Conductivity Tensor and Dispersion Equation for a Plasma

Abstract

Periodic plane waves are considered in a plasma pervaded by a uniform magnetic field. The appropriate linearized Boltzmann equations for the distribution functions of the electrons and of each type of ion are solved exactly. Collisions are taken into account by the inclusion of a simplified collision term. The solutions are used to compute the electric current, from which the conductivity tensor of each ionic species is found. The total conductivity is then used in Maxwell's equations to determine the electromagnetic field, and this leads to the dispersion equation for plane waves. This equation is solved in various parameter ranges for the case of longitudinal waves when the conductivity of only one species is taken into account. The solutions of Landau, Gordeyev, Gross, Bernstein, and others are recovered when the collision frequency vanishes. In addition, various power series and asymptotic expansions for the conductivity tensor are given, and it is shown to reduce to that of the magneto‐ionic theory under suitable conditions. The Appendix contains a systematic study of a function which plays a central role in the theory.