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The three-dimensional (3D) coordinates of stereoscopically triangulated loopsprovide strong constraints for magnetic field models of active regions in thesolar corona. Here we use STEREO/A and B data from some 500 stereoscopicallytriangulated loops observed in four active regions (2007 Apr 30, May 9, May 19,Dec 11), together with SOHO/MDI line-of-sight magnetograms. We measure theaverage misalignment angle between the stereoscopic loops and theoreticalmagnetic field models, finding a mismatch of $\mu=19^\circ-46^\circ$ for apotential field model, which is reduced to $\mu=14^\circ-19^\circ$ for anon-potential field model parameterized by twist parameters. The residual erroris commensurable with stereoscopic measurement errors ($\mu_{SE} \approx8^\circ-12^\circ$). We developed a potential field code that deconvolves aline-of-sight magnetogram into three magnetic field components $(B_x, B_y,B_z)$, as well as a non-potential field forward-fitting code that determinesthe full length of twisted loops ($L \approx 50-300$ Mm), the number of twistturns (median $N_{twist}=0.06$), the nonlinear force-free $\alpha$-parameter(median $\alpha \approx 4 \times 10^{-11}$ cm$^{-1}$), and the current density(median $j_z \approx 1500$ Mx cm$^{-2}$ s$^{-1}$). All twisted loops are foundto be far below the critical value for kink instability, and Joule dissipationof their currents is found be be far below the coronal heating requirement. Thealgorithm developed here, based on an analytical solution of nonlinearforce-free fields that is accurate to second order (in the force-free parameter$\alpha$), represents the first code that enables fast forward-fitting tophotospheric magnetograms and stereoscopically triangulated loops in the solarcorona.

First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted Force-Free Fields