Magnetohydrodynamic Simulations of Solar Chromospheric Dynamics Using a Complete Electrical Conductivity Tensor

Abstract

A 1.5-dimensional, time-dependent magnetohydrodynamic (MHD) model that includes an energy equation and anisotropic electrical conductivity tensor for a variably ionized, multispecies plasma is presented. The model includes an algorithm that reduces the numerical dissipation rate far below the dissipation rate determined by the conductivity tensor. This is necessary for accurate calculation of resistive heating rates. The model is used to simulate the propagation of Alfven waves launched near the base of the middle chromosphere. The background state is the FAL CM equilibrium with a vertical magnetic field. The initial magnetic energy of a wave is almost completely damped out in the chromosphere by the time the disturbance propagates a distance of one wavelength. The energy is converted mainly into thermal energy. The remainder is converted into bulk flow kinetic energy and a Poynting flux with nonzero divergence. The thermal energy is generated almost entirely by Pedersen current dissipation. The corresponding heating rates are close to the FAL CM values near the base of the middle chromosphere. Dynamo action is observed. The damping of a continuously driven Alfven wave train is also simulated, yielding results similar to those of the single wave cases. It is the strong magnetization and weak ionization of the chromosphere that allows for strong heating by Pedersen current dissipation. This distinguishes the chromosphere from the weakly magnetized and weakly ionized photosphere, and the strongly magnetized and strongly ionized corona where Pedersen current dissipation is not significant on the length and timescales simulated.