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

Abstract

Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to arbitrary magnetogram (or vector magnetograph) data combined with (stereoscopically triangulated) coronal loop 3D coordinates. We test the code here by forward-fitting to six potential field and six nonpotential field cases simulated with our analytical model, as well as by forward-fitting to an exactly force-free solution of the Low and Lou (1990) model. The forward-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 (${\alpha }_{\mathrm{fit}}/{\alpha }_{\mathrm{model}}\approx 0.9-1.0$ for simulations and ${\alpha }_{\mathrm{fit}}/{\alpha }_{\mathrm{model}}\approx 0.7\pm 0.3$ for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-forcefree magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing {\sl nonlinear force-free field (NLFFF)} codes based on photospheric magnetograms without coronal constraints.

Solar PHysics, (in press), 25 pages, 11 figures

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• Towards a Quantitative Comparison of Magnetic Field Extrapolations and Observed Coronal Loops
• Nonlinear force-free coronal magnetic stereoscopy
• Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124
• Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops
• Torsional Alfvénic Oscillations Discovered in the Magnetic Free Energy During Solar Flares
• Global Energetics of Solar Flares. IX. Refined Magnetic Modeling
• Optimizing Global Coronal Magnetic Field Models Using Image-Based Constraints
• Image-Optimized Coronal Magnetic Field Models