DIRECT EXCITATION OF RESONANT TORSIONAL ALFVEN WAVES BY FOOTPOINT MOTIONS

The present paper studies the heating of coronal loops by linear reson ant Alfven waves that are excited by the motions of the photospheric f ootpoints of the magnetic field lines. The analysis is restricted to t orsionally polarised footpoint motions in an axially symmetric system so that only torsional Alfven waves are excited. For this subclass of footpoint motions, the Alfven and cusp singularities are absent from t he analysis which means that resonant coupling between global modes of the loop and localised oscillations is avoided. Instead, the focus is on the resonances due to the finite extent of the loop in the longitu dinal direction: at the radii where Alfven waves travelling back and f orth along the length of the loop are in phase with the footpoint moti ons, the oscillations grow unbounded in ideal MHD. Inclusion of electr ical resistivity and viscosity as dissipation mechanisms prevents sing ular growth and we can look at the steady state in which the energy in jected at the photospheric part of the loop is balanced by the energy dissipated at the dissipative layer around the resonance. In this sens e, we show that the direct excitation of Alfven waves by torsionally p olarised footpoint motions leads to a very efficient heating mechanism for coronal loops, even without resonant coupling to global modes.