Re: Spheres vs Toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

Actually, the problem's not as complex as all that...

1) This has been studied quite a bit in the context of Rod gaps and EHV
breakdown where the fields are non-uniform.
2) Once the streamer has any sort of length to it, it starts to look just
like a wire (a crooked one, but small in diameter), with the fields easy to
approximate.

A more tricky aspect is that you can't just ignore all the dynamic effects,
since they greatly affect streamer growth. In particular, the issue of
successive bangs growing along the same channel.  The EHV literature is more
concentrated on single pulses representative of lightning or switching
transients.  One also has to deal with the effects of convection/wind


----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Monday, November 03, 2003 6:32 AM
Subject: Re: Spheres vs Toroids


 > Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk>
 >
 > Hi All,
 >
 > Thanks for everybody's comments.
 >
 > I'll continue this opportunity to plug the thesis that
 > the topload should be treated as the most important
 > component of the system, and that it should be chosen to
 > give a good 'throw' to the streamers. Then the rest
 > of the TC is designed to support the chosen topload in
 > that role.
 >
 > As far as the issue of controlling the field gradient around
 > the top of the secondary is concerned, I think that's a
 > comparatively trivial matter.
 >
 > If a topload chosen for best breakout field happens not to
 > give good control to the top of the secondary, you can always
 > fit a small corona-ring type toroid specifically for this,
 > and this accessory would not significantly alter the field
 > in the breakout region around the main toroid.
 >
 > John Couture wrote:
 >  > Whether you start with the toroid or the TC you will still
 >  > be confronted with those difficult to coordinate E-fields
 >  > that were mostly left out in the past discussions.
 >
 > Yes, and until we make that confrontation I don't think we'll
 > make much progress in putting up a theoretical basis for
 > optimum topload shape and size.
 >
 > Spheres and toroids are the convention, but maybe some other
 > shape is best for putting out long streamers.  Maybe an
 > inverted cone with rounded edges, or some such...
 >
 > I think it would be quite interesting to examine a wide
 > variety of topload shapes to see which offers the best
 > field for streamer formation.  For each shape we would
 >
 >   a) compute the location of the breakout point - easy.
 >   b) compute the path that a streamer would most likely
 >      follow - harder but do-able.
 >
 > (Remember, for now we can forget issues of coil, Fres,
 >   BPS, etc at this stage and just consider a static field.)
 >
 > Note that we're not trying to say how far the streamers
 > would actually develop along that path in a given case -
 > the suggestion is merely to predict the path they are
 > likely to follow given that they have enough umph behind
 > them.  I need to talk more about 'umph' later...
 >
 > We might find that neither sphere, spheroid, or toroid
 > is the best shape, and something more exotic would be
 > better.
 >
 > I should say that finding such an optimum shape would not
 > likely make a vast improvement on current performance
 > of toroids, which may well already be around optimum.
 > The fact is, once you get a reasonable distance away
 > from the terminal, the field becomes much the same
 > regardless of what shape the terminal is.
 >
 > But it can do no harm to explore theoretically what
 > shapes might give the best start to the streamers. We
 > already know from experience that toroids do better
 > than spheres in this respect, so there is definately
 > something in the shape to be optimised.
 >
 > Oh, I seem to be talking myself into another of those
 > number crunching sessions...
 > --
 > Paul Nicholson
 > --
 >
 >