  Recent observations have shown that in many large solar energetic particle
(SEP) events the event-integrated differential spectra resemble double power
laws. We perform numerical modeling of particle acceleration at coronal shocks
propagating through a streamer-like magnetic field by solving the Parker
transport equation, including protons and heavier ions. We find that for all
ion species the energy spectra integrated over the simulation domain can be
described by a double power law, and the break energy depends on the ion
charge-to-mass ratio as $E_B \sim (Q/A)^\alpha$, with $\alpha$ varying from
0.16 to 1.2 by considering different turbulence spectral indices. We suggest
that the double power law distribution may emerge as a result of the
superposition of energetic particles from different source regions where the
acceleration rates differ significantly due to particle diffusion. The
diffusion and mixing of energetic particles could also provide an explanation
for the increase of Fe/O at high energies as observed in some SEP events.
Although further mixing processes may occur, our simulations indicate that
either power-law break or rollover can occur near the Sun and predict that the
spectral forms vary significantly along the shock front, which may be examined
by upcoming near-Sun SEP measurements from Parker Solar Probe and Solar
Orbiter.
