From: Bert Hickman
Date: Wed, 23 May 2001 23:26:02 -0500
Subject: Re: [TSSP] Genetic optimisation
Hi Paul, all, Paul wrote: > > Hi Bert, All, >> > If I've understood things right, the leader formation begins and > continues as long as this gradient can be maintained just ahead of the > leader. I guess the significant threshold involves meeting this value at > the surface of the smooth toroid and once a leader begins to form, its > sharp point will then ensure that the leader forms rapidly for quite > some distance - even though the 'background' field from the > topload would, by itself, fall below the 26kV/cm threshold only a little > way from the surface. Subject to the toroid having enough charge > available to support that formation. What stops the leader formation? > I guess either it hits earth or it runs out of charge - the toroid is > depleted and the 26kV/cm cannot be maintained at the tip? So a big > toroid would be reluctant to break out (modest surface gradient), but > it would throw a long streamer as soon as it did (lots of charge > available)? > You understand correctly. Once formed, a leader acts as a "lossy" extension of the toroid. Initial breakout occurs preferentially when the HV terminal is positively polarized. And, once an initial cathode-directed leader has formed, it's conductivity immediately begins to decrease, reducing the effective potential at the leader tip. This is due to ion recombination and channel cooling through thermal diffusion and radiation. High channel conductivity can only be maintained by passing additional displacement current into the leader capacitance and transfering additional charge into the streamers that fan outwards from the leader tip. A leader will continue to propagate only if the HV terminal voltage is increased sufficiently to overcome channel losses so as to maintain an E-field of at least 26 kV/cm at the leader tip. If the terminal voltage continues to rise at a sufficiently rapid rate, the leader will continue to advance (albeit in jumps). Leader propagation ceases as we approach peak terminal voltage and dv/dt approaches zero. Now if the terminal voltage begins to decline (as we pass the first positive voltage peak), channel current can now actually reverse direction as we begin to "pull" charge out of the region surrounding the leader tip, and as we discharge channel capacitance. While the resulting displacement current will not (usually) extend the leader, it does help maintain leader conductivity until we begin the NEXT positive half cycle. > I'm afraid I've got some more questions! > > > A long spark (>6 cm) is characterized by multiple avalanches in an > > evolutionary sequence: streamer flash(es) --> leader propagation > > (fed by groups of streamers) --> spark (if leader > bridges the gap). > > Can we assume that this whole sequence takes place in a timescale short > compared with an RF cycle - I suppose thats so because if not there > would be a bigger frequency dependence? > The timescale of a given "step" is much shorter than an RF cycle - in fact, multiple steps can occur on the way towards the peak positive voltage in a given RF cycle. While leader growth will preferentially occur on the rising half of positive half-cycles, displacement current heating (maintaining channel conductivity) will occur during both positive and negative cycles. > When the HT falls away, do things recombine and settle down sufficiently > that on the next half cycle there is no 'memory' of the previous half > cycle? There's certainly a "memory" effect between successive RF cycles, and also between "beats" (primary-secondary energy transfer cycles) due to displacement current heating. There's also ample empirical evidence of memory effects between successive "bangs" (at least in in disruptive systems running at breakrates of ~100 BPS or above). This may be due to residual imbalances in the space charge surrounding the toroid from the previous discharges, or preferential reignition of the "warm" path left by the previous leader's root. > > Ultimately what I'm fishing around for is some confidence that some > acceptable and realistic account can be taken of the breakout > thresholds, otherwise attempts at non-linear time domain modeling will > founder on that point. I feel as though we are on top of the technical > matter of computing the response and now, quite suddenly it seems, we > are up against this more difficult problem of finding a load conductance > function which provides an acceptable summary description of the > breakout dynamics. > > If I've got things right, then Terry should be able to calculate quite > easily the top voltage at which streamers should suddenly start to form, > and we might also be able to calculate an estimate of streamer length > too (as a function of topvolts). Given those two separate figures (or > functions) we would then have the choice of optimising for max topvolts > or max streamer length, using the same genetic software but with two > different merit functions. Sounds like a good starting point... BTW, some pictures showing the bright blue "glow" of collective streamer flashes and streamers extending beyond the tips of leaders can be seen in the excellent pictures taken by Mike Hammer and Sue Gaeta - check out: http://www.aquila.net/bert.hickman/photos/corona2.jpg http://www.aquila.net/bert.hickman/photos/P1300073.jpg > > Cheers, > -- > Paul Nicholson, > Manchester, UK. > -- Best regards, -- Bert -- -- Bert Hickman Stoneridge Engineering Email: bert.hickman@aquila.net Web Site: http://www.teslamania.com
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.