Smith-Purcell radiation in the “pre-wave” zone

A model is proposed for calculating the angular distributions of the intensity of resonant diffraction radiation generated by a charged particle moving near a plane conducting periodic structure (Smith-Purcell radiation) with allowance for the effect of the so-called pre-wave zone. It is shown that the criterion of the location of a detector in the pre-wave zone for this kind of radiation in the relativistic case is determined by the geometric sizes of the grating and is almost independent of the Lorentz factor of the particle. The characteristics of the radiation in the pre-wave zone are calculated by numerical integration over the grating surface. It is shown that the line of Smith-Purcell radiation is broadened in this case, whereas the results of the calculations for the “wave” zone are in satisfactory agreement with the known analytical model of the resonant diffraction radiation.