Heating of the solar atmosphere by strong damping of Alfven waves

The heating of the solar atmosphere by strongly damped Alfven waves that produce heating through plasma-neutral collisions is studied by solving analytically a self-consistent one-dimensional model of the plasma-neutral-electromagnetic system. We compute the vertical profile of the wave spectrum and power by a novel method, which includes the damping effect neglected in previous treatments, and find that the damping depends on the magnetic field strength. The damping is extremely strong for weaker magnetic field and less strong for strong field. Under either condition, the high-frequency portion of the source power spectrum is strongly damped at the lower altitudes, depositing heat there, whereas the lower-frequency perturbations are nearly undamped and can be observed in the corona and above when the field is strong. The chromosphere behaves like a low-pass filter. The magnetic field strength determines the upper cutoff frequency. As a result, the power and spectrum of the waves observed above the corona is weak for regions of weaker background magnetic field and only a fraction of those at the photosphere for regions of strong magnetic field. Contrary to what was supposed in some earlier Alfven wave damping models, the spectrum observed above the chromosphere in general does not represent the energy input. We show, using the parameters of a semi-empirical model for quiet-Sun conditions, that this mechanism, without invoking any anomalous processes, can generate sufficient heat to account for the radiative losses in the atmosphere, with most of the heat deposited as required at lower altitudes.