Enhanced phase mixing of Alfvén waves propagating in stratified and divergent coronal structures^*

¹ Institute for Materials Research, University of Salford, Greater Manchester, M5 4WT, UK e-mail: p.d.smith@pgr.salford.ac.uk
² Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK

Received: 4 July 2007
Accepted: 24 September 2007

Abstract

Aims.We explore the solar coronal heating enigma by an analytical and numerical study of the enhanced phase mixing of harmonic Alfvén waves propagating in gravitationally stratified coronal structures of varying magnetic field divergence.

Methods.Corrected analytical solutions are derived to model the dissipation of Alfvén waves propagating in divergent and stratified coronal structures. These analytical solutions are validated and further explored using a newly developed 2.5D visco-resistive linear MHD code.

Results.Corrected analytical solutions describing the enhanced phase mixing of Alfvén waves in divergent and stratified coronal structures are presented. These show that the enhanced phase mixing mechanism can dissipate Alfvén waves at heights less than half that is predicted by the previous analytical solutions. In divergent and stratified coronal structures, the enhanced phase mixing effect occurs only when the ratio of the magnetic and density scale heights, . The enhanced phase mixing of 0.1 Hz harmonic Alfvén waves propagating in strongly divergent,  Mm, stratified coronal structures,  Mm, can fulfill of an active region heating requirement, by generating viscous heating fluxes of  J m^-2 s^-1. The Alfvén waves in this configuration are fully dissipated within 20 Mm, which is six times lower than would occur as a result of standard phase mixing in uniform magnetic fields. This results in the heating length scale, , defined as the height at which of the Alfvén wave poynting flux has dissipated, being lowered by a factor of six, to less than half of an active region density scale height. Using the corrected analytical solutions it was found that, for a given wave frequency, the generation of a heating length scale of  Mm, by enhanced phase mixing in strongly divergent magnetic fields, requires a shear viscosity eight orders of magnitude lower, than required by standard phase mixing in uniform magnetic fields. It was also found that the enhanced phase mixing of observable,  rads s^-1, Alfvén waves, in strongly divergent magnetic fields,  Mm, can generate heating length scales within a density scale height,  Mm, using classical Braginskii viscosity. It is therefore not necessary to invoke anomalous viscosity in corona, if phase mixing takes place in strongly divergent magnetic fields. This study shows that the importance of enhanced phase mixing as a mechanism for dissipating Alfvén waves in the solar corona (a stratified and divergent medium), has been seriously underestimated.