Energy Loss of Ultrahigh Energy Protons in Strong Magnetic Fields

TL;DR

This paper calculates how ultrahigh energy protons lose energy through pion production in strong magnetic fields, highlighting significant energy loss for protons above 10^19 eV in fields around 10^9 Gauss.

Contribution

It provides a detailed calculation of the mean free path for energy loss of ultrahigh energy protons in Gaussian random magnetic fields, considering isotropic and cylindrically symmetric cases.

Findings

Energy loss scales as E^3 <B^2>

Significant energy loss occurs for protons >10^19 eV in ~10^9 Gauss fields

Protons can lose a substantial fraction of energy in such conditions

Abstract

Ultrahigh energy protons in magnetic fields produce pions and thus lose energy. The mean free path of such a process is worked out for Gaussian random fields. Two cases are considered: an isotropic and a cylindrically symmetric distribution. The energy loss is proportional to E^3 <B^2>; it becomes significant for protons of energies larger than about 10^19 eV and magnetic fields of about 10^9 Gauss. For energies and magnetic fields of this magnitude, a proton injected into the magnetic field loses a substantial fraction of its initial energy due to pion production.