WAVE HEATING OF CORONAL ARCADES DRIVEN BY TOROIDALLY POLARIZED FOOTPOINT MOTIONS - STATIONARY BEHAVIOR IN DISSIPATIVE MHD

We study the heating of 2-D coronal arcades by linear resonant Alfven waves that are excited by photospheric footpoint motions of the magnet ic field lines. The analysis is restricted to toroidally polarised foo tpoint motions so that Alfven waves are excited directly. At the magne tic surfaces where Alfven waves, travelling back and forth along the l oop-like magnetic field lines, are in phase with the footpoint motions , the oscillations grow unbounded in ideal linear MHD. Inclusion of di ssipation prevents singular growth and we can look at the steady state in which the energy input at the photospheric base of the arcade is b alanced by the energy dissipated at the resonance layer. In the presen t study we take the toroidal wave number to be non-zero which means th at also fast waves, including quasimodes, can be excited by the purely toroidally polarised footpoint motions. In this case resonant Alfven 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 lo op model : for some footpoint motions the direct and indirect contribu tions to the resonance counteract each other leading to virtually no h eating (anti-resonance) while, for values of the driving frequency and the toroidal wave number corresponding to a quasi-mode, the two contr ibutions act in concert leading to enhanced heating.