Study on the Influence of Two Relativistic Circular Electron Beam Columns Placed in an Elliptical Dielectric Waveguide on Excitation and Amplification of Electromagnetic Waves Using Finite-Element Method

In this paper, the finite-element method (FEM) is applied for an exact solution of the dispersion of hybrid electromagnetic waves excited in a novel combined elliptical waveguide. This special configuration is included of an elliptical metallic waveguide filled with a dielectric material, whereas two axial hollows with circular cross section have been created in it. A hollow is placed in one of focuses of the elliptical waveguide and second hollow is located in another focus or shifted from it. Two straight relativistic electron beams with the same currents and velocities in opposite directions are injected inside the hollows. Here, we apply an accurate approach in which the electromagnetic fields described by the FEM and satisfies boundary conditions at the interfaces of different regions. Then, the time growth rate of slow waves amplified by the electron beam is numerically calculated. The excited waves are in microwave range. The effects of accelerating voltage and current density of electron beams, and geometrical parameters such as radius and location of electron beam, on the frequency spectra, the growth rate, and profiles of axial electric and magnetic fields of excited slow waves are studied. Our research shows, the novel waveguide studied in this paper is superior to other waveguide structures in wave amplification with applying minimum input electrical power.