Start current of dielectric-loaded grating in Smith-Purcell radiation

Abstract

In this paper, a three-dimensional dielectric loaded grating (DLG) is proposed for the Smith-Purcell (SP) device. Taking into the considerations of thickness and width of electron beam, the dispersion equation is derived by using field matches method. The complex frequency is obtained by the numerical solution of dispersion equation, in which the imaginary part represents linear growth rate. The impacts of the electron beam filling factor (EBFF) on growth rate are discussed under the condition that the beam current and beam current density are kept as constants, respectively. In addition, the start current for SP oscillator is obtained by using the dispersion relation combined with boundary conditions. The relationship between the start current and other parameters is discussed and compared with the conventional metal grating. The results show that with the increasing of EBFF, the peak growth rate increases rapidly firstly and then decreases slowly, in which the current and current density are kept as constants, respectively. For the SP oscillator, the start current is increased with the shifting up beam voltage, but it is decreased with the improved EBFF, and only it has a slightly increasing trend when EBFF is close to 1. In addition, the start current is decreased with the increasing of relative dielectric constant, which indicates that by introducing DLG, the start current can be effectively reduced. Theoretical results are in good agreement with that of the simulations.