Self consistent 1D numerical calculation of the temperature profile of solar corona heated by Alfvén waves

Alfven mechanism [H. Alfven, Granulation, magnetohydrodynamic waves, and the heating of the solar corona, Mon. Not. R. Astron. Soc. 107, 211-219 (1947)] for heating the solar corona by magnetosonic waves is numerically examined for completely ionized one-dimensional hydrogen plasma. As a boundary condition we suppose a fixed spectral density of the coming from the chromosphere Alfven waves. The numerical solution to the derived MHD equations gives the width of the transition layer between the chromosphere and the corona as a self-induced opacity of high-frequency Alfven waves (AWs). The domain wall is a direct consequence of the self-consistent MHD treatment of AWs' propagation. The low-frequency MHD waves coming from the Sun are strongly reflected by the narrow transition layer, while the high-frequency waves are absorbed-that is why we predict considerable spectral density of the AWs in the photosphere.