An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

Abstract

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.