A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests

摘要

Based on a second-order approximation of nonlinear force-free magnetic fieldsolutions in terms of uniformly twisted field lines derived in Paper I, wedevelop here a numeric code that is capable to forward-fit such analyticalsolutions to arbitrary magnetogram (or vector magnetograph) data combined with(stereoscopically triangulated) coronal loop 3D coordinates. We test the codehere by forward-fitting to six potential field and six nonpotential field casessimulated with our analytical model, as well as by forward-fitting to anexactly force-free solution of the Low and Lou (1990) model. Theforward-fitting tests demonstrate: (i) a satisfactory convergence behavior(with typical misalignment angles of $\mu \approx 1^\circ-10^\circ$), (ii)relatively fast computation times (from seconds to a few minutes), and (iii)the high fidelity of retrieved force-free $\alpha$-parameters ($\alpha_{\rmfit}/\alpha_{\rm model} \approx 0.9-1.0$ for simulations and $\alpha_{\rmfit}/\alpha_{\rm model} \approx 0.7\pm0.3$ for the Low and Lou model). Thesalient feature of this numeric code is the relatively fast computation of aquasi-forcefree magnetic field, which closely matches the geometry of coronalloops in active regions, and complements the existing {\sl nonlinear force-freefield (NLFFF)} codes based on photospheric magnetograms without coronalconstraints.