The hard X-ray luminosity of impulsive solar flares indicates that electrons in the low corona are bulk energized to energies of order 25 keV. LaRosa & Moore pointed out that the required bulk energization could be produced by cascading MHD turbulence generated by Alfvénic outflows from sites of strongly driven reconnection. LaRosa, Moore, & Shore proposed that the compressive component of the cascading turbulence dissipates into the electrons via Fermi acceleration. However, for this to be a viable electron bulk energization mechanism, the rate of proton energization by the same turbulence cannot exceed the electron energization rate. In this paper we estimate the relative efficiency of electron and proton Fermi acceleration in the compressive MHD turbulence expected in the reconnection outflows in impulsive solar flares. We find that the protons pose no threat to the electron energization. Particles extract energy from the MHD turbulence by mirroring on magnetic compressions moving along the magnetic field at the Alfvén speed. The mirroring rate, and hence the energization rate, is a sensitive function of the particle velocity distribution. In particular, there is a lower speed limit Vmin ≍ VA, below which the pitch-angle distribution of the particles is so highly collapsed to the magnetic field in the frame of the magnetic compressions that there is no mirroring and hence no Fermi acceleration. For coronal conditions, the proton thermal speed is much less than the Alfvén speed and proton Fermi acceleration is negligible. In contrast, nearly all of the electrons are super-Alfvénic, so their pitch-angle distribution is nearly isotropic in the frame of the magnetic compressions. Consequently, the electrons are so vigorously mirrored that they are Fermi accelerated to hard X-ray energies in a few tenths of a second by the magnetic compressions on scales of 105-103 cm in the cascading MHD turbulence. We conclude that dissipation of reconnection-generated MHD turbulence by electron Fermi acceleration plausibly accounts for the electron bulk energization in solar flares.
The Astrophysical Journal
Digital Object Identifier (DOI)
LaRosa, T.N., Moore, R.L., Miller, J.A., Shore, S.N. New promise for electron bulk energization in solar flares: preferential Fermi acceleration of electrons over protons in reconnection-driven magnetohydrodynamic turbulence. Astrophys. J. 467, 454–464, 1996.