Radiation of a charge intersecting the boundary between a homogeneous area and bilayer one in a circular waveguide

Abstract

The problem of the electromagnetic field of a charge moving along the cylindrical waveguide axis is considered. The charge flies from the homogeneously filled area to the area composed of a dielectric layer and a channel. The solution is performed by representing the electromagnetic field in each waveguide area as a sum of known “forced” field (the source field in an infinite regular waveguide) and a “free” field conditioned by the transverse boundary influence. The free field is written in the form of eigenfunction expansion for corresponding waveguide area. Shown that the problem is reduced to solving an infinite system of linear algebraic equations for the free field mode amplitude. Expressions for the components of the free field “cherenkov” part are obtained using the methods of complex variable theory. It is shown that there is a compensation effect between cherenkov part of the free filed and wakefield. It leads to the decreasing of the number of the “total Cherenkov field” modes with increasing distance from the charge. The generation area border for each cherenkov mode is determined by the its group velocity. The wakefield formation process is demonstrated using the original numerical algorithm. Refs 17. Figs 2.