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On the problem of application of diffracted transition radiation for indication of relativistic electron beam parameters

The diffracted transition radiation (DTR) produced by a beam of relativistic electrons traversing a thin single-crystal plate in the Laue scattering geometry is considered. We have obtained the expression describing the angular density of the DTR for the case when the path length of the electron in the target is far less than the extinction length of X-rays in the crystal. It is shown that in this case the considered DTR process has the explicit kinematic character. The numerical calculations of the yield of DTR photons in the direction of Bragg scattering performed for various values of the registration solid angle show a significant influence of the electron beam divergence on the photon yield. We have arrived at a conclusion that the measured photon output of DTR radiation emitted in a given solid angle can be used for indication of the electron beam divergence. The model calculations of the electron beam divergence parameters on the base of “measured” yield of DTR photons traversing through a slit collimator are carried out. The results of the calculation show that the proposed in this work formula can be successfully used as a base for the development of methods for measuring the divergence of beams of relativistic ultrahigh-energy electrons based on DTR angular distribution.