Analysis of Reconstruction Methods for Nonlinear Force-Free Fields

We focus on quantitative evaluation of several methods for the reconstruction of force-free magnetic fields in the solar corona. We have studied two topics. The first is to carry out a comparison test of two approaches to implement the optimization method: (1) using a boundary layer with a weighting function and (2) involving an optimization algorithm for unknown boundary field vector values. The second approach is shown to provide a better approximation to a desired true solution that is finite in an unlimited semispace. The approximation obtained by the second approach is reasonably close to the true solution up to the boundaries of the reconstruction region. Among the applications of the optimization method to real data, we demonstrate its ability to obtain accurate enough energy estimates and find that the pre- to post-flare energy difference is sufficient in powering the flare.