From: Paul
Date: Sun, 03 Nov 2002 05:39:24 +0000
Subject: Re: [TSSP] Top Voltage
Hi All,
During a busy week I've had just a little time to look at
the paper
> AUTHOR: Bondiou, A.; Gallimberti, I.
> TITLE: Theoretical modelling of the development of the positive
> spark in long gaps
> SOURCE: Journal of Physics D (Applied Physics), vol.27, no.6,
p. 1252-66
which Bert kindly provided for me.
At first glance, this paper provides a good starting point for
constructing a model of breakout. It provides a flow chart of
the modelling, along with the relevant equations for each step.
I thought I might have a bash at computing the first 'step'
of the model, which is to determine the streamer inception
voltage.
For streamer inception, the charge within the streamer head
must exceed a minimum stability charge. Below this minimum
charge, there is insufficient field around the head to cause
the head to extend by drawing further avalanches to it.
Above the minimum charge, streamer development progresses.
The first step is to compute this streamer stability charge
and the terminal voltage at which the streamer head exceeds
this minimum.
The formula given for the streamer head charge is an integral
over the active region which involves ionisation and attachment
coefficients (alpha and eta), or alternatively, by a simplified
model, coefficients (beta and mu) for energy loss and gain.
The paper refers to earlier work for the values of these
coefficients, as well as the stability charge Nstab (which is
a function of the background (geometric) field).
Bert, are any of these earlier papers available? If we
could calculate this, it would move us beyond the use of
a fixed field (eg 30kV/cm) as a threshold.
We need the ionisation and attachment coefficients, and
the streamer stability charge, all as functions of the field
strength. It isn't quite clear to me which of the earlier papers
actually provide these functions.
The paper gives an example of streamer onset using long rod-plane
gap, of 800kV. If I compute this using north/tssp 30kV/cm surface
field, the value is nearer 300kV. Hence a proper computation
of streamer onset may move us nearer to measured values.
--
Paul Nicholson,
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.