Nonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma

We propose an approximation of pair correlations for solving the equations of the kinetic theory of long-wave (or large-scale) fluctuations in gaseous media. The basic ones are the general nonlinear equations of the large-scale fluctuations theory at the kinetic stage of system evolution, derived from the first principles of statistical mechanics. We show that based on the equations of the long-wave fluctuations kinetics in the case of weak interaction between particles, in the approximation of pair fluctuations it is possible to reproduce the main results of the quasi-linear theory of plasma. Thus, the well-known quasi-linear theory of plasma is provided with a first-principle justification.