Cerenkov modulation of the electron beam

It is shown that a quantum modulation of a beam at the frequency of the wave and its harmonics takes place during the interaction of electrons with an electromagnetic wave in a medium. The modulation is produced by a direct and an inverse induced Cerenkov effect (taking account of the quantum recoil). The amount of modulation is of order one, even at rather small intensities of the wave. An experiment for obtaining a modulated beam of electrons at optical frequencies and its harmonics is proposed. (Auth.)