Shock acceleration of electrons and ions in solar flares

The simultaneous first-order Fermi shock acceleration of electrons, protons, and alpha particles are compared to observations of solar energetic particle events. For each event, a unique shock compression ratio in the range of approximately 1.6-3 produces spectra in good agreement with observation. The range in compression ratios predicts that the more than five orders of magnitude spread in electron-to-proton intensity ratios observed at MeV energies is compressed to about three orders of magnitude at an assumed injection energy of 100 keV. The remaining spread can be accounted for with a modest range of injection conditions. The model predicts that the acceleration time to a given energy will be approximately equal for electrons and protons, and for reasonable solar parameters, can be on the order of 1 s to approximately 100 MeV.