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

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 (Astrophys. J. 352, 343, 1990) model. The forward-fitting tests demonstrate: i) a satisfactory convergence behavior (with typical misalignment angles of μ≈1° - 10°), ii) relatively fast computation times (from seconds to a few minutes), and iii) the high fidelity of retrieved force-free α-parameters (α_fit/α_model≈0.9 - 1.0 for simulations and α_fit/α_model≈0.7±0.3 for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-force-free magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing nonlinear force-free field (NLFFF) codes based on photospheric magnetograms without coronal constraints.