Study on the region of instable beam-wave interaction in a relativistic backward wave oscillator

A theoretical research was developed for relativistic backward wave oscillators (RBWO) composed of a thin annular electron beam guided by a strong magnetic field through a slow wave structure (SWS) consisting of a cylindrical waveguide with a sinusoidally varying wall radius. Firstly, the analytic expressions of dispersion relations were derived from Swegle's analytic theory of RBWO. Then one code written by Matlab was used to solve the dispersion equations. Through drawing contour lines in the complex plane, the whole dispersion curves of SWS with electron beams were obtained and detailed study on the region of instable beam-wave interaction was carried out. The microwave growth rate and energy efficiency were calculated too. The simulation results illustrate that this interaction, which