Evolution of energetic protons in twisted magnetic loops

Abstract

We study the evolution of an ensemble of energetic (1 GeV) protons in a twisted force-free magnetic loop. The protons are followed with a bounce-average method and they are subjected to collisions with ambient gas and pitch-angle scattering by plasrma turbulence in the loop. The proton loss is initially by drift and later by scattering into the loss cone. Gamma rays are produced by pion decays resulting from nuclear reactions of these lost protons. It is found that in order to have long-lasting protons, one of the following scenarios should hold: (1) For small loops (of length ∼ 2 × 109 cm), the twist angle should be about 2π and the turbulence level below 10−8 erg cm−3. (2) For large loops (≳ 1010 cm), the turbulence level should be below 10−6 erg cm−3. These set the conditions for testing the trapping picture as a viable explanation for the observed eight-hour gamma-ray emission.