Inverse stimulated bremsstrahlung of slow electrons under Coulomb scattering

A simple new analytic expression has been obtained fur the rate of inverse stimulated bremsstrahlung of slow electrons scattered by the Coulomb charge Ze. The initial and final electron energies are assumed to be small compared to the Rydberg energy mZ(2)e(4)/h(2). Weak linearly polarized light of frequency omega is considered, and only one-photon emission and absorption of the light are taken into account. High-frequency (omega;>> mv(3)/Ze(2)) and low-frequency to (omega << mv(3)/Ze(2)) limits are considered (v is the electron velocity). Both the quantum cases <(h)over bar omega> similar to p(2), <(h)over bar omega> > p(2) and the classical limit <(h)over bar omega> << p(2) are considered. The rate is averaged over the direction of the final electron momentum and over the angle between the light polarization and the direction of the initial electron momentum. It was found that in both laser frequency limits the rate of one-photon absorption is larger than the rate of one-photon emission, analogous to the well known opposite Born limit of rapid electrons. Therefore, the energy of a slow electron increases with time (inverse stimulated bremsstrahlung). The rate of energy gain for slow electrons decreases with increasing laser frequency w. The rates are averaged over Maxwell distribution of electrons. It was also found that the energy gain in the Born limit (rapid electrons) coincides with the energy gain for slow electrons if omega << mv(3)/Ze(2). The rates of electron-ion collisions in plasma are discussed in various limits.