Influence of a strong electromagnetic wave on stimulated bremsstrahlung of electrons

Cross sections of many-photon transitions are found for the scattering of a nonrelativistic electron by an ion in the field of two plane monochromatic waves. A study is made of the relationship between the classical and quantum-mechanical descriptions of stimulated bremsstrahlung. Asymptotic behavior is predicted of the absorption coefficient $\alpha$ at a frequency $\omega_1$ for high values of the intensity $E_0$ of the second field of frequency $\omega_0$ $\alpha\sim E_0^{-1}$. Resonances of the absorption coefficient are expected at $\omega_1\approx n\omega_0$, where $n=1,2,3,\dots$. The conditions for negative absorption are considered.