A New Global Nonlinear Force-Free Coronal Magnetic-Field Extrapolation Code Implemented on a Yin–Yang Grid

The solar magnetic field dominates and structures the solar coronal plasma. Detailed insights into the coronal magnetic field are important to understand most physical phenomena there. While direct, routine measurements of the coronal magnetic field are not available, field extrapolation of the photospheric vector-field measurements into the corona is the only way to study the structure and dynamics of the coronal field. Here we focus on global coronal structures traditionally modeled using spherical grids and synoptic vector magnetograms as boundary conditions. We developed a new code that performs nonlinear force-free magnetic-field extrapolations in spherical geometry. Our new implementation is based on a well-established optimization principle on a Cartesian grid and a single spherical finite-difference grid. In the present work, for the first time, the algorithm is able to reconstruct the magnetic field in the entire corona, including the polar regions. The finite-difference numerical scheme that was employed in previous spherical-code versions suffered from numerical inefficiencies because of the convergence of those grids on the poles. In our new code, we implement the so-called Yin–Yang overhead grid, the structure of which addresses this difficulty. Consequently, both the speed and accuracy of the optimization algorithm are improved compared to the previous implementations. We tested our new code using the well known semi-analytical model (Low and Lou solution). This is a commonly used benchmark for nonlinear force-free extrapolation codes.