Multi-species kinetic generalization of the Appleton–Hartree dispersion formula

Abstract

This paper calculates, on a kinetic basis, the dispersion relation and field polarization for waves propagating linearly through a homogeneous magnetoplasma when thermal velocities are far less than the phase velocity. Approximations are brought in only as necessary and their physical significance explained. The result is an improved derivation of the Sen–Wyller generalization of the Appleton–Hartree formula for velocity-dependent collision frequency. Further generalization to several charged species is made, and the dispersion relation is also considered in terms of the angle between the ambient magnetic field and the group (rather than phase) propagation direction. Special case reduction to the Appleton-Hartree formula is confirmed. Complications concerning the limit of weak spatial dispersion are discussed. The analysis is restricted to weakly ionized plasmas in which the charge to neutral particle mass ratios are small, collisions are weak, and the wave vector is predominantly real.