Diagram-addition method in turbulent-plasma theory

Abstract

This article suggests using for plasma-turbulence description a diagram technique analogous to the one suggested by Wyld for hydrodynamic turbulence Such an approach enables one to abandon the perturbation-theory limits used for the study of weakly turbulent pulsations and to obtain approximate equations with the aid of which turbulence with γ ≈ ω can be investigated.With this purpose in mind, a precise solution of the Vlasov equation has been found for some types of turbulent-plasma pulsations in a magnetic field without assumption of smallness of the pulsation amplitud. This solution has the appearance of an infinite series in powers of the potential of the electric field. Each term of this series has a corresponding graphical picture. The further procedure for obtaining turbulence equations for a plasma is in many respects similar to that of ref. 1: series expansion is performed with respect to a random potential as well as averaging of the products of the random potentials over a Gaussian statistical ensemble and addition of infinite diagram subseries. The resulting equations represent a system of an infinite number of integral equations of infinite order for an infinite number of functions. By way of one or another reasonable dis-continuity of this system of equations, a closed system of a finite number of finite-order equations can be obtained. In this article one of these approximate-equation systems is constructed, representing a certain analogy with the hydrodynamic equations of Kraichnan.