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The diffusion approximation to the Fokker-Planck equation is commonly used tomodel the transport of solar energetic particles in interplanetary space. Inthis study, we present exact analytical predictions of a higher order telegraphapproximation for particle transport and compare them with the correspondingpredictions of the diffusion approximation and numerical solutions of the fullFokker-Planck equation. We specifically investigate the role of the adiabaticfocusing effect of a spatially varying magnetic field on an evolving particledistribution. Comparison of the analytical and numerical results shows that thetelegraph approximation reproduces the particle intensity profiles much moreaccurately than does the diffusion approximation, especially when the focusingis strong. However, the telegraph approximation appears to offer no significantadvantage over the diffusion approximation for calculating the particleanisotropy. The telegraph approximation can be a useful tool for describingboth diffusive and wavelike aspects of the cosmic-ray transport.

astrophysical journal/the astrophysical journal

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