From: "Malcolm Watts"
Date: Mon, 6 Nov 2000 12:55:33 +1300
Subject: Re: [TSSP] NSVPI - Latter Results
On 5 Nov 00, at 22:36, Paul wrote: > Malcolm Wwrote: > > > ...If you buy the notion suggested by a crude analysis of that > > behaviour that gap loss is predominantly V.I rather than I^2.R > > and that Vconducting is approaching constancy, you can see why. > > Yes, I see, it's the small constant Vgap. I suppose by definition the > gap loss must be V.I, so long as V changes sign promptly when I does, > ie we can ignore the self inductance and capacitance of the gap. Also > by definition I^2.R applies, so it's not a case of one rather than the > other - its just that we have to accept that R is a function R(I). The characterization I gave is a crude first order one and not exact as Martin's work (amongst others) shows. Vcond is not entirely constant but is not linearly inversely proportional to I either. There is an asymptotic tendency in the curve as I increases. I agree one cannot ignore R as such since it is the only way to model a dissipative function. Inherently it is built into a VI consideration. I is of course a sinusoidal fn in a ringing circuit which makes R one as well. > A couple more questions, > > Recently Barry posted: > > > ...J.C.Martin in the book "J.C.Martin on Pulsed power" > > ... he gives the formula for spark gap impedance as > > > ((1.7 * L)/ r) + Z > > where L is the inductance of the spark channel, > > r is the length of the resistive phase, and > > Z is the impedance on Ohms of the circuit driving the spark gap. > > > ... he gives his famous formula for the resistive phase of spark > > formation as (88/(Z**(1/3) * F**(4/3))) * (rho/rho-zero)**(1/2) > > where the time is in nanoseconds, Z is the impedance driving the > > plasma channel in Ohms, F is the field along the chammel in units of > > 10 KV per centimeter, rho is the density of gas used, and rho_zero > > is the density of air at STP. Rho will change with bang rate. > > Let me guess that the resistive phase is a short period of constant > resistance during which the arc gets established. It looks to be on > the order of nanoseconds and is presumably relevant to fast pulse > discharges in accelerator and fusion supplies. I take it we can ignore > this resistive phase, since tesla gaps conduct for many tens of > microseconds? It is probably more appropriate to consider it when looking at the physics on sub-uS timescales. Since it doesn't really show up in the longer term smoothed waveforms and doesn't seem terribly relevant to the view one obtains at Fr where the circuit is highly selective I personally haven't bothered with it too much. Others may think otherwise. > I guess it ought to be relatively straightforward, given a > digital scope, to capture and store the V/I curves for a > range of gap lengths and widths. I take it they would come out > looking a bit like two diodes back to back in parallel? Are > the V/I curves a function of frequency too, or would one set of > curves do for all? Very much, although my expts with both zeners and anti-parallel diodes show linear envelopes only with specific starting voltages for a given LC circuit. In fact diode junction voltages follow a different law from a gap and I have seen both log and antilog envelopes generated by this means. > If such curves exist, are they 'square' enough so that a gap > can be reliably characterised by a 'forward voltage drop' which > is just a function of the gap dimensions and independent of > current? I wonder. Perhaps an active voltage source or sink used in place of the simpler devices might show this for sure. Could easily be tried. > It seems to me that such a set of curves would provide the > essential raw material from which an effective loss resistance > (ie an integrated loss per cycle divided by the mean square > current) could be established for a given gap. > > > My expts also suggest (and appear to be well supported by the > > experiences of others) that as one moves to the high L/C - high V > > regime, quenching type #2 (avoiding power ARCS) becomes more and > > more of a bugbear. John Freau is one excellent experimenter whose > > experiments with high L/C primaries have seen his efficiencies climb > > markedly. > > Thanks, was wondering about that. Is there a primary L/C > record holder I wonder? I've been thinking about rigging up > a high energy single shot primary, using a voltage multiplier > to accumulate about 60kV across the tank. Don't know. I seem to recall that voltages approaching 100kV have been tried but couldn't swear to it. Not by anyone I know anyway. Regards, malcolm
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.