Amplification of electromagnetic field in the course of the nonrelativistic electron scattering by ion in the presence of the field of the medium-intensity elliptically polarized light wave

The amplification factor of the electromagnetic field is theoretically studied for the scattering of nonrelativistic electrons by ions in the presence of the field of the elliptically polarized electromagnetic wave. A simple analytical formula for the gain is derived for the medium-intensity range. The formula supplements and extends the domain of applicability of the known Marcuse formula for the linear polarization in the presence of a weak field. It is demonstrated that the maximum gain is reached when the initial electron velocities belong to the polarization plane of the electromagnetic wave. In the range of optical frequencies, the amplification factor of the laser radiation can be significant for relatively high powers of electron beams.