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Recent observations have shown that in many large solar energetic particle(SEP) events the event-integrated differential spectra resemble double powerlaws. We perform numerical modeling of particle acceleration at coronal shockspropagating through a streamer-like magnetic field by solving the Parkertransport equation, including protons and heavier ions. We find that for allion species the energy spectra integrated over the simulation domain can bedescribed by a double power law, and the break energy depends on the ioncharge-to-mass ratio as $E_B \sim (Q/A)^\alpha$, with $\alpha$ varying from0.16 to 1.2 by considering different turbulence spectral indices. We suggestthat the double power law distribution may emerge as a result of thesuperposition of energetic particles from different source regions where theacceleration rates differ significantly due to particle diffusion. Thediffusion and mixing of energetic particles could also provide an explanationfor the increase of Fe/O at high energies as observed in some SEP events.Although further mixing processes may occur, our simulations indicate thateither power-law break or rollover can occur near the Sun and predict that thespectral forms vary significantly along the shock front, which may be examinedby upcoming near-Sun SEP measurements from Parker Solar Probe and SolarOrbiter.

Double-power-law feature of energetic particles accelerated at coronal shocks