Model Equations for Strong Turbulence in a Vlasov Plasma

Abstract

Approximate integrodifferential equations are proposed to determine the ensemble mean and covariance of the particle-distribution function for the one-species self-consistent Vlasov problem and for acceleration of particles in a prescribed stochastic electric field. The approximations correspond to the direct-interaction approximations for incompressible Navier—Stokes turbulence and turbulent convection. The final equations are exact statistical descriptions of model dynamical systems. This assures realizability of the covariance and conservation of energy, momentum, and probability. In addition, the model representation implies irreversible relaxation of the initial distribution. The relation of the proposed approximations to quasilinear theory and to the strong-turbulence theories of Mikhailovskii, Kadomtsev, and Dupree is analyzed. The diffusion limit and short-time limit of the stochastic-acceleration model are examined by an adaptation of Roberts' analysis for turbulent convection.