Electrostatic Electron Oscillations in Cylindrical, Nonneutral Plasmas

The character and stability of electrostatic electron waves which propagate both parallel to B (wavenumber β) and perpendicular to B (azimuthal mode numberl) in nonneutral plasmas in cylindrical geometry are studied. The background ions are taken to be infinitely massive and so provide a partial neutralization of the unperturbed electron space charge; this neutralization ranges from the completely unneutralized electron plasma case to the more familiar case of a completely neutral plasma. It is found that the axisymmetric mode (l = 0) is stable for arbitrary radial density variation when the charge density is not too high. For l ≥ 1 and electron and ion densities constant out to r = a and zero beyond, the system is stable for all frequencies independent of the degree of neutralization and the location of a conducting outer wall. The dispersion relation is analogous to that for a neutral plasma permitting separate low- and high-frequency propagation bands. For low frequencies and low, nonincreasing electron, ion, and net charge densities, it is found that the presence of a resonant layer (zero frequency as seen by the electrons) within the electron cloud is necessary but not sufficient for instability. In general, finite axial wavenumber increases the tendency towards stability.