Three-dimensional modeling of the solar active region

In this study we developed an extrapolation code based on theMHD relaxation method to reconstruct a threedimensional (3D) coronal magnetic field. A 3D magnetic field based on a nonlinear force-free field (NLFFF) was extrapolated from a photospheric vector-field map. A benchmark test using the semi-analytical solution introduced by Low & Lou (1990) found that the extrapolated solution were able to well reproduce an original Low and Lou solution. We then applied the NLFFF extrapolation to solar active region (AR) NOAA 10930. The energy accumulation region formed by the strong magnetic shear above the polarity inversion line was resultantly reproduced and this structure is greatly different from the potential field characterized by the minimum energy state. In this paper we discuss the reliability of our extrapolated field and a relationship between quasi-separatrix layers (QSLs) and a flare ribbon from the CaII image observed by Hinode/SOT.