Nonlinear Kinetics of Plasma. II. Fundamental Equations Relating to Ion Plasma Wave

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The kinetic equations relating to ion plasma wave (ion wave) in a weakly turbulent plasma are discussed from the viewpoint of the Hamiltonian formalism. The interaction Hamiltonians which describe various elementary processes occurring among electron, ion, electron plasma waves and ion waves are derived by extending the Bohm-Pines’ collective description of the electron plasma to a plasma in which both ions and electrons behave collectively. The wave-wave interactions of ion waves by the participation of ion and electron are discussed in detail. The equations describing the linear interactions between ion wave and electron (or ion) and three-wave interaction among electron plasma waves and ion wave are consistent with corresponding equations derived from the usual kinetic theory of a plasma.

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