On the theory of polarization radiation in media with sharp boundaries

Abstract

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity ɛ(ω) = ɛ′ + iɛ″ and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on the parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity (ɛ″ → ∞), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.