The dynamic theory of coherent X-ray radiation, excited in a periodic layered medium by a divergent beam of relativistic electrons in the Bragg scattering geometry, is developed. In framework of the two-wave approximation of the dynamic theory of diffraction, expressions describing the spectral-angular and angular distributions of parametric X-ray radiation (PXR) and diffracted transition radiation (DTR) are obtained taking into account the multiple scattering of the relativistic electrons by the atoms of the target. Based on the expressions obtained, the possibilities of the manifestation of the effects of dynamical diffraction in coherent X-rays were investigated. The influence of the asymmetry of the electron Coulomb field reflection with respect to the target surface (the reflecting layers situate nonparallel to target surface) on the spectral-angular characteristics of the PXR and the DTR under conditions of the electron multiple scattering is estimated. It is shown that at a fixed Bragg angle the width of the PXR spectrum increases when the angle of incidence of the electron on the target decreases, which leads to an increase in the PXR angular density. In the same conditions the width of the frequency domain of total external reflection and the amplitude of the DTR spectrum also increase, which leads to a significant increase in the angular density of the DTR. The obtained analytical expressions can be used to determine the optimal parameters of the experiment on confirmation of the predicted dynamic effects.

中文翻译：

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由层状周期结构中的相对论电子束激发的相干 X 射线辐射

发展了相干 X 射线辐射的动力学理论，在周期性分层介质中由布拉格散射几何中的相对论电子发散束激发。在衍射动力学理论的两波近似的框架内，考虑到参数 X 射线辐射 (PXR) 和衍射跃迁辐射 (DTR) 的光谱角和角分布的表达式，目标原子的相对论电子。基于得到的表达式，研究了相干X射线中动态衍射效应表现的可能性。估计电子库仑场反射相对于目标表面（反射层与目标表面不平行）的不对称性对电子多重散射条件下 PXR 和 DTR 的光谱角特性的影响。结果表明，在固定的布拉格角下，当电子在靶上的入射角减小时，PXR 谱的宽度增加，从而导致 PXR 角密度增加。在相同条件下，外全反射频域宽度和DTR频谱幅度也增加，导致DTR角密度显着增加。