Coherent X-Ray Radiation Generated Near the Axis of the Beam of Relativistic Electrons in an Artificial Periodic Structure

A theory of the coherent X-ray radiation produced by a beam of relativistic electrons in an artificial periodic structure and propagating along the electron-beam axis is developed. Expressions describing the spectral-angular densities of parametric X-ray radiation in the direction close to the electron velocity vector (FPXR) and of transition radiation (TR) and their interference are obtained in the Bragg scattering geometry. An analysis based on the obtained expressions for the spectral-angular density shows possibilities of their use to determine the optimal parameters of the experiment recording the FPXR. The advantages of the experiment recording the FPXR at low electron energies ( $${{E}_{e}} \leqslant $$ 50 MeV) are shown.