Coupling of fast and Alfvén waves in a straight bounded magnetic field with density stratification

Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain e-mail: arregi@hubble.uib.es;ramon.oliver@uib.es;dfsjlb0@uib.es

Corresponding author: J. L. Ballester, dfsjlb0@uib.es

Received: 8 October 2002
Accepted: 14 February 2003

Abstract

The theoretical understanding of the linear standing or propagating magnetohydrodynamic waves in a variety of solar coronal structures is far from complete since analytical solutions to the linearised MHD equations can only be found for very simple magnetic configurations. In this paper, we use a numerical code to solve the linear fast and Alfvén wave equations in a very simple, bounded magnetic configuration that incorporates two features that are not usually considered in similar works, namely the longitudinal magnetic field component and wave propagation in the longitudinal direction (). We use a numerical code (Arregui et al. 2001) that has been modified by including a staggered mesh that allows us to properly capture the spatial behaviour of solutions to the wave equations. Coupling between fast and Alfvén modes has been studied in detail and it has been found that it does not take place when the longitudinal field component is zero and the frequency of the fast mode is outside the Alfvén continuum with the same spatial structure along field lines. Under these circumstances, fast modes retain their global spatial behaviour and are also characterised by varying linearly with , such as in a uniform medium (although here the Alfvén speed changes exponentially in the direction normal to field lines). Regarding mode coupling, its main feature is the blend of fast and Alfvén solutions with close frequencies in some modes with a mixture of their properties, namely discontinuities or jumps around certain magnetic surfaces (such as in pure Alfvén waves), global spatial distribution of the normal velocity component and non-zero density perturbations (such as in fast waves).