Spontaneous Smith-Purcell radiation described through induced surface currents

Abstract

An analytic solution for the radiated intensity distribution produced by an electron beam passing over a metallic diffraction grating (the Smith-Purcell effect) is derived. The approach is based upon an expression for the current traveling over the grating surface and the method can deal with arbitrary grating profiles. Although collective behavior in the electron beam is neglected, very high power density is predicted if high energy, short electron bunches are employed. The electron beam characteristics of various accelerators are used to illustrate the potential of high energy, accelerator based Smith-Purcell radiation sources.