Application of the Novikov-Furutsu theorem to the random acceleration problem

Abstract

The problem of calculating the average propagator of a particle accelerated by a turbulent electric field is treated in a new way. Using a theorem of Novikov (1965) and Furutsu (1963), the formulation of the problem is transformed into one in which the random field does not appear explicitly. A hierarchy of approximations is devised which converges on a closed equation for the propagator. This leads to a Dupree-like theory, but with short-time, rather than long-time, propagators in the resonance functions.