Gain coefficient in the course of the electron scattering by ions in a weak electromagnetic field: General relativistic case

For weak electromagnetic field the gain coefficient in the scattering of electrons by ions in the elliptically polarized light wave is theoretically studied in the general relativistic case. Simple analytical expression for a field amplification constant in logarithmic approach is obtained. It is shown for the ultrarelativistic electron energies the gain coefficient depends on energy as a cubic degree of energy and can be major enough. Results obtained may be experimentally verified, for example, by the scientific facilities at the SLAC National Accelerator Laboratory and FAIR (Facility for Antiproton and Ion Research, Darmstadt, Germany).