Numerical Study of the Dispersion Properties of an X-band Backward Wave Oscillator with Rectangularly Rippled Wall Resonator

Abstract

Backward Wave Oscillators (BWOs) are devices that transform the electron beam energy into electromagnetic radiation at microwave frequencies. O-type BWOs consist of an axial electron beam propagating through a resonant cavity comprising of a slow wave structure (SWS). The electron beam is guided by a strong magnetic field while propagating through the cavity. The SWSs are used in BWOs in order to slow down the phase velocity of the electromagnetic wave so that the electron beam can resonantly interact with the wave which is the prerequisite of microwave generation. Dielectric loaded periodic structures were used as SWSs during the early stage of development of BWOs. However, this method of slowing down the wave suffers from dielectric breakdown as it cannot support high electric field. In order to prevent the dielectric breakdown, periodically corrugated metallic hollow waveguides are now being used as SWSs in BWOs. The sinusoidally corrugated SWS (SCSWS) has received the greatest attention among different corrugation profile. However, the fabrication process of this profile is complex and requires sophisticated tools. In an attempt to mitigate the fabrication problem, SWSs with simpler geometry have been proposed by the researchers. In this work, an earlier work on rectangularly corrugated SWS (RCSWS), which was investigated for non-relativistic electron beam has been extended for relativistic BWO in the X-band frequency range. The dispersion properties and the temporal growth rate of the axisymmetric transverse magnetic (TM) modes of have been analyzed numerically. In order to avoid the complicated boundary condition at the discontinuous boundaries of the rectangular radial profile, Fourier series has been used to approximate the axial profile of the SWS and the linear Rayleigh-Fourier theory has been utilized to determine the dispersion properties. The study shows that the growth rate of microwave for the RCSWS is somewhat lower than that for the case of SCSWS; however, a design tradeoff can be made to obtain a comparable performance.