Potentials and Fields of Space-Charge Waves in the Coaxial Elliptical Waveguide Consisting of An Annular Plasma in the Presence of An Axial Magnetic Field

In the present paper, the propagation of space-charge waves through elliptical plasma waveguide in an axial magnetic field is investigated. First we consider a metallic coaxial waveguide with an elliptical cross section including an annular vacuum-plasma-vacuum and then an elliptical plasma waveguide is considered. In the electrostatic approximation, by using the Poisson, continuity and momentum equations and so applying boundary conditions, dispersion relations of the waves are derived. The potentials, the components of the electric fields, the electron density, and electron velocity components in terms of Mathieu functions are introduced. The results of the numerical study and the discussion are presented as well.