The paper is focused on reliable modeling of the effects associated with the resonant transformation of the field of a plane, density modulated electron beam, flying over the periodically uneven boundary of a natural or artificial medium, in the field of volume outgoing waves. Here, the general information (analytical basis) is presented on the peculiarities and principal characteristics of electromagnetic fields arising in the situations under consideration, on the procedures for regularization of model boundary value problems describing these situations, and on possible eigenmodes of periodic structures. Without relying on this information, it is impossible to advance considerably effectively in solving numerous urgent physical problems(establishing the conditions providing anomalously high levels of Vavilov-Cherenkov and/or Smith-Purcell radiation; diagnostics of beams of charged particles, artificial materials and media) and in practical implementation of new knowledge aboutthe effects of diffraction radiation and their wave analogues in new devices and instruments of optoelectronics, high-power electronics, antenna, and accelerator technology.
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