Application of Wiener-Hermite Expansion to Strong Plasma Turbulence

Expansion of a random function in terms of an orthogonal random base was introduced by Cameron and Martin [1] and Wiener [2], Meecham and Siegel [3] and Meecham and Jeng [4] applied this technique to the problem of hydrodynamic turbulence. Recently, Jahedi and Ahmadi [5] used it in their study of nonlinear structures subjected to random loads. The technique is now well known as the Wiener-Hermite expansion method. The possible utility of the Wiener-Hermite expansion in closure of strong plasma turbulence was pointed out by Ahmadi [6]. In the present work the Wiener-Hermite method is applied to the problem of strong electrostatic plasma turbulence. Statistically orthogonal random base functions in phase space are introduced. The random distribution functions of ions and electrons are expanded in terms of the Wiener-Hermite set and the equations for the deterministic kernels are derived. "Closure" is achieved by discarding the forth and higher order terms in the Wiener-Hermite series. Deterministic evolution equations for the Wiener-Hermite kernel functions are derived and discussed.