The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering

TL;DR

This paper compares the diffusion and telegraph approximations for modeling solar energetic particle transport, showing the telegraph model's improved accuracy in intensity profiles under strong focusing conditions.

Contribution

It provides the first exact analytical predictions of a higher order telegraph approximation and demonstrates its superior accuracy over the diffusion approximation in certain conditions.

Findings

Telegraph approximation better reproduces particle intensity profiles than diffusion approximation.

Telegraph approximation does not significantly improve anisotropy predictions.

Analytical predictions align well with numerical solutions of the Fokker-Planck equation.

Abstract

The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wavelike aspects of the cosmic-ray transport.