Smith-Purcell radiation from a line charge moving parallel to a reflection grating with rectangular profile

Abstract

A rigorous solution is obtained for the problem of radiation from an electric line charge that moves, at a constant speed, parallel to an electrically perfectly conducting grating with a rectangular profile. Through the method of separation of variables, which is performed separately in the region containing the grooves and the half-space above the grating, the solution of the wave equation is obtained. By imposing the continuity condition at the open end of the grooves, and the boundary condition at the remaining part of the interface, an infinite system of linear algebraic equations for either the amplitudes of the scattered waves or the amplitudes of the groove modes are derived. Numerical results pertaining to the radiation intensities are presented.