Generalized weak turbulence theory

In this article we present the derivation of a generalized weak turbulence kinetic equation for unmagnetized collisionless plasmas in a uniform medium . For the sake of simplicity the present formulation assumes longitudinal e lectrostatic interaction only, and the effects of spontaneous thermal fluct uations are ignored. In spite of these simplifications, the present formali sm represents a generalization of the existing weak turbulence theory in th at a nonlinear eigenmode excited in a turbulent plasma with frequency close to twice the plasma frequency is incorporated into the discussion; Traditi onal weak turbulence theory emphasizes various linear and nonlinear interac tions among wave modes in quiescent plasmas (i.e., Langmuir and ion-sound w aves). In contrast, the present formalism describes linear and nonlinear in teractions among Langmuir, ion-sound, and the new nonlinear eigenmode. Nonl inear wave kinetic equations for these modes are systematically derived, an d the particle kinetic equation which generalizes the well known quasilinea r diffusion equation, is also derived. (C) 2000 American Institute of Physi cs. [S1070-664X(00)01312-4].