Particle acceleration by slow modes in strong compressible magnetohydrodynamic turbulence, with application to solar flares

Energetic particles that undergo strong pitch-angle scattering and diffuse through a plasma containing strong compressible MHD turbulence undergo diffusion in momentum space with diffusion coefficient D-p. If the rms turbulent velocity is of the order of the Alfven speed upsilon(A), the contribution to D-p from slow-mode eddies is similar or equal to(2p(2)upsilon(A)/9iota)[ln(iotaupsilon(A)/D-parallel to) + 2gamma = 3], where iota is the outer scale of the turbulence, gamma similar or equal to 0.577 is Euler's constant, and D-parallel to is the spatial diffusion coefficient of energetic particles, which is assumed to satisfy D-parallel to much less than iotaupsilon(A). The energy spectrum of accelerated particles is derived for this value of D-p, taking into account Coulomb losses and particle escape from the acceleration region with an energy-independent escape time. Slow modes in the D-parallel to much less than iotaupsilon(A) limit are an unlikely explanation for electron acceleration in solar flares to energies of 10-100 keV, because for solar. are conditions, the predicted acceleration times are too long, and the predicted energy spectra are too hard. The acceleration mechanism discussed in this paper could in principle explain the relatively hard spectra of gyrosynchrotron-emitting electrons in the 100-5000 keV range, but only if D-parallel to much less than iotaupsilon(A) for such particles.