Comparison of Smith-Purcell radiation models and criteria for their verification

The paper presents the analysis of the angular distributions of the incoherent Smith-Purcell radiation (SPR) generated by a charged particle passing over a periodic conducting structure (grating). The calculations were carried out for a grating which consists of conducting strips separated by vacuum gaps and a lamellar grating with the use of three models of this radiation: van den Berg`s model, the surface current model, and the resonant diffraction radiation model. The two last models predict sufficiently close results for different geometries, while the results obtained with van den Berg`s model predict primarily the SPR intensity which is by a few orders of magnitude lower for the electron energy ≈6 MeV. The authors propose simple criteria to verify the SPR models by comparing the SPR yields between the volume (with the thickness comparable with a grating period) and flat (with the thickness which is much less than that of a period) gratings; by comparing the azimuth dependencies of the SPR intensities from the flat gratings; by comparing the dependencies of the SPR intensity on the Lorentz factor of a particle.