Dielectric properties of an inhomogeneous plasma

Abstract

An expression is derived for the specific-inductive-capacitance tensor of an inhomogeneous plasma contained by a constant magnetic field. In calculating the tensor, attention is directed mainly to a calculation of the effects associated with drift movements of the plasma particles, effects which are important for waves with a very small phase velocity (that is, of the same order as the velocity of the drift movements). It is suggested that a calculation of the tensor, once and for all, would be highly useful for calculating the oscillations and the stability of an inhomogeneous plasma as one would then only have to solve Maxwell's equations; a solution of the charge-movement equations for each separate case would be avoided. The dielectric tensor is' calculated for a plasma in "plane geometry"; in other words, the lines of force of the magnetic field are assumed to be straight and parallel to one another. An imaginary gravitational field is introduced in order to obtain a qualitative evaluation of the curvature of the lines of force. It is assumed that the equilibriumvalue gradients and the gravitational field are sufficiently small and perpendicular to the magnetic field. The oscillation frequency is considered to be large compared with particle-collision frequency.