NONLINEAR FORCE-FREE EXTRAPOLATION OF THE CORONAL MAGNETIC FIELD BASED ON THE MAGNETOHYDRODYNAMIC RELAXATION METHOD

Abstract

We develop a nonlinear force-free field (NLFFF) extrapolation code based on\nthe magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD\nrelaxation method in two important ways. First, we introduce an algorithm\ninitially proposed by cite{2002JCoPh.175..645D} to effectively clean the\nnumerical errors associated with $nabla cdot vec{B}$. Second, the multi-grid\ntype method is implemented in our NLFFF to perform direct analysis of the\nhigh-resolution magnetogram data. As a result of these two implementations, we\nsuccessfully extrapolated the high resolution force-free field introduced by\ncite{1990ApJ...352..343L} with better accuracy in a drastically shorter time.\nWe also applied our extrapolation method to the MHD solution obtained from the\nflux-emergence simulation by cite{2012ApJ...748...53M}. We found that NLFFF\nextrapolation may be less effective for reproducing areas higher than a\nhalf-domain, where some magnetic loops are found in a state of continuous\nupward expansion. However, an inverse S shaped structure consisting of the\nsheared and twisted loops formed in the lower region can be captured well\nthrough our NLFFF extrapolation method. We further discuss how well these\nsheared and twisted fields are reconstructed by estimating the magnetic\ntopology and twist quantitatively.\n