Abstract
The paper is focused on a reliable modeling and analysis of the effects connected with the resonant transformation of the field of a plane density-modulated electron beam flying in vacuum over the periodic boundary of a natural or artificial medium. It turns out that the main role in the formation of non-standard responses of such a boundary to the corresponding excitation (and, in particular, in the realization of effects associated with an anomalously high intensity of Vavilov-Cherenkov and Smith-Purcell radiation generated in the medium and free space) is played by eigen surface waves of the boundary. The results of the theoretical study of such waves and the specification of the physical particularities of the fields caused by their excitation for the interface of so-called plasma-like medium make up the main content of this work.