Coherent X-ray emission from relativistic electrons in a three-layer target

In this paper, a coherent X-ray radiation of relativistic electrons in a composite target is developed. The composite target consists of two amorphous layers and one layer having a structure of a periodic layered medium with three different layers per period, located at a given angle relative to the target surface. The paper considers coherent X-ray radiation behind the rear surface of a target, i.e. radiation in a periodic layered medium, in the Laue scattering geometry. Within the framework of the two-wave approximation of the dynamic theory of X-ray diffraction in a periodic layered medium, expressions are obtained that describe the amplitudes of parametric X-ray radiation and diffracted transition radiation. Then, the case when the second layer is a vacuum is considered. Expressions are obtained that describe the spectral-angular and angular densities of PXR, DTR and their interference. The possibility of significantly increasing the spectral-angular density of DTR due to the total contribution to it of transition radiation waves from the amorphous layer, the front boundary of the periodic layered structure and their constructive interference is shown. The possibility of increasing the spectral-angular and angular densities of DTR due to the choice of the asymmetry of the reflection of the electron field and X-ray radiation in the third layer is shown.