Degenerate mixing of plasma waves on cold, magnetized single- species plasmas

In the cold-fluid dispersion relation ω = ω_p/[1+(k_⊥/k_z)^(2]1/2) for Trivelpiece-Gould waves on an infinitely long magnetized plasma cylinder, the transverse and axial wavenumbers appear only in the combination k_⊥/k_z. As a result, for any frequency ω<ω_p, there are infinitely many degenerate waves, all having the same value of k_⊥/k_z. On a cold finite-length plasma column, these degenerate waves reflect into one another at the ends; thus, each standing-wave normal mode of the bounded plasma is a mixture of many degenerate waves, not a single standing wave as is often assumed. A striking feature of the many-wave modes is that the short-wavelength waves often add constructively along resonance cones given by dz/dr = ±(ω_p^2/ω^2-1)^(1/2). Also, the presence of short wavelengths in the admixture for a predominantly long-wavelength mode enhances the viscous damping beyond what the single-wave approximation would predict. Here, numerical solutions are obtained for modes of a cylindrical plasma column with rounded ends. Exploiting the fact that the modes of a spheroidal plasma are known analytically (the Dubin modes), a perturbation analysis is used to investigate the mixing of low-order, nearly degenerate Dubin modes caused by small deformations of a plasma spheroid.