Alfvén wave dissipation and topological properties of 3D coronal force-free magnetic fields

Dipartimento di Fisica, Università della Calabria, via P. Bucci, 87036 Rende (CS), Italy e-mail: malara@fis.unical.it

Received: 27 September 2006
Accepted: 7 February 2007

Abstract

We study the propagation and dissipation of Alfvénic perturbation in a 3D equilibrium structure within a WKB model. We assume small amplitude and small wavelength of the perturbation. The generation of small scales in the perturbation is related to the property that nearby magnetic lines move apart from each other locally. This property is quantified by means of the Kolmogorov entropy H of magnetic lines. We numerically calculate the distribution of H for a 3D complex force-free equilibrium, which models the magnetic field above a quiet-Sun region, both for nonvanishing current and for a potential field. It is found that H decreases slightly with the altitude due to the decreasing complexity of the field, but it is relatively uniform except for the presence of sharp peaks, where H reaches much higher values than the average. These locations are those where Alfvén waves are preferentially dissipated. By analyzing the magnetic topology at these locations, we find that they correspond to separator lines which are intersections of separatrix surfaces. Then, in a high-Reynolds number plasma, such as in the solar corona, heating due to Alfvén wave dissipation takes place mainly at magnetic separatrices.