A Study of Alfvén Wave Propagation and Heating the Chromosphere

Alfvén wave propagation, reflection, and heating of the chromosphere are studied for a one-dimensional solar atmosphere by self-consistently solving plasma, neutral fluid, and Maxwell’s equations with incorporation of the Hall effect and strong electron–neutral, electron–ion, and ion–neutral collisions. We have developed a numerical model based on an implicit backward difference formula of second-order accuracy both in time and space to solve stiff governing equations resulting from strong inter-species collisions. A non-reflecting boundary condition is applied to the top boundary so that the wave reflection within the simulation domain can be unambiguously determined. It is shown that due to the density gradient the Alfvén waves are partially reflected throughout the chromosphere and more strongly at higher altitudes with the strongest reflection at the transition region. The waves are damped in the lower chromosphere dominantly through Joule dissipation, producing heating strong enough to balance the radiative loss for the quiet chromosphere without invoking anomalous processes or turbulences. The heating rates are larger for weaker background magnetic fields below ∼500 km with higher-frequency waves subject to heavier damping. There is an upper cutoff frequency, depending on the background magnetic field, above which the waves are completely damped. At the frequencies below which the waves are not strongly damped, the interaction of reflected waves with the upward propagating waves produces power at their double frequencies, which leads to more damping. The wave energy flux transmitted to the corona is one order of magnitude smaller than that of the driving source.