Nonlinear interactions in coronal heating

Abstract

The dynamics of the solar corona as well as its very existence are due to the dynamics of plasmas and magnetic fields which, at the global scales of coronal loops, prominences and helmet streamers may be described by magnetohydrodynamics. Here, we discuss the importance and role of nonlinear interactions in the heating of the solar corona, which relies on the transfer, storage and dissipation of the mechanical energy present in photospheric motion [Einaudi, G., Velli, M., Phys. Plasmas 6, 4146, 1999]. Nonlinear interactions including the coupling of coronal fields to the motions and emerging flux through the photosphere determine both the rate of heating and the topology of coronal magnetic fields. We present the first results of a 3D reduced MHD simulation that models the small-scale magnetic activity of coronal flux tubes. The equations are solved inside a box of dimensions l × l × L (axial direction), with an aspect ratio L/ l of the order of 10. The box is initially threaded by a constant sinusoidal velocity field at one base (corresponding to one photospheric footpoint of the loop), of amplitude 1 km/s, (the axial Alfvén speed is about 1000 km/s), whereas the other footpoint is anchored, i.e., no photospheric motions are present. In the transverse directions, periodicity is assumed. Our numerical calculations show that the magnetic field lines change their topology continuously and often reconnect at small scales, forming typical coronal loop-like structures. Energy release events which provide a steady supply of energy are associated with the reconnection.