Radiation on a semi-infinite plate and the Smith-Purcell effect in the X-ray range

Abstract

Smith-Purcell radiation is usually detected at the motion of an electron above a grating of metal strips. However, for high frequencies (exceeding the plasma frequency of the grating material) no substance can be considered a conductor, but instead should be considered a dielectric with plasma-type permeability. Therefore, new approaches are required to describe the Smith-Purcell radiation in the high frequency range. In this article a previously developed variant of eikonal approximation is applied for description of the radiation on a set of parallel semi-infinite plates. The derived equations describe the radiation generated both by the particles passing across the plates (usually referred to as “transition radiation”) and by the particles traveling above the grating formed by the edges of the plates (usually referred to as “diffraction radiation,” or, taking into account the periodicity of the grating, as the Smith-Purcell radiation).