Newsgroups: sci.physics.plasma
From news@CUBoulder.Colorado.EDU Mon Jan 23 22:17:43 1995
From: fcrary@benji.Colorado.EDU (Frank Crary)
Organization: University of Colorado, Boulder
Subject: Re: plasma dispersion function

I'm sorry to be replying to myself, but...

In article <3g0ch3$ian@mojo.eng.umd.edu>,
Frank Crary <fcrary@rintintin.Colorado.EDU> wrote:
>>I have a question regarding the numerical solution of plasma dispersion
>>equations...
>>...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 am curious how such a distribution function could be produced...
>...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...

This should read b = pi, not b = 0. I guess I've been
spending too much time around planetary scientists,
where zero angle is the equator rather than the pole...
b=0 would be some sort of bulk flow, not a pick-up
distribution. Also, c >> 1 isn't exactly true.
This translated to an anisotropy of order unity. In
fact, anisotropies of order 10 have been observes
in relatively stable plasmas. What I really meant
to say was that this parameter, c, can't be
very much greater than 1, translating into an
anisotropy not much larger than 10. What I was really
curious about is how you could get a reasonably
stable distribution with a strong, maximum at
some pitch angle other than 0 (a flow or beam) or
pi (a pickup distribution.) I suppose I can imagine
particle-wave instabilities that would drive
such a thing, but I don't quite see how this
would be stable enough to produce a background
plasma with this feature.

Frank Crary
CU Boulder