Reconstruction of Coronal Magnetic Fields Using a Poloidal–Toroidal Representation

Abstract

A new method for reconstruction of coronal magnetic fields as force-free fields (FFFs) is presented. Our method employs poloidal and toroidal functions to describe divergence-free magnetic fields. This magnetic field representation naturally enables us to implement the boundary conditions at the photospheric boundary, i.e., the normal magnetic field and the normal current density there, in a straightforward manner. At the upper boundary of the corona, a source surface condition can be employed, which accommodates magnetic flux imbalance at the bottom boundary. Although our iteration algorithm is inspired by extant variational methods, it is nonvariational and requires far fewer iteration steps than most others. The computational code based on our new method is tested against the analytical FFF solutions by Titov & Démoulin. It is found to excel in reproducing a tightly wound flux rope, a bald patch, and quasi-separatrix layers with a hyperbolic flux tube.