The light amplification effect in the scattering of electron by a nucleus in the electromagnetic field

This review is devoted to the amplification effect of an electromagnetic radiation in the electron scattering by ions in external electromagnetic field. Known papers at the given problem and original results are observed. The cases of circular and linear polarization of the electromagnetic waves, Born´s approximation on the interacting of an electron with a nuclear field and a quasi-classical approximation are observed. The light amplification effect was studied for the nonrelativistic-, relativistic- and ultrarelativistic energies of electrons. The gain coefficient in the field of two electromagnetic waves propagating in the same direction is studied. All cases of possible amplification of an electromagnetic radiation are observed. Estimations of the gain coefficient in the optical and radio frequencies region are done. Practical importance of the given effect is shown.