The Use of Mathematical Finite Element Method to find the Optimum Waves Amplification by a Novel Elliptical Waveguide

In this paper, a combinatorial elliptic-circular waveguide is introduced to amplify electromagnetic waves. The cross-section of this waveguide is elliptic and filled by a dielectric medium; while two axial circular cavities have been created in it, just outside the center. A cavity has been filled by an unmagne- tized cold plasma and a relativistic pencil electron beam(RPEB) is injected in other cavity. By applying an adaptive finite element method(FEM), elec- tromagnetic slow waves amplification in the waveguide is investigated. We study variations of growth rate of excited microwaves under influence of dif- ferent factors. The purpose of examining the effect of various parameters of this waveguide such as plasma and electron beam radiuses, the RPEB location, dielectric constant and beam current intensity; is to introduce the waveguide with optimal configuration and parameters to obtain the highest wave growth rate.