From: Paul
Date: Thu, 23 May 2002 20:34:52 +0100
Subject: Re: [TSSP] Topload breakout potentials
> The cap measured 65nF tonight. Thanks, that fits then. That's quite a change in Cpri. Is it an MMC? Perhaps there's a dry joint on one of the strings which is coming and going? Anyway, everything about your coil's tuning adds up now, and fits with the model. Interesting that your MCTV would give 40.1kV/cm at the surface but the 12% detune just happens to bring that down to 26kV/cm. Is that a coincidence? That means that the coil will just reach breakout in its detuned setup, at which point about 60% of the coil's stored energy is still in reserve - trapped in the primary. As the streamers develop, the secondary is detuned down towards the primary enabling the remaining energy to transfer across. If the detuning was such that all the available energy transfered to the secondary, while the streamers maintained the topload at around its breakout voltage (590kV) then the total effective capacitance required of topload + streamers to hold that energy would be Ceff = 2 * E/V^2 = 2 * 16.4 J/ 590kV^2 = 94pF. Now the resonator has a Cee of around 40pF so 54pF must come from the streamers - 54 streamer-feet at 1pF/foot, that's nine at 6 foot. And that loading would detune the secondary by 50%. Now undoubtably a lot of that available energy will be dissipated in the streamers themselves - lets try to get a ballpark figure on that... Let's see, taking 1pF and 220k per some length of streamer, that's a Q of 1/(2 * pi * 66kHz * 1pF * 220k) = 11. Pretty low, eh? That means in one cycle, the streamer dissipates a fraction 2*pi/Q of its stored energy. So in a half cycle, whatever energy flows into a streamer, only a fraction (1-pi/Q) is returned at the end. Supposing 6 half-cycles were required for the total energy transfer, then we retain a fraction of the order of (1-pi/11)^6 ~= 10% of the energy survives. Now that's a worst case because this naive arithmetic assumes all the energy passes through the streamers on every half cycle which is obviously not the case. At each half cycle the streamers extend a little, take some proportion of the reserved primary energy, and return (1-pi/Q) =~ 70% of it back to the coil. At the next half cycle the streamers are bigger so the proportion of reserved primary energy borrowed from the coil is that much larger too, and so on. If we start out with 16.4J, then 7J are required to fill the coil's Cee to the breakout voltage, and 9.4J are reserved in the primary. If streamers formed over 6 half-cycles then only around 1J would be available at the end of the process, requiring a streamer capacitance of (2 * 1J/590kV^2) = 6pF, or 6 streamer feet, and a secondary detune of 7%. While these are extremely ball-park figures they do suggest that the sort of offset tunings that we're seeing are of a reasonable order. Working the other way now, if we take Bart's -12% offset tuning, that would need an extra 10pF of streamer loading to drop the secondary Fres down to match (do you have two at 5 foot?). Those streamers hold an energy 0.5 * 10pF * 590kV^2 = 1.7J which is all that remains of the primary's initial reserve at breakout of 9.4J. So how're we going to measure topvolts now? We're stacking a lot of assumptions onto this 26kV/cm surface field threshold but we know that space charge will alter that and allow the topvolts to rise further. A scope trace of topvolts should match the model to within the accuracy of the firing voltage estimate (less a bit for loss) up to the breakout point, so that's something we can use to qualify a measurement method. Throw in a simultaneous base current measurement and you can forget losses and firing voltage - from the Ibase we can calibrate the topvolts to around 1% pre-breakout. Therefore don't worry about calibrating a topvolts detector if you can provide the Ibase. Those E-field pickup things won't do - they respond to topload (+streamer) charge rather than potential, and we need the potential. The two are related by the topload+streamer capacitance, which of course is varying. The E-field pickup doesn't really give any more information than an Ibase trace, since Ibase = total external E-field pickup. Both Ibase and E-field pickups tells us about the charge displacement, but that's only half the story - we need the top potential too. If the system was linear, either Ibase or Vtop alone would tell all about the resonator. To get at the varying load C, we need both. Given the two in the form of scope data capture, we can calculate pretty accurately (say 2-3%) the variation of Ctop as we go through the RF cycles of the beat envelope. We should be able to see whether it increases in steps or smoothly, and by how much and when. We can use this info to calculate the final energy in the way described above, (but with the accurate figures) and that gives us an end-end cross-check on the whole process. Tcma will need a little modification to sweep for the 'chirp' of the modes so that should be quite interesting. So I think that despite some apparently intractable difficulties with understanding the dynamics of the streamer formation, we do have a fairly well defined procedure for accurately measuring and quantifying the effect of the load on the coil - a procedure which is within our reach because we have the requisite instruments, coils, and software. And there are no approximations involved, at this stage it remains unequivocal measurements linked by precision modeling in the way that we've become used to. We're just applying it to observe a function Ctop(time) which will give us a lot of reliable information about how quickly the streamers form, when they form, how much charge and energy they take, etc. We just need that topvolts measurement method. -- Paul Nicholson, --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.