The work investigates the diffracted transition radiation of a relativistic electron crossing a single-crystal plate in the Bragg scattering geometry. Expressions are obtained that describe the spectral-angular density of diffracted transition radiation with and without the multiple scattering of the relativistic electron in a single-crystal plate taken into account. The influence of multiple scattering on the spectrum of diffracted transition radiation of the relativistic electron is shown.

The parametric X-rays and diffracted transition radiation of a beam of relativistic electrons crossing a target with a periodic layered structure in the Bragg scattering geometry are studied. The general case of asymmetric reflection of the electron field relative to the target surface is considered, i.e., the case when the target layers are located at an arbitrary angle to its surface. Expressions are obtained within the two-wave approximation of the dynamic theory of diffraction, which describe the angular densities of parametric X-rays and diffracted transition radiation and their interference. Numerical calculations of the angular densities of radiation are performed for various values of the target and electron-beam parameters. A dependence of the angular densities of parametric X-ray radiation and diffracted transition radiation on the divergence of the electron beam and relationship between the thicknesses of the periodic structure layers are demonstrated. With an increase in the electron energy, the dependence of the angular density of the diffracted transition radiation on the electron-beam divergence increases.

In this paper, we study the influence of multiple scattering of a relativistic electron on diffracted transition radiation (DTR), which arises when this particle crosses a single-crystal target in the Bragg scattering geometry. For this case we have obtained the expressions describing the angular density of DTR both with and without allowance for multiple scattering of the relativistic electron in the target. The paper shows that the multiple scattering leads to a significant increase in the DTR angular density at low energies of the electron.

Parametric X-ray radiation generated by a beam of relativistic electrons in a single-crystal wafer is studied in the Bragg geometry under conditions of multiple electron scattering at target atoms. Expressions are obtained that describe the spectral-angular and angular radiation density under conditions of multiple electron scattering. An increase in the influence of multiple scattering on the spectral-angular radiation density is demonstrated both with an increase in the target thickness and a decrease in the energy of relativistic electrons. It is shown that the asymmetry of the electron-field reflection relative to the target surface considerably affects the spectral-angular and angular densities of parametric X-ray radiation under the condition of strong multiple scattering.

A theory of coherent X-ray radiation generated by a beam of relativistic electrons in a single crystal in the direction close to the electron-beam axis is developed in the Laue scattering geometry. The theory takes into account asymmetry of the electron-field reflection with respect to the crystal surface and the electron-beam divergence. Expressions describing the spectral-angular densities of parametric X-ray radiation near the electron-velocity direction, of transition radiation, and their interference are obtained. The influence of the electron-beam divergence and asymmetry of the electron-field reflection with respect to the target surface on the spectral-angular radiation densities is studied.