From: Paul
Date: Thu, 16 May 2002 18:08:38 +0100
Subject: Re: [TSSP] Topload breakout potentials
Looking at http://www.abelian.demon.co.uk/tssp/cmod/ we might have some hope of predicting the total amount of streamers, as a product of average streamer length times the number of streamers. But now I'm wondering how the coil decides whether to turn say 12 streamer-feet worth of surplus charge into 3 streamers of 4 foot, or 24 streamers of 6 inches, etc. As a hypothesis, consider the following: As the voltage rises over an RF quarter-cycle, and the surface field approaches 26kV/cm, electron avalanches will begin to occur here and there over the topload surface. Given suitable conditions, whichever of those initial avalanches that happens to be the strongest will draw charge away from the other proto-streamers and will be the only one to develop. The suitable condition I suppose is that the speed of signal propagation across the topload surface is such that each proto- streamer has time to become 'aware' of the presence of the others. If the RF rise time is fast enough, the initial avalanches will have time to develop independently of the others because news of each others existence hasn't had time to propagate across the whole topload. In these circumstances, many short streamers will form. With a relatively slow RF rise, the streamers have time to become aware of each other, and therefore have the opportunity to compete and to evolve a single or just a few dominant streamers. One deciding factor therefore, is the ratio of the duration of an RF quarter cycle to the propagation delay over the topload surface. The latter will be of order d/c, where d is a linear size of the topload, say PI times the outer radius, and c is the velocity of light. In general we would expect lower frequency coils to develop fewer but longer streamers compared to the same topload at the higher frequency. For Johns two toploads we have: 13"x4": Risetime = 1.3uS, propagation time = 1.7nS, ratio = 1.3 24"x6": Risetime = 1.7uS, propagation time = 3.2nS, ratio = 1.9 where I've absorbed a factor of 1000 in the ratio. Since the larger topload appears to have a higher topload propagation ratio than the smaller, we might expect the breakout in the larger topload to be more concentrated into fewer streamers than with the smaller topload. So far, that agrees with observation of the two toploads. For Marc's coil, we have 30.5"x6.5": Risetime = 6.5uS, propagation time = 4.1nS, ratio = 0.6 and for Bart's coil: 30"x9": Risetime = 3.6uS, propagation time = 4.1nS, ratio = 1.1 Gathering these together in order of ratio gives: Marc 30.5"x6.5": ratio = 0.6, multiple streamers Bart 30"x9": ratio = 1.1, multiple streamers. John 13"x4": ratio = 1.3, 2 or 3 simultaneous streamers John 24"x6": ratio = 1.9, only one streamer in which the ratio does seem to follow the progression. The factor that I've not allowed for in the above simplistic analysis is the fraction of the RF quarter-cycle over which the streamers can negotiate for charge. This period doesn't begin until 26kV/cm is reached, so only a fraction of the quarter cycle is involved. If the surface gradient was trying to rise to x kV/cm then the period involved is a fraction arccos(26/x)/PI of the quarter-cycle. Recalculating the ratios using this reduced risetime gives: Marc 30.5"x6.5": ratio = 0.9, multiple streamers John 13"x4": ratio = 2.4, 2 or 3 simultaneous streamers John 24"x6": ratio = 6.1, only one streamer (can't do this ratio for Bart's because it's not supposed to be breaking out! arccos(26/16.8) is undefined!). So the larger the ratio, the greater the chance that multiple initial avalanches will be able to communicate and evolve into just a single winning streamer. A low ratio isolates the initial avalanches from one another so that they all develop into a large number of smaller streamers. If I can think of a good name for this ratio, I'll add it to the web page. -- Paul Nicholson, --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.