQ/dt) a bit like an equation of state for whatever dynamics decide the disposition of the available surplus charge. We expect this function to clamp the topload to a voltage commensurate with a 26kV/cm surface field, but how firm is that clamping? How sharp is the knee of the V/Q curve? If it's very sharp it could have an interesting effect on the rest of the resonator. These questions could be answered if there was a way to get at the topvolts with a scope probe. Just picking up the E-field isn't going to work, because that's related to Q, not V. So I'm interested to hear of any ideas that might shed light on the processes, equilibria, whatever, that are taking place here. For instance this idea of fixed formation rate - does that hold any water? Probably not, but it's an example of the kind of rule that would enable us to predict the breakout performance of a coil and thus compute its optimum topload. John wrote: > A question too about how breakrate applies to all this, > since sometimes a very low breakrate causes many short > streamers instead of just one or a few long ones. It would > be interesting too to see if the variation in streamer quantity > varies with toroid size in a similar way at both high and > lower breakrates. Yes, that's a real difficulty, because in my mind and calculations I'm only thinking as far as the first breakout during a run, so that there is no prior memory of earlier breakout. The trouble is, the descriptions of the coil's breakout are based on running at a certain BPS and I'm not taking account of this. Maybe we need real slow BPS eg 1 per second in order to find observations that can test these primitive models. Trying to go beyond the first bit of breakout at the moment is just too onerous a task to contemplate. For now, I just want to know at what voltage the breakout starts, and how the V/Q evolves over the rest of that quarter-cycle. I think the notion of 'surplus charge' is sound, so long as there's a fairly well defined topvoltage at which breakout begins, and I think it's reasonable to estimate the total length of streamers by dividing this charge by a notional pF/foot of streamer - regardless of whatever dynamics are involved in the actual formation, so long as there is some kind of knee to the V/Q curve. Oh well, there's just a few more thoughts to confuse the issue ;) -- Paul Nicholson, --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.