Oscillations of a Plasma in a Static Magnetic Field

Abstract

We consider the propagation of waves through an infinite homogeneous plasma permeated by a static magnetic field. The Boltzmann equation is linearized by the usual perturbation method and the distribution function obtained in the form of an integral. From the expression for the distribution function we calculate the current density, which on insertion into Maxwell's equations gives the dielectric tensor relating the components of the displacement to those of the electric field. Explicit expressions are given for the components of the dielectric tensor in the particular case when the mean Larmor radius of the particles is considerably less than the wavelength of the oscillation and the wave velocity considerably greater than the mean thermal velocity of the particles. Under these conditions, the change in the wave velocity due to thermal effects is calculated by means of an eigenvalue method which uses the wave velocity in the absence of thermal effects and the dielectric tensor we have calculated.