On the nonlinear kinetics in a weakly turbulent plasma

The nonlinear kinetics of waves in a weakly turbulent classical plasma is investigated from a quantum mechanical viewpoint. It is shown that the lowest order nonlinear effects in the long wave length region arise not only from the Compton scattering of plasmons by electrons, which is the only process previously considered, but also from the absorption and emission of plasmons accompanied by a collision between two electrons. The latter has an effect to smooth out the spectral distribution of the waves, while the former (the Compton scattering, process) exhibits two distinct effects depending on the magnitude of the total wave energy E; for E smaller than a certain critical value E_C the Compton scattering process smooths out the wave distribution, while for E greater than E_C the wave energy is directed towards the longest wave length region. The value of E_C is roughly estimated to be four times the thermal level. (author)