Reconstruction of coronal force-free fields with a poloidal-toroidal representation of magnetic field

Coronal magnetic fields are often approximated by force-free fields (FFFs). An FFF problem is well-posed when the boundary normal magnetic field and the boundary normal current density should both be prescribed under the condition that the divergence-freeness of magnetic field is guaranteed. In the vector potential formulation, which is divergence-free, the two boundary conditions cannot be prescribed by fixing the values of vector potentials at the boundary. In the poloidal-toroidal formulation, fixing the values of the poloidal and toroidal functions at the boundary prescribes the two boundary conditions once for all. We have devised a novel iteration scheme for FFFs using a poloidal-toroidal representation of magnetic field and developed a computational code based on it. The performance of this code is tested against Titov & Demoulin’s analytical FFF modes and compared with that of other existing codes. Our new code is found to excel others not only in figures of merits, but also in reproducing topological features of the Titov-Demoulin FFFs. We have also used the code to reconstruct time sequence of FFFs for AR 11974 which includes two M-class solar flares and a halo CME. This sequence reveals the changes of field connectivity, which are considered responsible for the eruptive phenomena occurred in the active region.