An optimization principle for the computation of MHD equilibria in the solar corona

¹ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, Germany e-mail: wiegelmann@mps.mpg.de
² School of Mathematics and Statistics, University of St. Andrews, St. Andrews, KY16 9SS, UK

Received: 27 March 2006
Accepted: 22 June 2006

Abstract

Aims.We develop an optimization principle for computing stationary MHD equilibria.

Methods. Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements. The program uses photospheric vector magnetograms and coronal EUV images as input. We tested our reconstruction code with the help of a semi-analytic MHD-equilibrium. The quality of the reconstruction was judged by comparing the exact and reconstructed solution qualitatively by magnetic field-line plots and EUV-images and quantitatively by several different numerical criteria.

Results. Our code is able to reconstruct the semi-analytic test equilibrium with high accuracy. The stationary MHD optimization code developed here has about the same accuracy as its predecessor, a non-linear force-free optimization code. The computing time for MHD-equilibria is, however, longer than for force-free magnetic fields. We also extended a well-known class of nonlinear force-free equilibria to the non-force-free regime for purposes of testing the code.

Conclusions. We demonstrate that the code works in principle using tests with analytical equilibria, but it still needs to be applied to real data.