We have considered transient radiation of a charged particle that moves at a constant velocity perpendicularly to the axis of a regular waveguide filled with an anisotropic magnetodielectric medium. Wave equations and analytical expressions for transverse electric (ТЕ) and transverse magnetic (ТМ) fields in the waveguide have been found. Energies of transient radiation of the particle moving in a rectangular waveguide have been determined. We have obtained conditions of occurrence, the frequency, and the energy of Vavilov-Cherenkov radiation.

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