Absorption of electromagnetic energy by slow electrons under scattering from Coulomb centers

Simple analytical expressions are obtained for the rate of the inverse stimulated bremsstrahlung absorption under electron scattering from a Coulomb center with charge Z in the presence of the electromagnetic field. The initial and final values of electron energy are assumed to be small compared to the Rydberg energy Z ² (atomic units are used throughout). Single-photon processes of absorption and induced radiation of photon by electron are treated. It is assumed that the electromagnetic field frequency ω is rather low, so that the condition Zω/p ³ ? 1, where p is the electron momentum, and the condition ?ω ? p ² are valid. However, this frequency is assumed to be fairly high compared to the electron-Coulomb center collision frequency: ω ? v _nei. The dependences of the rates of photon absorption and induced radiation on the angle θ between the direction of incident electron and the electromagnetic field polarization vector (assumed to be linearly polarized) are obtained. It is demonstrated that, for any angles θ, the rate of photon absorption is higher than the rate of induced radiation and, therefore, the Marcuse effect for slow electrons (electromagnetic field amplification) is absent. It is further demonstrated that a slow electron on the average absorbs double ponderomotive energy per collision with an ion (Coulomb center) in Maxwellian plasma. This agrees both with the known results calculation for fast electrons and with the known results of the calculation based on the classical Boltzmann kinetic equation for plasma.