Newsgroups: sci.physics.plasma
From news@CUBoulder.Colorado.EDU Fri Jan 20 22:04:33 1995
From: fcrary@rintintin.Colorado.EDU (Frank Crary)
Organization: University of Colorado, Boulder
Subject: Re: plasma dispersion function

In article <3fgjj6$bma@mojo.eng.umd.edu>,
Roque Donizete de Oliveira <oliveria@down.engin.umich.edu> wrote:
>I have a question regarding the numerical solution of plasma dispersion
>equations...

>I have a code that solves the local dispersion equation D(k,omega,z) = 0
>where z is the axial position, for an electron distribution that
>is made up of a Maxwellian in speed and a Gaussian pitch angle, like
> f(v,theta) ~ exp(-v^2/a^2) * exp( -(theta - b)^2/c^2)

I'm afraid I don't have any answers to your problem. (At least
not at the moment.) But I am curious how such a distribution
function could be produced. At first glance, I would expect
that this distribution would be extremely unstable (assuming
b and c were of the same order of magnitude.) The "loss
cone" instability ought to rapidly scatter particles into
the angles, theta < b, and I would expect some other
instability I've never heard of would also scatter them
into angles, theta > b. I'm used to the distribution
if b=0 and c >> 1. This is what you get from a plasma
produced by "pick-up" particles, initially ionized with a
large velocity across the magnetic field, but which have
had a short time to settle into a more stable, bi-Maxwellian
distribution, on the way to becoming a isotropic Maxwellian.
But the case you refer to seems to be much more unstable. I'm
very curious to find out what circumstances would actually
produce this.

Frank Crary
CU Boulder