On a sphere of applicability of the Vlasov equation

Summary form only given. Here we demonstrate that the sphere of application of the Vlasov equation should be reduced. Consider a plasma with large spatial scales of slow motions. In this plasma a smooth distribution can be defined by averaging of the usual Klimontovich-Dupree´s distribution (the microdistribution further on) over small (but voluminous with respect to the particle content) vicinities of points in phase space. The Vlasos´s distribution cannot but coincide with this averaged microdistribution. But the time derivative of the latter differs with the Vlasov equation. This derivative is defined by the difference of the particle currents entering the domain of averaging and leaving it. Apart from the terms that correspond to the Vlasov equation, this difference contains some correlative terms that are due to the plasma discreteness. Their contribution is stressed in comparison with the former terms, because of the electron screening of the ion electric fields.