Particle acceleration in solar flares

A model for second-phase acceleration in solar flares is presented. It is argued that particles are accelerated by the flare shock wave as it passes through the corona, and that the combined effects of first-order Fermi acceleration at shock waves and second-order Fermi acceleration by resonant scattering off hydromagnetic waves successfully explain the observed interplanetary proton and electron spectra. The model reproduces quantitatively the correlations of nonrelativistic with relativistic electron spectral indices and the correlation of nonrelativistic electrons with proton indices as a function of one parameter, the Alfvenic shock wave Mach number MA. The range in MA needed to fit the observations is 1.1-3.6, indicating shock velocities of 1000-2000 km/s. It is shown that the model allows the acceleration of electrons to tens, and of protons to hundreds, of MeV in times on the order of seconds. 39 references