Transverse Dielectric Tensor for a Free-Electron Gas in a Uniform Magnetic Field

Publisher Website
Google Scholar
Abstract
An elementary method of calculating that part of the tensor dielectric coefficient which determines the propagation of transverse electromagnetic radiation through a free‐electron gas in a uniform external magnetic field is presented. The method presented here is based on a particle‐orbit analysis and is somewhat analogous to a generalized version of the Kramers‐Heisenberg quantum theory of gaseous dispersion. It is shown that the elements of the transverse dielectric tensor can be obtained from a knowledge of the quantum‐mechanical transition probabilities for emission and absorption of photons (that is, from a knowledge of the Einstein A and B coefficients). The formal expression for the dielectric tensor thus obtained is shown to be valid for both the degenerate and the nondegenerate system of electrons. The dielectric tensor thus obtained is shown to reduce in the classical limit to the familiar results of the conventional classical hot plasma kinetic theory. The first quantum correction to the classical hot plasma dielectric tensor is explicitly given and it is shown that, under suitable conditions, this quantum correction will play a significant role in the analysis of the experimental studies of the electrodynamic behavior of ``classical electron‐hole plasmas'' in a uniform external magnetic field.