Solution of wave equations for a moving charge in the media with discontinued dielectric properties

Abstract

This chapter discusses the solution of wave equations for the moving elementary charge with non trivial boundary conditions and the radiation arising in this case is considered. The solution is based on the wave approach provides the adequate description of the phenomenon of transformation of an electromagnetic field of the moving charge at crossing the interface among media with different dielectric properties. The solution for an electromagnetic field a point charge for two media should satisfy two conditions: it should be the solution of corresponding system of Maxwell's equations for the given medium in the given time interval and coordinates, and should satisfy the exact boundary condition. The given problem represents a case of Maxwell's equations with discontinued boundary conditions and can be considered within the framework of the theory of functional solutions. The analysis of such an approach can be used for a wide class of problems on radiation. Use of the exact solution of wave equations gives the adequate description of transition radiation near a trajectory of movement of a charge that essentially develops the theory of transition radiation and opens opportunities of research of more thin effects, for example occurrence of coherent X-ray, surface transition waves.