Newsgroups: sci.physics.plasma
From news@engin.umich.edu Thu Jan 19 21:18:01 1995
From: oliveria@down.engin.umich.edu (Roque Donizete de Oliveira)
Organization: University of Michigan Engineering, Ann Arbor
Subject: dispersion equation for cyclotron waves in magnetized plasma
Keywords: dispersion, plasma, waves

The plasma dispersion equation for cyclotron waves in a magnetic
field is usually (I haven't found another way)
derived for the initial value problem in which k (the wavenumber)
is assumed real and omega (the frequency) is complex.

If one then wants to consider boundary value problem (k complex and
omega real) one can use the same equation.

My question is: is this always right ?

Would that same dispersion equation (whose analytic continuation for
Im(omega) <= 0 is done via, say, the plasma dispersion function) be
valid for omega real and complex wavenumbers (I'm solving for k for
different values of omega) whose real and imaginary parts can be
either positive or negative ?

I can't understand how the same dispersion equation can be used
(that is what I've been lead to believe). I fail to see how the analytical
continuation of the plasma dispersion function Z(zeta) of Fried&Conte
for Im(zeta) <= 0 can cover all the possible ways one can approach
the real omega axis.

If anyone has an explanation for these doubts (most likely I'm wrong)
or knows of any reference where the dispersion equation (using
Maxwell-Boltzman equations) is derived with the boundary value problem
in mind please let me know.

Thanks.

Roque
oliveria@engin.umich.edu