Nonlinear force-free modeling of the corona in spherical coordinates

TL;DR

This paper introduces a spectral code for solving nonlinear force-free magnetic field equations in spherical coordinates, enabling accurate modeling of the solar corona's magnetic structure.

Contribution

The authors develop a spherical spectral implementation of the Grad-Rubin method for nonlinear force-free fields, with no boundary assumptions, and demonstrate its convergence and self-consistency.

Findings

Successfully applied to a bipolar test case with analytic boundary conditions.

Demonstrated convergence of the Grad-Rubin method.

Produced self-consistent magnetic field solutions.

Abstract

We present a code for solving the nonlinear force-free equations in spherical polar geometry, with the motivation of modeling the magnetic field in the corona. The code is an implementation of the Grad-Rubin method. Our method is applicable to a spherical domain of arbitrary angular size. The implementation is based on a global spectral representation for the magnetic field which makes no explicit assumptions about the form of the magnetic field at the transverse boundaries of the domain. We apply the code to a bipolar test case with analytic boundary conditions, and we demonstrate the convergence of the Grad-Rubin method, and the self-consistency of the resulting numerical solution.