A Perturbation Theory for Strong Plasma Turbulence

A new perturbation theory for solving the Vlasov equation is derived. The theory is especially designed to cope with time secularities and nonanalyticity in the expansion parameter (the field strength). The method is based on the use of a statistical set of exact particle orbits instead of the unperturbed orbits conventionally used in perturbation solutions of the Vlasov equation. A principal result of the theory is a modification of the particle-wave interaction and a ``broadening'' of the associated resonant denominator (ω − k·v)−1. The nature of the time secularities associated with the streaming modes exp ik·vt is discussed. A simple application to velocity-space diffusion and trapping and its effect on wave growth is described.