The telegraph approximation for focused cosmic-ray transport in the presence of boundaries

TL;DR

This paper develops a modified telegraph equation to model cosmic-ray transport in magnetic fields with boundaries, providing analytical and numerical solutions to improve understanding of cosmic-ray behavior near boundaries.

Contribution

It introduces boundary conditions for a modified telegraph equation and evaluates its accuracy for modeling focused cosmic-ray transport with boundaries.

Findings

Derived reflecting and absorbing boundary conditions.

Presented analytical and numerical solutions for boundary problems.

Discussed the applicability and accuracy of the telegraph approximation.

Abstract

Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term. Analytical and numerical solutions of illustrative boundary problems are presented. The applicability and accuracy of the telegraph approximation for focused cosmic-ray transport in the presence of boundaries are discussed, and potential applications to modeling cosmic-ray transport are noted.