Longitudinal Modes in Magnetized Nonuniform Plasma Columns

Abstract

Certain resonant frequencies of magnetized cylindrical plasma columns were calculated using the theory of Buchsbaum and Hasegawa as well as an improved theory that takes into account the ambipolar electric field and the anisotropy of the electron velocity distribution. Attention is restricted to longitudinal modes with no propagation along the column axis and with frequencies near the second harmonic of the electron cyclotron frequency. For azimuthally symmetric modes (and for analogous planar models), the resonant frequencies calculated numerically using these two theories differ little; both theories agree with experiment to within the experimental uncertainties. Modes that are not azimuthally symmetric are described by a fourth-order differential equation that has not been solved exactly. An approximate perturbation theory treatment we have carried out suggests that the true eigenfrequencies are close to those obtained from a much simpler second-order equation.