Measuring the Transverse Sizes of an Electron Beam by the Angular Distribution of the Coherent Radiation of Electrons in a Crystal

A technique for determining the transverse sizes of a beam on a target from the two-dimensional angular distributions of the radiation for two distances between the emitting crystal and a coordinate detector is proposed. The desired sizes are obtained from the results of fitting, in which the fitted function is the distribution at a shorter distance and the fitting function is the convolution of the angular distribution at a greater distance with a two-dimensional Gaussian distribution with the parameters uniquely related to the beam sizes on the target and crystal-to-detector distance. The limits of applicability of the proposed technique are determined.