On the use of the perturbation technique for the kinetic analysis of nonlinear problems of plasma electrodynamics

We discuss the validity of the perturbation technique (i.e., power-series expansion in terms of the high-frequency field amplitude) applied for solving the kinetic equation. The case where the validity conditions of this method are formally violated for a "strongly localized" distribution function is considered. It is shown that in this case, the asymptotic expressions for the distribution-function moments remain correct not only in the linear, but also in quadratic approximation with respect to the field.