Reconstruction of Coronal Magnetic Fields Using a Poloidal-Toroidal Representation

TL;DR

This paper introduces a novel poloidal-toroidal method for reconstructing coronal magnetic fields as force-free fields, simplifying boundary condition implementation and reducing computational iterations.

Contribution

A new non-variational iterative method using poloidal and toroidal functions for efficient coronal magnetic field reconstruction with improved boundary condition handling.

Findings

Accurately reproduces flux ropes and magnetic structures

Requires fewer iteration steps than existing methods

Successfully tests against analytical solutions

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 non-variational and requires far fewer iteration steps than most of them. The computational code based on our new method is tested against the analytical FFF solutions by Titov & D\'{e}moulin (1999). It is found to excel in reproducing a tightly wound flux rope, a bald patch and quasi-separatrix layers with a hyperbolic flux tube.