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 Alfvén speed v_A, the contribution to D_p from slow-mode eddies is ≃(2p²v_A/9l)[ln(lv_A/D_||) + 2γ - 3], where l is the outer scale of the turbulence, γ ≃ 0.577 is Euler's constant, and D_|| is the spatial diffusion coefficient of energetic particles, which is assumed to satisfy D_|| ≪ lv_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_|| ≪ lv_A limit are an unlikely explanation for electron acceleration in solar flares to energies of 10-100 keV, because for solar flare 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_|| ≪ lv_A for such particles.