Solar 3He-rich events and electron acceleration in two stages

The heating, acceleration, and enhancement of electrons in solar He-3-rich events are studied according to the two-stage acceleration model proposed for the enhancement of He-3 and heavy ions. First, electrostatic ion cyclotron instabilities destabilized by electron currents are theoretically and numerically investigated for a plasma consisting mainly of H, He-4, and electrons. Since the parallel phase velocities of the ion cyclotron waves are smaller than around the electron thermal velocity, electrons can have strong Landau resonance (omega(r) - k(parallel to) upsilon(e, parallel to) = 0) with the ion cyclotron waves. Here omega(r) and k(parallel to) are, respectively, the real frequency and wavenumber parallel to the external magnetic field and upsilon(e,parallel to) is the parallel electron velocity. Second, preferential heating of electrons by the ion cyclotron waves is studied through the quasi-linear theory. It is shown that H cyclotron waves are very efficient at heating electrons through the Landau resonance. Third, these preheated electrons can be further accelerated to high energies in the Fermi acceleration process. The abundance ratio (e/H) of high-energy electrons and protons is estimated. The abundance ratio is very high when electrons are sufficiently heated relative to protons and agrees well with observations. Therefore, the present two-stage model explains all aspects of acceleration (He-3, electrons, and heavy ions) in flares in a self-consistent way.