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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