Nonlinear Kinetics of Plasma. I. Nonlinear Interaction of Electron Plasma Oscillation

The Hamiltonian formalism for nonlinear kinetics of collisionless electron plasma is established. The method deriving the fundamental equations of the nonlinear kinetics is based on a quantum statistical perturbational treatment for the interaction Hamiltonians which describe the elementary processes of the nonlinear coupling of electron plasma oscillation. The interaction Hamiltonians are obtained by the Bohm-Pines theory in an approximation of long wave-length. The lowest order process of the nonlinear interactions derived by this theory is the coupling between two modes of the oscillation in the participation of the electron. The nonlinear characters of oscillation arising from this coupling are investigated under the Maxwellian momentum distribution of electrons. From the standpoint of our theory, some remarks for several previous works are made.