Radiation in transition of charged particles through rough interfaces

A theory of transition radiation is presented for the rough interface having sufficiently sloping and smooth inhomogeneities with large curvature radius in each point of the surface. Characteristic size of roughness slowly varies over the distance of the emitted quantum wavelength. The advantage of this method is that no limitation is imposed on the dielectric constants of media. The general case of an interface with two-dimensional roughness is considered. The physical picture of the radiation from a rough surface is determined by both longitudinal and transverse effects. Angular and spectral distribution of the intensity are obtained under penetration of a charge into the target at arbitrary angle, both for the forward and backward radiation. For periodically distributed roughness, specific examples of expansion coefficients are considered, characterizing the type of surface. For random surfaces, statistical parameters of the radiation field are found (averaged over the ensemble of surfaces). Particularly, for the two-dimensional Gaussian distribution of roughness, the average intensity of radiation is obtained. All our expressions transform into known ones when the interface is plane. Numerical calculations were carried out whose results agree with experimental data. The research is practically important, since its results may be used for diagnostics of surfaces.