  The so-called regularized Biot-Savart laws (RBSLs) provide an efficient and
flexible method for modeling pre-eruptive magnetic configurations of coronal
mass ejections (CMEs) whose characteristics are constrained by observational
images and magnetic-field data. This method allows one to calculate the field
of magnetic flux ropes (MFRs) with small circular cross-sections and an
arbitrary axis shape. The field of the whole configuration is constructed as a
superposition of (1) such a flux-rope field and (2) an ambient potential field
derived, for example, from an observed magnetogram. The RBSL kernels are
determined from the requirement that the MFR field for a straight cylinder must
be exactly force-free. For a curved MFR, however, the magnetic forces are
generally unbalanced over the whole path of the MFR. To minimize these forces,
we apply a modified Gauss-Newton method to find optimal MFR parameters. This is
done by iteratively adjusting the MFR axis path and axial current. We then try
to relax the resulting optimized configuration in a subsequent line-tied
zero-beta magnetohydrodynamic simulation toward a force-free equilibrium. By
considering two models of the sigmoidal pre-eruption configuration for the 2009
February 13 CME, we demonstrate how this approach works and what it is capable
of. We show, in particular, that the building blocks of the core magnetic
structure described by these models match to morphological features typically
observed in such type of configurations. Our method will be useful for both the
modeling of particular eruptive events and theoretical studies of idealized
pre-eruptive MFR configurations.
