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 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.
A sidewall grating for the Smith-Purcell device is proposed to enhance the coupling of the optical mode with the electron beam and, consequently, relax the stringent requirements to the electron beam. With the help of three-dimensional particle-in-cell simulations, it has been shown that, comparing with the general grating, the usage of a sidewall grating improves the growth rate and dramatically shortens the time for the device to reach saturation. It is also found that the sidewall grating holds the potential to reduce the start current for the operation of a Smith-Purcell backward wave oscillator.
A simulation of coherent and super-radiant Smith-Purcell radiation is performed in the gigahertz regime using a three-dimensional particle-in-cell code. The simulation model supposes a rectangular grating to be driven by a single electron bunch and a train of periodic bunches, respectively. The true Smith-Purcell radiation is distinguished from the evanescent wave, which has an angle independent frequency lower than the minimum allowed Smith-Purcell frequency. We also find that the super-radiant radiations excited by periodic bunches are emitted at higher harmonics of the bunching frequency and at the corresponding Smith-Purcell angles.
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