Shock Acceleration of Solar Energetic Protons: The First 10 Minutes

Proton acceleration at a parallel coronal shock is modeled with self-consistent Alfven wave excitation and shock transmission. 18 - 50 keV seed protons at 0.1% of plasma proton density are accelerated in 10 minutes to a power-law intensity spectrum rolling over at 300 MeV by a 2500km s-1 shock traveling outward from 3.5 solar radius, for typical coronal conditions and low ambient wave intensities. Interaction of high-energy protons of large pitch-angles with Alfven waves amplified by low-energy protons of small pitch angles is key to rapid acceleration. Shock acceleration is not significantly retarded by sunward streaming protons interacting with downstream waves. There is no significant second-order Fermi acceleration.