Damping of Magnetohydrodynamic Turbulence in Solar Flares

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Abstract
(Abridged) We describe the cascade of plasma waves or turbulence injected, presumably by reconnection, at scales comparable to the size of a solar flare loop to scales comparable to particle gyroradii, and evaluate their damping by various mechanisms. We show that the classical viscous damping 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 or nonthermal protons is negligible compared to that of electrons except for quasi-perpendicular propagating waves or for rare proton dominated flares with strong nuclear gamma-ray line emission. Using the rate for damping we determine the critical scale below which the damping becomes important and the spectrum of the turbulence steepens. This critical scale, however, has strong dependence on the angle of propagation with respect to the magnetic field direction. The waves can cascade down to very small scales, such as the gyroradii of the particles at small angles (quasi-parallel propagation) and possibly near 90 degree (quasi-perpendicular propagation) giving rise to a highly anisotropic spectral distribution.Comment: 23 pages, 3 figures, submitted to Ap
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