Linear analysis of a backward wave oscillator with triangular corrugated slow wave structure

Abstract

In this work, a backward wave oscillator (BWO) with triangularly corrugated periodic metallic slow wave structure (TrCSWS) driven by an infinitely thin annular electron beam is studied using linear theory. The electron beam is assumed to be guided by a strong magnetic field. The triangular axial profile of the SWS is approximated by a Fourier series in order to apply the linear Rayleigh-Fourier (R-F) theory that has long been used in the theoretical analysis of BWOs with sinusoidally corrugated SWS (SCSWS). The dispersion equation for various beam parameters has been solved and the temporal growth rate (TGR) of the electromagnetic wave for the fundamental $ TM_{01}$ mode is calculated numerically. The TGR values for different beam parameters have been compared with those of the BWO with SCSWS, semi-circularly corrugated SWS (SCCSWS) and trapezoidally corrugated SWS (TCSWS). In order to compare the TGR values, the amplitude of corrugation of the TrCSWS is varied so that its dispersion curve of $ TM_{01}$ mode almost coincides with that of the SCSWS and TCSWS. The study reveals that the performance (in terms of TGR) of the proposed BWO with TrCSWS is comparable to that of other BWOs with SCSWS and TCSWS for the same set of beam parameters and it provides significantly better performance than SCCSWS. So, the proposed TrCSWS that can easily be constructed may replace SCSWS, SCCSWS or TCSWS as their viable alternative.