Parametric X-rays and diffracted transition radiation in perfect and mosaic crystals

Abstract

The amplitude of X-ray emission by relativistic electrons in a single crystal, calculated in the kinematical approach, is decomposed unambiguously in Diffracted Transition Radiation (DTR) and Parametric X-rays (PXR). DTR becomes significant for γ ≳ ω P ,γ being the Lorentz factor and ω P the plasma frequency. It is more collimated than PXR and, above threshold, its flux increases logarithmically with γ. However, it saturates with thickness at the Bragg primary extinction length l e. This saturation is accounted for only in the dynamical approach, the formulas of which are compared to the kinematical ones. The respective contributions of DTR and PXR are calculated for a simple model of mosaic crystal, taking into account saturation of DTR with thickness. The PXR flux is basically the same as in a perfect crystal. If the size of the domains is larger than l e, the DTR flux is multiplied by the number of domains crossed by the electron. For domains smaller than l e and γ ≳ ω P , the DTR and PXR fluxes are of the same order of magnitude, up to logarithmic factors. In any case, mosaicity increases the total yield of X-ray photons.