Wave heating of coronal arcades driven by toroidally polarised footpoint motions Stationary behaviour in dissipative MHD

Westudy the heating of 2-D coronal arcades by linear resonant Alfvén waves that are excited by photospheric footpoint motions of the magnetic field lines. The analysis is restricted to toroidally polarised footpoint motions so that Alfvén waves are excited directly. At the magnetic surfaces where Alfvén waves, travelling back and forth along the loop-like magnetic field lines, are in phase with the footpoint motions, the oscillations grow unbounded in ideal linear MHD. Inclusion of dissipation prevents singular growth and we can look at the steady state in which the energy input at the photospheric base of the arcade is balanced by the energy dissipated at the resonance layer. In the present study we take the toroidal wave number to be non-zero which means that also fast waves, including quasimodes, can be excited by the purely toroidally polarised footpoint motions. In this case resonant Alfvén waves are not only excited directly by the footpoint motions but also indirectly through coupling to the fast waves. Our results confirm the phenomena previous found by Berghmans & Tirry (1997) for a coronal loop model : for some footpoint motions the direct and indirect contributions to the resonance counteract each other leading to virtually no heating (anti-resonance)while, for values of the driving frequency and the toroidal wave number corresponding to a quasi-mode, the two contributions act in concert leading to enhanced heating.