Dispersion relation for space-charge waves in a warm plasma-filled elliptical waveguide in an infinite axial magnetic field

Abstract

Aperfectly conducting elliptical cylinder filledwith a warm plasma and immersed in an infinite axial magnetic field is considered. Using Maxwell’s equations and dielectric tensor, a Mathieu differential equation for axial component of electric field is obtained. Considering the boundary conditions, dispersion relation for waves in a plasma of warm electrons and immobile ions, which fills an elliptical waveguide and it is under the action of infinite axial magnetic field are calculated. Furthermore, dispersion relation and scalar potential in the quasi-static approximation in a cold magnetized plasma elliptical waveguide is calculated.The obtained results are graphically presented.