The Cosmic‐Ray Diffusion Tensor in Nonaxisymmetric Turbulence

Abstract

Previous investigations of magnetic field line random walk and charged particle transport in turbulence mostly employed an axisymmetric turbulence model. However, real turbulence is assumed to be nonaxisymmetric. In this article we employ a simple model for nonaxisymmetric turbulence based on a very recent article. By analytically describing the random walk of magnetic field lines and by combining these results with a general compound transport model, we derive the cosmic-ray diffusion tensor. As demonstrated, the nonaxisymmetry leads to different components of the cosmic-ray diffusion tensor in the perpendicular direction. These new results are essential for several applications such as solar modulation studies.

Magnetic Field Line Random Walk for Disturbed Flux Surfaces: Trapping Effects and Multiple Routes to Bohm Diffusion

“…In the present work we assume axisymmetry, with statistical rotational symmetry around the mean field direction,ẑ, so that fluctuations are statistically identical in the x-and y-directions (the assumption of axisymmetry was relaxed in some FLRW studies; see Pommois et al 2001;Ruffolo et al 2006;Weinhorst et al 2008). Axisymmetry implies statistically identical properties of field line trajectories along x and y.…”

Random walk of magnetic field lines: analytical theory versus simulations

“…At least for interplanetary studies, a common assumption is that the magnetic field fluctuations admit a strong component of A. Shalchi nearly two-dimensional character with δ B( x) = δ B(x, y), comprising perhaps 80%-90% of the turbulent inertial range energy budget (see, for example, Matthaeus et al 1990;Zank and Matthaeus 1993;Bieber et al 1996). The rest of the magnetic energy can be represented by so-called slab modes with δ B( x) = δ B(z).…”

Nonlinear Guiding Center Theory of Perpendicular Diffusion: Derivation from the Newton‐Lorentz Equation

“…Some examples are the nonlinear guiding center (NLGC) theory (Matthaeus et al 2003), the weakly nonlinear theory (Shalchi et al 2004b), and the compound diffusion model based on the Chapman-Kolmogorov approach (Webb et al 2006;Shalchi & Kourakis 2007;Weinhorst et al 2008). The latter approach is more systematic than the other approaches, but can, however, only be applied for magnetostatic turbulence models and for situations in which the particles are tied to a single magnetic field line.…”