Radiation of a Charge in a Waveguide with a Boundary between Two Dielectrics

We analyze the electromagnetic field of a charged particle moving uniformly and crossing a boundary between two homogenous dielectrics in a metal cylindrical waveguide. We make an analysis of exact expressions for components of waveguide modes with the methods of the complex variable function theory. An original algorithm for computation of the field components is presented as well. Two instances are investigated in detail: the particle is flying from vacuum into dielectric and from dielectric into vacuum. In the first case, Cherenkov radiation (so-called 'wakefield') is partially compensated with the free field. We demonstrate areas where the waveguide modes practically coincide with ones in the regular waveguide and areas where the boundary influence is principal. For the second case, we demonstrate the possibility of generation of large quasi monochromatic radiation (Cherenkov-transition radiation) in the vacuum region at certain conditions.