Damping of Magnetohydrodynamic Turbulence in Solar Flares

Abstract

We describe the cascade of plasma waves or turbulence injected, presumably by reconnection, at scales comparable to the size of a solar flare loop, L $ 10 9 cm, to scales comparable to elementary particle gyroradii and evaluate their damping at small scales by various mechanisms. We show that the classical viscous damping valid on scales larger than the collision mean free path ($10 8 cm) is unimportant for magnetically dominated or low-plasmas and the primary damping mechanism is the collisionless damping by the background particles. We show that the damping rate is proportional to the total random momentum density of the particles. For solar flare conditions this means that in most flares, except the very large ones in which essentially all background electrons are accelerated into a nonthermal distribution, the damping is dominated by thermal background electrons. In general, damping by protons is negligible compared to that of electrons except for rare proton-dominated flares with strong nuclear gamma-ray line emission and for quasi-perpendicular propagating waves. We also determine the critical scale below which the damping becomes important and the spectrum of the turbulence steepens. We show that this scale has a strong dependence on the propagation angle of the waves with respect to the background magnetic field, resulting in a highly anisotropic spectral distribution, with quasi-parallel and quasi-perpendicular waves cascading undamped to small scales.