Acceleration of relativistic protons in a solar wind perturbed by a coronal mass ejection
We investigated the impact of a coronal mass ejection (CME) on the transport and acceleration of relativistic protons in the solar wind using a coupled 3D magnetohydrodynamics (MHD) simulation and a test-particle approach. The CME is driven by a spheromak injected into a Parker solar wind at a heliocentric distance of 0.139 AU. We integrated the trajectories of 5 GeV protons, injected toward the CME from 3 AU, in the guiding-center approximation and scattered the particles in velocity space with a mean free path $\lambda_{\|}$. Our results show that the CME can increase the protons' energy by several gigaelectronvolts. The acceleration occurs while particles stream along the portion of a magnetic field line downstream of the quasi-perpendicular portion of the CME-driven shock. In our configuration, the maximum energy gain, which is on the order of a few percent per passage through the acceleration region, occurs when the shock approaches 0.3 AU. Large energy gains require multiple passes through the acceleration region, made possible by the combined action of the mirror force and pitch-angle scattering. The efficiency of the acceleration on timescales on the order of hours scales as $\lambda_{\|}^{-3/2}$. Energy spectra harden with decreasing parallel mean free path $\lambda_{\|}$.