A relative diffusion theory based on stochastic equations of motion and the weak-plasma-turbulence approximation

Abstract

A set of nonlinear equations describing the relative diffusion process of charged particles, or the decay process of clumps, in turbulent electric fields is systematically derived from the stochastic equations of motion using the weak-plasma-turbulence approximation. The solutions show that (r2(t)) varies as (u2(t)) varies as exp (t/trd) in the initial stage and (r2(t)) varies as (u2(t))3 varies as (t/tsd)3 in the final stage, where r and u are separations in position and velocity between two particles treated as a pair, respectively. Note that trd>tsd for broad k spectra and trd=tsd for a semibroad k spectrum. A divergent effect due to long-wavelength waves is excluded in the initial stage of the relative diffusion process owing to the fact that each pair of particles behaves in a strongly correlated way in this stage.