The Acceleration of Energetic Particles at Coronal Shocks and Q/A Dependence of Spectral Breaks

In large gradual solar energetic particle (SEP) events, particles are believed to be accelerated mainly by fast CME-driven shocks via diffusive shock acceleration mechanism. Recent observations have shown double power-laws in the event-integrated differential spectra in many large SEP events, with the break energy ordered by the ion charge-to-mass ratio (Q/A) for different species. In this work we perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer coronal magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field . We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV/nuc mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. This indicates that the streamer magnetic field can be an important factor in producing large SEP events. We also show that for all species (H, He, O, Mg, Fe) the ion energy spectra integrated over the simulation domain resemble a double power-law, due to a mixture of two distinct populations accelerated in the streamer and non-streamer regions where the particle acceleration rates are significantly different. The break energy has a power-law dependence on the ion's Q/A, with the spectral index varying from 0.2 to 1.3 by considering different turbulence spectra. Since the event-integrated spectra observed at 1 au may sample SEPs from different sources due to cross-field diffusion, we suggest that the mixing effect may be an important factor in the formation of double power-laws in large SEP events.