Radiation of a Bunch Crossing a Boundary between a Vacuum and Cold Magnetized Plasma in a Waveguide

We analyze the electromagnetic field of a small bunch that uniformly moves in a circular waveguide and transverses a boundary between an area filled up with cold magnetized electron plasma and a vacuum area. The magnetic field is supposed to be strong but finite so the perturbation technique can be applied. Two cases are studied in detail: the bunch is flying out of the plasma into a vacuum, and, inversely, the bunch is flying into the plasma out of the vacuum area of waveguide. The investigation of the waveguide mode components is performed analytically with methods of the complex variable function theory. The main peculiarities of the bunch radiation in such situations are revealed.