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

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