On the theory of plasma turbulence

Microscopic to macroscopic transitions in classical, nonequilibrium, particle-field systems pose a class of stochastic perturbation problems that can be solved via the formal theory of scattering. Such solutions permit the nonlinear microscopic equations descriptive of a turbulent plasma field to be ensemble averaged into macroscopic particle- and wave-kinetic equations. The method is essentially operator theoretical. The original microscopic operator is first conventionally decomposed into deterministic and stochastic parts and then via scattering theory its inverse is evaluated in terms of explicit, formally exact, operator expressions that admit rapidly convergent, nonsecular, series representations. These results may be obtained by either operator algebra or diagram methods, the former being preferred. The derivation appears to be more physically and analytically transparent than in most existing procedures and has the virtue of exhibiting explicitly higher order terms, some of which are novel. The theory is illustrated for the case of a simple isotropic electron plasma by the derivation of kinetic equations for particles and for waves.