Optimization of Magnetic Flux Ropes Modeled with the Regularized Biot–Savart Law Method

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