Damping of MHD turbulence in Solar Flares

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 ∼ 109 cm, to scales comparable to elementary particle gyro radii, 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 (∼ 108 cm) is unimportant for magnetically dominated or low beta 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, the damping is dominated by thermal background electrons. For large flares one requires acceleration of essentially all background electrons into a nonthermal distribution so that the accelerated electrons can be important in the damping of the waves. In general, damping by thermal protons is negligible compared to that of electrons except for quasi-perpendicular propagating waves. Damping due to nonthermal protons is also negligible compared to nonthermal electrons in most flares which are electron dominated, except for rare proton dominated flares with strong nuclear gamma-ray line emission. Thus for common flares collisionless damping by background thermal electrons is the primary damping mechanism. Using the rate for this process we determine the critical scale (or wave vector kc) below which (i.e. for k > kc) the damping becomes important and the spectrum of the turbulence steepens. This critical scale, however, has strong dependence on the angle of propagation of the waves with respect to the Department of Applied Physics, Stanford University, Stanford, CA 94305 current address: CITA, University of Toronto, Canada