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Peculiarities of the Resonant Interaction of the Transition Radiation of a Charged Particle with a Bi-Periodically Modulated Medium in a Waveguide

In this article some aspects of the interaction of the transition radiation of a charged particle with bi-periodically modulated in space filling of a regular waveguide in the frequency region of “strong” (resonant) interaction between the transition radiation and periodically modulated filling are considered, provided that the modulation depths are small. In addition, it is assumed that the charged particle moves uniformly perpendicular to the axis of the waveguide of an arbitrary cross-section. The frequency and width of the frequency region of strong interaction are found. Analytical expressions are obtained for the energy losses of the charge on transition radiation with an accuracy up to terms proportional to the modulation depths. Conditions for the occurrence of Cerenkov radiation in the frequency region of the strong interaction are found in the case of rectangular waveguide.