Coherent X-ray radiation generated by a beam of relativistic electrons in a single crystal under conditions of multiple scattering

The dynamic theory of the coherent X-ray radiation of a divergent beam of relativistic electrons generated in a single-crystal wafer under conditions of the multiple scattering of incident particles is developed. Radiation cross sections are averaged over the divergent beam of rectilinear trajectories of electrons. Expressions describing the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation under conditions of multiple scattering are obtained. Conditions under which the contribution of diffracted brehmsstrahlung can be disregarded are shown, and the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation are calculated numerically for such conditions.