Compound and perpendicular diffusion of cosmic rays and random walk of the field lines: II. Non-parallel particle transport and drifts

Abstract

Compound transport of energetic charged particles across the mean magnetic field due to field line random walk is investigated by means of a Chapman–Kolmogorov equation. The probability distribution function (pdf) for the particle transport across the field P⊥ is given as a convolution of the pdf for random walk of the magnetic field, PFRW, with the pdf Pp, for particle transport relative to the random walking field. The particle propagator Pp includes the effects of advection, drift, parallel diffusion and local perpendicular diffusion of particles relative to the random walking field. At early times, the particles sub-diffuse across the field due to field line random walk. At late times, the effective cross-field diffusion coefficient has the form κ⊥e = κ⊥ + κF. The diffusion coefficient κ⊥ is the local cross-field diffusion coefficient due to particle scattering in the random magnetic field. The diffusion coefficient κF is due to coherent particle advection parallel to the mean magnetic field B0 coupled with transverse random walk of the magnetic field. Estimates of cross-field diffusion due to field line random walk, advection and drift are obtained both near to the heliospheric current sheet at Earth and at higher helio-latitudes. Cross-field diffusion due to field line random walk and advection is shown to be an important transport mechanism for low-energy particles near the current sheet, where the effects of drifts are negligible. Drift effects and field line random walk are also assessed at higher helio-latitudes off the current sheet, for a model interplanetary magnetic field, with a flat current sheet in the helio-equatorial plane.