Wave dispersion theory in a plasma column bounded by a cylindrical waveguide

Abstract

A unified theory of the electromagnetic wave propagation in a plasma column immersed in an axial magnetic field is developed, including the important influence of finite geometrical effects on wave dispersion properties. The analysis is carried out within the framework of a macroscopic cold fluid model. Coupled eigenvalue equations for the electromagnetic perturbations are obtained for an arbitrary density profile. For a flat-top density, a closed algebraic dispersion relation of the electromagnetic wave is obtained without any prior approximation. This transcendental dispersion relation is analytically solved in special cases of (a) uniform plasma, (b) infinite magnetic field, (c) zero magnetic field, (d) electrostatic perturbations, and (e) the low-frequency whistlerlike mode. In order to demonstrate the important influence of finite geometrical effects, the low-frequency whistlerlike mode is rigorously investigated for axisymmetric waves in a completely filled waveguide. From the analysis, it is shown that the whistlerlike mode propagates in the axial direction only when the total electron line density exceeds a critical line density. Moreover, the conventional dispersion relation of the low-frequency whistler mode is recovered only for a large plasma radius. Otherwise, the plasma geometrical effects play a pivotal role in wave propagation.