Quantum modulation of an electron beam by an electromagnetic wave in an undulator

The quantum modulation of an electron beam at the frequency of the wave and its harmonics in magnetic and electric undulators has been found. The modulation is produced by direct and inverse stimulated effects in the undulator (taking into account quantum recoil). The depth of modulation is of the order of unity for actual parameters of undulator and wave. An experiment for obtaining a modulated beam of electrons at the optical frequencies and their harmonics is proposed. (orig.)