Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion

Abstract

A discussion is given of test particle transport in the presence of specified stochastic magnetic fields, with particular emphasis on the collisional limit. Certain paradoxes and inconsistencies in the literature regarding the form of the scaling laws are resolved by carefully distinguishing a number of physically distinct correlation lengths, and thus identifying several collisional subregimes. The common procedure of averaging the conventional fluid equations over the statistics of a random field is shown to fail in some important cases because of breakdown of the Chapman-Enskog ordering in the presence of a stochastic field component with short autocorrelation length. A modified perturbation theory is introduced which leads to a Kubo-like formula valid in all collisional regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length L_K appears explicitly. A higher-order renormalized kinetic theory in which L_K appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments.