The transition radiation in the anisotropic magneto dielectric plate in a waveguide at passing of a charged particle perpendicular to the waveguide axis

Properties of transition radiation of charged particle in anisotropic magneto dielectric plate in a regular waveguide are considered at passing of charged particle perpendicular to the waveguide axis. Describing the transverse-magnetic (TM) field in different regions of the waveguide with help of the longitudinal component of the electric filed the wave equations and the analytical expressions for TM filed in the waveguide are found. The energy of transition radiation of moving charged particle is calculated using the obtained analytical expressions for TM filed and Poynting vector. The properties of transition radiation in the case of rectangular waveguide are analyzed. An analytical expression for the energy of transition radiation in the case when in the waveguide is placed a thin anisotropic magneto dielectric plate is calculated too. The frequency at which it is possible the Vavilov-Cerenkov radiation is found. On the Vavilov-Cerenkov radiation indicates the appearance of a sharp peak in the spectrum of the transition radiation.