Numerical simulations of linear magnetohydrodynamic waves in two-dimensional force-free magnetic fields

Abstract

High resolution observations of the solar corona made with instruments onboard the SOHO and TRACE spacecrafts have provided new evidence for the presence of oscillations in a variety of coronal magnetic structures. Most of these observations have been interpreted in terms of linear standing or propagating magnetohydrodynamic (MHD) waves, but the theoretical understanding is far from complete since analytical solutions to the linearised MHD wave equations can only be found for very simple magnetic congurations. Taking into account that the solar corona is basically structured by force-free magnetic elds, our purpose in this paper is to present the derivation of the linear MHD wave equations for a two-dimensional force-free magnetic eld conguration having longitudinal invariance, as well as to introduce a numerical code to solve the resulting system of coupled partial dierential equations. The accuracy of the code has been checked by numerically solving two cases for which analytical or simple numerical solutions exist. To our knowledge, this is the only two-dimensional code developed to study the normal MHD modes of oscillation of a general force-free eld with longitudinal invariance.