Smith-Purcell radiation in the high conductivity and plasma frequency limits

Radiation is calculated from currents produced by a nonrelativistic point charge that moves at a constant velocity above a conducting grating. Two different limits are considered. In the high conductivity limit, the surface charge is calculated from a nonretarded image charge, surface currents from the continuity equation, and the far field vector potential from the surface current. In the plasma frequency limit of the grating substrate a nonretarded electric potential is calculated from a two-region problem, bulk current from an interior potential, and the far field vector potential from the bulk current.