Some Remarks on Plasma Oscillations and the Kinetic Theory of Plasmas

In the linearized Vlasov's equation, the solution to the distribution function can be split into two parts. The one which takes the form of the free-particle propagation makes the neglected term in the linearized theory grow in t. A method of coping with such difficulty is suggested. The method is applied to some very simple cases where in the long time limit one needs a modification of the first-order distribution function, but not the first-order electric field. In general, it is believed that both these quantities have to be modified. The nature of higher-order corrections to the plasma kinetic equation is discussed. It is shown by the order of magnitude argument that the kinetic equation of a plasma cannot be extended beyond the first-order approximation with the adiabatic assumption of Bogoliubov.