Stochastic heating of charged particles by two modes of plasma oscillations

As it is well known, temporal dependence of the particles distribution due to their interaction with some (longitudinal) waves in turbulent plasma is described in the first approximation by a quasilinear equation. Taking into account a nonlinear wave interaction results only in some modification of the quasilinear diffusion coefficient. Thus it does not change the principal form of the equation. But besides these corrections to the diffusion coefficient connected with the scattering and/or the resonance broadening there is also a new nonlinear effect which changes the general form of the collision integral. This effect appears in the third order in field approximation and corresponds to a nonlinear interaction of plasma particles simultaneously with two types of oscillations: the resonant ones for which the Cherenkov resonance condition is fulfilled, and the nonresonant ones. The nonlinear interaction modifies also the heating process. 3 refs