Probabilistic Model of Plasma Turbulence

To obtain convergent series in plasma turbulence theory, it is necessary to include the effects of the turbulent fields in the particle propagator. The assumptions and different approaches of previous workers, notably Dupree, Rudakov and Tsytovich, and Weinstock, are clarified. Their results may be obtained by a simple assumption: that particles in phase space diffuse in a Markovian way under the action of the stochastic turbulent fields. From statistical arguments similar to those of Weinstock, a quite general expression for the diffusion coefficient D(V) emerges. This result holds without assuming weak turbulence if the wave spectrum is sufficiently broad. From the Markovian view above there follows immediately, without involved calculation, the familar expression for D(V) found by Dupree. Using probabilistic arguments, the particle propagator for a broad-band spectrum is calculated, allowing statistical spreading of trajectories in both position and velocity. This is identical to the usual method of obtaining a Green's function from a differential equation, but simpler. This new approach is valid whenever the turbulence is sufficiently broad-banded.