Amplification of circularly polarized electromagnetic wave in the coulomb centre scattering of nonrelativistic electron

The gain coefficient in the scattering of the nonrelativistic electrons by ions in the circularly polarized light wave is theoretically studied. The simple analytical formula for the gain coefficient in the medium-field is obtained. It is shown, that the maximum amplification of the wave takes place when the electron velocity locates in the polarization plane. The laser gain coefficient can be not small for the powerful electron beams.