Particle acceleration at a pair of parallel shocks near the Sun

A "twin-coronal mass ejection (CME)" scenario has been proposed recently to account for extreme solar energetic particle (SEP) events. In this scenario, two CMEs erupt from the same or nearby active regions within a short period of time. They both drive shocks, and the presence of the first CME-driven shock leads to a more efficient particle acceleration process at the second shock. All Ground Level Enhancement events in solar cycle 23 and many large SEP events support the twin-CME scenario. In a subset of these events, the two CMEs are separated by only a few minutes and particle acceleration is further enhanced due to particles reflecting between the two shocks. Here we examine particle acceleration at a parallel shock pair using a test particle approach. We follow single-particle trajectories using two methods: close to the shock we follow particle's motion by solving the Lorentz equation directly; beyond certain distances, we ignore the gyration degree of freedom of a particle and approximate its motion by its guiding center motion and pitch angle scattering. We do not consider wave generation due to the streaming protons at both shocks. Instead, we assume the background turbulence upstream of the first shock is given and follow its transmission to the downstream of the second shock. Our results show that the intensity of accelerated particles in the shock pair case is significantly enhanced over a single shock case, and the maximum energy obtained in a shock pair system can be a few to 10 times that of a single shock case.