Smith–Purcell Radiation with Three-Dimensional Simulation

Abstract

An investigation of Smith–Purcell radiation is carried out with a three-dimensional particle-in-cell simulation. The simulation model consists of a rectangular grating with limited length and width, which is driven by a single electron bunch, a train of periodic bunches, and a continuous beam. Smith–Purcell radiation is observed and distinguished from an evanescent wave, which travels near the surface of the grating. We found that the evanescent wave has a frequency lower than the allowed minimum Smith–Purcell frequency, and does not radiate until it reaches the ends of the grating. It is also shown that superradiant radiation can be excited by periodic electron bunches. With the present parameters, superradiant radiations are emitted at higher harmonics of the bunch frequency and at corresponding Smith–Purcell angles. The initially continuous beam can be bunched by the interaction with the evanescent wave when the beam current is above a certain threshold, and consequently induces the superradiant Smith–Purcell radiation. The threshold current is derived as well.