Prompt simultaneous acceleration of protons and electrons to relativistic energies by shock waves in solar flares

It is shown by theory and fully relativistic, electromagnetic particle simulation that a collisionless fast magnetosonic shock wave can promptly accelerate protons and electrons to relativistic energies; proton energies > approx 109 eV and electron energies > approx 106 eV. The strong nonstochastic acceleration occurs in a rather strong magnetic field such that ωce > approx ωpe, where ωce is the electron cyclotron frequency, and ωpe is the electron plasma frequency. The time needed for the proton acceleration is of the order of the ion cyclotron period and is quite short (much less than 1 s for solar plasmas). The electron acceleration time is shorter than the ion cyclotron period. The present shock acceleration mechanism can explain important features of observed particle acceleration in the impulsive phase of solar flares: simultaneous and prompt acceleration of protons and electrons to relativistic energies. (author)