Grating Optimization for Smith–Purcell Radiation: Direct Correlation Between Spatial Growth Rate and Starting Current

Abstract

Smith–Purcell radiation (SPR) is generated when electrons travel close to a metallic periodic grating. It was found that the starting current of SPR varies by orders of magnitude by simply varying the grating parameters (groove’s heights and widths) while keeping the grating period and the electron beam properties fixed. In this article, we demonstrate that this strong dependence of starting current on the grating parameters is directly related to the spatial growth rate of the SPR. Using the hot-tube dispersion relation, we optimize the grating parameters to minimize the starting current to excite coherent SPR.