Minimizing Starting Current of Smith-Purcell Radiation by Grating Optimization Using Dispersion Relation

Smith-Purcell radiation (SPR) is generated when electrons travel close to a periodic grating [1]. The operating frequency of SPR changes with different grating parameters according to the cold-tube dispersion relation [2], [3] when the grating period is fixed. It was found 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 [3]. In this work, we demonstrate that the spatial growth rate of SPR calculated from the hot-tube dispersion relation has the same scaling dependence on the grating parameters as the starting current calculated from PIC simulations [3], [4]. Thus, we confirm that the spatial grow rate calculation using hot-tube dispersion relation can be used to predict the optimal grating parameters to minimize the starting current of SPR. This approach has a significantly reduced computation cost compared to direct PIC simulations. Both the cold-tube and hot-tube dispersion relations can be used in combination to minimize the starting current at a desired radiation frequency [4].