From: Paul
Date: Mon, 14 Oct 2002 18:54:41 +0100
Subject: Re: [TSSP] Top Voltage
Boris,
Please use as much repetition as you feel necessary in order
to enforce some clarity on the situation.
> prior to breakout Q~90 and when inital field reaches
> high enough value discharge starts,it lasts while
> lowering Q to about 32,and stops when voltage falls to
> about 63kv.After that Q recovers.
> Correct?
Yes, that's correct. There appears to be a step change
in the Q at around 350uS, about 13 cycles into the event.
>From a resonant peak of 2.3 amps, the current has decayed
to 0.6 amps peak, so that 7% of the stored energy remains
at this point. From an efficiency of 59%, that means we've
accounted for 7% of the lost 41%.
> Emin~28A(1 + 0.54/SQRT(Axr))
Terry's middle sphere is 1.72cm radius, so with A=1,
we have
Emin ~= 28 * (1 + 0.54/sqrt( 1.72))
~= 40 kV/cm
That translates to a topvolts of 135 kV, with the
measured breakout around 200kV.
I take it this formula describes a raising of the required
surface field due to field non-uniformity affecting the
corona formation process. Is it intended to apply to
what's effectively an isolated sphere?
One thing about the field around the low sphere (at which
we get ballpark agreement for breakout): it is likely to
be more uniform (ie the gradient doesn't fall off so steeply
as you move away from the sphere) than the field from
the same sphere elevated several inches above the protection
of the toroid. In this exposed position the gradient will
fall away quicker, ie it may be 40kV/cm near the surface, and
be only 10kV/cm a few mm away. Maybe this non-uniformity
holds off breakout by a factor of 2 in our case.
My breakout calculations involve the surface field only. Should
I try to calculate how quickly the field drops away as you move
away from the sphere? Perhaps this is the key. Maybe 26 or 30kV/cm
is not enough by itself, but also requires the field to be fairly
uniform in the space around the surface.
In cases where we know 30kV/cm applies, it is say between two
spheres, where the field within the gap is pretty uniform.
Note that this is not a space charge thing, it's a geometry
issue. If breakout 'constants' like 26kV/cm or 30kV/cm only
apply in cases where the field is pretty uniform (electrodes close)
then we are in business.
Perhaps we should recompute breakout thresholds using an average
field over a radial distance extending a few cm from the surface
of the terminal? In a uniform field, that would equal the existing
value. In a non-uniform field, it would predict a rather higher
breakout.
Well I'll have to go plot some fields now. I shall try to work
out how many radial cm I must average over in order to match
observed breakout for the high sphere.
Hope all that make sense!
--
Paul Nicholson,
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.