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 approx. 1.6 to 3 produces spectra in good agreement with observation. The range in compression ratios predicts that the more than 5 orders of magnitude spread in electron to proton intensity ratios observed at MeV energies is compressed to about 3 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 second to approx. 100 MeV.