A Magnetostatic Grad–Rubin Code for Coronal Magnetic Field Extrapolations

Abstract

The coronal magnetic field cannot be directly observed, but, in principle, it can be reconstructed from the comparatively well observed photospheric magnetic field. A popular approach uses a nonlinear force-free model. Non-magnetic forces at the photosphere are significant, meaning the photospheric data are inconsistent with the force-free model, and this causes problems with the modeling (De Rosa et al., Astrophys. J. 696, 1780, 2009). In this paper we present a numerical implementation of the Grad–Rubin method for reconstructing the coronal magnetic field using a magnetostatic model. This model includes a pressure force and a non-zero magnetic Lorentz force. We demonstrate our implementation on a simple analytic test case and obtain the speed and numerical error scaling as a function of the grid size.