Generalized weak turbulence theory

Abstract

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 electrostatic interaction only, and the effects of spontaneous thermal fluctuations are ignored. In spite of these simplifications, the present formalism represents a generalization of the existing weak turbulence theory in that a nonlinear eigenmode excited in a turbulent plasma with frequency close to twice the plasma frequency is incorporated into the discussion. Traditional weak turbulence theory emphasizes various linear and nonlinear interactions among wave modes in quiescent plasmas (i.e., Langmuir and ion-sound waves). In contrast, the present formalism describes linear and nonlinear interactions among Langmuir, ion-sound, and the new nonlinear eigenmode. Nonlinear wave kinetic equations for these modes are systematically derived, and the particle kinetic equation which generalizes the well known quasilinear diffusion equation, is also derived.