Analysis of Reconstruction Methods for Nonlinear Force-Free Fields

Abstract

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.

A Challenging Solar Eruptive Event of 18 November 2003 and the Causes of the 20 November Geomagnetic Superstorm. III. Catastrophe of the Eruptive Filament at a Magnetic Null Point and Formation of an Opposite-Handedness CME

“…We used the method of the NLFF extrapolation (Rudenko and Myshyakov, 2009) to compute two kinds of the current helicity maps. The first kind of map, the photospheric h c density map, presents the distribution of h c at the photospheric layer.…”

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

“…This is due to an assumption in the original optimal algorithm of Yan and Li [2006] which is only valid at low altitudes [Rudenko and Myshyakov, 2009]. To avoid the increasing errors at the field points with higher altitude, improved the original algorithm of Yan and Li [2006], and devised the upward boundary integration computational scheme for NLFFF extrapolations of coronal magnetic fields in solar active regions.…”

Broadband microwave sub-second pulsations in an expanding coronal loop of the 2011 August 10 flare

“…6) agree well. (2) The reconstructed magnetic field lines obtained by the nonlinear force-free approach using an optimization method (Rudenko & Myshyakov, 2009) also agree well, but in this case we cannot see fine details (twisted magnetic field lines) because of the limb effects. (3) The results agree well with the theoretical modelling for a gyrosynchrotron model of the radio emission, for instance (Kashapova et al 2013a).…”