Temporal Growth Study in Trapezoidally Corrugated Slow-Wave Structure for Backward-Wave Oscillator

Abstract

The temporal growth rate (TGR) in a trapezoidally corrugated slow-wave structure for a backward-wave oscillator is theoretically studied. An intense relativistic annular electron is used as the energy source for the device. The annular electron beam is assumed to be infinitesimally thin in the radial extent and guided by an infinitely strong magnetic field. The trapezoidal profile of the structure is approximated by a sinusoidal function using Fourier approximation, and the dispersion relation of the system is derived using the Rayleigh–Fourier method. To study the TGR of the electromagnetic wave inside the system, the dispersion equation is solved for different values of the beam parameters. The dimensions of sinusoidally corrugated comparable trapezoidal structure are determined by comparing their dispersion characteristics. For the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm TM}_{01}$</tex></formula> mode, TGR of instability that gives a qualitative measure of the microwave generation is calculated. The peak TGR of the proposed structure is found to be on average 1.5% higher than that of the sinusoidally corrugated slow-wave structure for the same set of beam parameters. Apart from its improved growth rate, the proposed structure has an added advantage of easy fabrication.