Coronal heating through Alfven waves

Sustaining the hot solar corona above polar regions, where the fast solar wind is accelerated, requires an energy flux of about 5 x 10(5) erg cm(-2) s(-1) whose source must be the photospheric motions below. The precise way this energy is transferred and damped remains an open question, though Alfven waves are the more natural candidates. Such waves are observed in situ in the fast solar wind and they are believed to provide heating through kinetic resonant dissipation. Recent observations suggesting strong anisotropic heating of heavy ions in coronal holes seem to confirm that this mechanism is at work in the corona too and thus Alfven waves must play a fundamental role there. However, in order for such waves to dissipate efficiently in the corona, extremely small scales must form because of the huge local magnetic Reynolds numbers. Hence, one must either assume that waves are directly generated at the dissipation scales, as suggested in models with chromospheric and transition region reconnection, or small scales must be reached through dynamical evolution. This should occur both thanks to the inhomogeneous coronal magnetic fields (resonant absorption, phase mixing) and to nonlinear wave-wave interactions. The traditional Kolmogorov-like cascade, involving interactions between incompressible modes, is inhibited, since for its development it requires waves propagating both upwards and downwards in the atmosphere. Therefore, coupling to compressible modes must play an important role, especially where strong transverse gradients in the Alfven velocity are not at disposal, such as in coronal holes. A source for effective dissipation of upward propagating Alfven waves via steepening of generated magnetoacoustic modes is provided by the parametric decay process, whose nonlinear stage will be studied here in two and three spatial dimensions. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.