Semi–Quasi‐Linear Description of Cosmic‐Ray Perpendicular Transport

Abstract

In several previous articles it has been demonstrated that a quasi-linear description of cosmic-ray transport perpendicular to a mean magnetic field is not appropriate. On the other hand, recently derived nonlinear theories for perpendicular transport are based on several ad hoc assumptions and are difficult to apply due to mathematical problems. In this article we present an alternative formulation for describing perpendicular scattering in turbulent magnetic systems. It is also shown that off-diagonal elements of the spatial diffusion tensor can be so calculated. By combining a quasilinear formulation for field line random walk with a compound transport model, we derive a semi-quasi-linear formula for calculating the perpendicular diffusion coefficient. By applying this theory onto isotropic turbulence, we demonstrate that test-particle simulations (from Giacalone & Jokipii) can be reproduced analytically. For limiting cases as regards the fraction of the perpendicular to the parallel diffusion coefficient, a simple analytic formula for the perpendicular diffusion coefficients as a function of the parallel diffusion coefficient can be derived. © 2008. The American Astronomical Society. All rights reserved.