Absorption in the medium, i.e. an imaginary part of the dielectric permittivity, can lead to arising of Cherenkov radiation at high frequencies – X-Ray and XUV. In this paper X-Ray Diffraction radiation from a bunch of ultra-relativistic electrons moving near an absorbing target is investigated theoretically. In these conditions the Cherenkov radiation arises even when trajectories of the particles does not cross the target. The spatial distribution of the radiation usually represents the cone with the axis in forward direction with thickness proportional to the imaginary part of dielectric permittivity. In this paper it is shown that taking into account the refraction and reflection of the waves at the surface of the target leads to essential changes in spatial distribution of radiation. We give analytical description of the XUV Cherenkov and diffraction radiation from the bunch of charged particles. We show that the spatial distribution of radiation is not symmetrical in relation to the top face of the target.
In this paper we consider X-Ray and EUV Transition radiation propagating in backward direction which is generated by the ultrarelativistic electron bunch crossing the target. The target consists of periodical set of thin wires with the rectangular cross-section. We obtain the analytical expressions for distribution of the energy of the transition radiation per solid angle and frequency. In high frequency region (X-Ray, EUV), where the wavelength of radiation is less than length of a beam, the main part of radiation is incoherent. In this case the radiation from electron bunches is described by the so called incoherent form-factor. We obtain and analyse the expression for incoherent form-factor. In this work we show that incoherent form-factor arises always when the size of a target is finite and that it depends on the ratio between the transversal size of the bunch and the production of wavelength and Lorentz-factor of the charged particles. The coherent effects of target and the electron bunch play an important role in increasing the intensity of radiation and also change the spatial distribution of radiation.