Plasma-Filled Waveguide with Axial Magnetization. I. Variational Determination of Normal Modes

Abstract

Propagation coefficients and field configurations of the normal modes of an axially magnetized, plasma‐filled waveguide are treated by the Rayleigh‐Ritz variational technique. The results are placed in the form of a matrix eigenvalue problem. The eigenvalues are approximations to the propagation coefficients, and the eigenvectors contain Fourier coefficients of the electric fields of the normal modes expanded in terms of fundamental functions. This form is well suited to computer calculation and is used in a following paper to compute reflection and transmission coefficients of waveguide sections of finite length. The axially symmetric normal modes are examined in detail and are found to possess certain interesting properties that have not been fully recognized. First of all, these modes are reciprocal. Furthermore, under certain conditions they can, like ``helicon'' waves, be divided into ``ordinary'' (``cut off'') and ``extraordinary'' (``lossless'') modes. The axially symmetric modes are not circularly polarized, however, but instead change shape in a rather remarkable manner as they propagate.