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

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.

8 pages, 6 figures, accepted in ApJ

References in corpus (3)

• Non Axi-symmetric Anisotropy of Solar Wind Turbulence
• Power Anisotropy in the Magnetic Field Power Spectral Tensor of Solar Wind Turbulence
• Simulating Heliospheric and Solar Particle Diffusion using the Parker Spiral Geometry

Cited by in corpus (22)

• A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
• CRPropa 3.2 -- an advanced framework for high-energy particle propagation in extragalactic and galactic spaces
• Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields
• Solar energetic particle access to distant longitudes through turbulent field-line meandering
• On Aspects Pertaining to the Perpendicular Diffusion of Solar Energetic Particles
• Anisotropic diffusion of galactic cosmic ray protons and their steady-state azimuthal distribution
• High rigidity Forbush decreases: due to CMEs or shocks?
• CRPropa 3.1 -- A low energy extension based on stochastic differential equations
• Modulation of Galactic Cosmic Rays in the Inner Heliosphere over Solar Cycles
• The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering
• Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements
• Moments of the anisotropic regularized $\kappa$-distributions
• On numerical turbulence generation for test-particle simulations
• Ionization rates in the heliosheath and in astrosheaths
• The Relation Between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares
• On the East-West Longitudinally Asymmetric Distribution of Solar Proton Events
• Pitch-angle scattering of energetic particles with adiabatic focusing
• The Dance of Odd-Diffusive Particles: A Fourier Approach
• Impact of anisotropic cosmic-ray transport on the gamma-ray signatures in the Galactic Center
• Diffuse Gamma Rays in 3D Galactic Cosmic-ray Propagation Models
• Hawking Radiation Signatures from Primordial Black Holes Transiting the Inner Solar System: Prospects for Detection
• Magnetohydrodynamic turbulence and the associated spatial diffusion tensor of cosmic rays in dynamical galactic halos