Pitch angle scattering and effective collision frequencycaused by stochastic magnetic fields

The motion of charged particles in a plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. In contrast to the well-known perpendicular (to an external magnetic field) transport, here the parallel transport is considered. The two cases of a strong guiding field and a weak mean magnetic field, respectively, are investigated. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. Generalizations to large Kubo numbers are discussed. It is shown that the magnetic field fluctuations are the source of diffusive motion along a strong guiding field even if binary collisions are absent. The case of small (or vanishing) mean fields is also investigated in the quasilinear limit. An effective collision frequency is derived which is consistent with the result for perpendicular quasilinear diffusion in strong guiding fields. The analytical results are checked by numerical simulations of the A-Langevin equation.