A Generalized Diffusion Tensor for Fully Anisotropic Diffusion of Energetic Particles in the Heliospheric Magnetic Field

TL;DR

This paper introduces a generalized diffusion tensor model for fully anisotropic cosmic ray diffusion in the heliosphere, improving the accuracy of particle transport simulations by accounting for anisotropic perpendicular diffusion.

Contribution

The authors develop a new transformation formula for the diffusion tensor that explicitly incorporates two principal local perpendicular axes, extending previous isotropic models.

Findings

The new tensor formulation significantly alters the predicted cosmic ray fluxes, with deviations up to 60% at low energies.

The generalized model better captures the effects of different magnetic field configurations on particle diffusion.

Numerical simulations demonstrate the importance of anisotropic diffusion modeling for accurate cosmic ray modulation predictions.

Abstract

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulas to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the 'traditional' diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we motivate the choice of the Frenet-Serret trihedron which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and the Parker field. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard 3D model for the modulation of galactic protons. For this we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the 'traditional' one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.