DYNAMICS OF COLLISIONAL PARTICLES IN A FLUCTUATING MAGNETIC-FIELD

The equations of motion of a test particle in a stochastic magnetic fi eld and interacting through collisions with a plasma are Langevin-type equations. Under reasonable assumptions on the statistical properties of the random processes (field and collisional velocity fluctuations) , we perform an analytical calculation of the mean-square displacement (MSD) of the particle. The basic nonlinearity in the problem (Lagrang ian argument of the random field) yields complicated averages, which w e carry out using a functional formalism. The result is expressed as a series, and we find the conditions for its convergence, i.e. the limi ts of validity of our approach (essentially, we must restrict attentio n to non-chaotic regimes). Further, employing realistic bounds (spectr al cut-off and limited time of observation), we derive an explicit for mula for the MSD. We show that from this unique expression, we can obt ain several previously known results.