A&A 494, 317-327 (2009)
DOI: 10.1051/0004-6361:200811106

On the validity of nonlinear Alfvén resonance in space plasmas

C. T. M. Clack, I. Ballai, and M. S. Ruderman

Solar Physics and Space Plasma Research Centre (SP2RC), Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK
    e-mail: [app06ctc;i.ballai;m.s.ruderman]@sheffield.ac.uk

Received 8 October 2008 / Accepted 21 November 2008

Abstract
Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD), it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfvén dissipative layer
Methods. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfvén dissipative layer.
Results. The nonlinear corrections to resonant waves in the Alfvén dissipative layer are derived, and it is proved that at the Alfvén resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy.

Key words: magnetohydrodynamics (MHD) -- methods: analytical -- Sun: atmosphere -- Sun: oscillations

© ESO 2009

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

• If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
• You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
• You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.