Wave energy dissipation by anisotropic viscosity in magnetic X-points

The viscous dissipation of axial field disturbances in planar magnetic X-points is examined. It is emphasized that an accurate treatment requires a nonisotropic tensor viscosity whose components are governed by the local magnetic field. Numerical solutions are constructed, which compare the buildup of viscous forces using the tensor formulation against a simplified model based on conventional shear viscosity. The scaling of the global energy-loss rate with the viscosity coefficient is shown to follow Pv similar to V-1/3 for both the traditional shear viscosity and the Braginskii bulk viscosity. This suggests that viscous wave dissipation can occur quite rapidly, in a few tens of Alfven times. The results imply that large-scale disturbances, generated by magnetic reconnection in the solar corona, should dissipate in a time on the order of a few minutes and significantly contribute to coronal heating.