Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation

This paper presents a study of coherent and superradiant Smith-Purcell (SP) radiation with the help of a two-dimensional particle-in-cell (PIC) simulation. The simulation model supposes a rectangular grating with period length of $173\text{ }\ensuremath{\mu}\mathrm{m}$ to be driven by a single electron bunch, a train of periodic bunches and a continuous beam, respectively. We chose 40 keV as the initial energy of electrons and therefore the SP radiation frequency falls in the THz regime. From our single bunch simulation we distinguish the true SP radiation separated in time from the emission of the evanescent wave. The evanescent wave radiates from both ends of the grating and is characterized by an angle independent frequency lower than the minimum allowed SP frequency. In order to avoid the buildup of beam bunching from an initially continuous beam, we use a train of periodic bunches to excite the grating and observe the superradiant phenomenon. The repetition frequency of the spatially periodic bunches is assumed to be 300 GHz. We find that the superradiant radiation is only emitted at higher harmonics of this frequency and at the corresponding SP angles. This result conforms to the viewpoint of Andrews and co-workers. The simulation with a continuous beam shows the dependence of the output power on the beam current. The power curve shows two regimes, one for the incoherent SP radiation and the other for the superradiance, which resembles the Dartmouth experimental result. And furthermore, the frequency spectrum shows an apparent difference for the two regimes, which is in contrast to the observations of Urata and co-workers.