A new global non-potential magnetic field model

The potential field source surface (PFSS) model remains the most widely used method for extrapolating the global coronal magnetic field. Given the current spatial resolution of the full Sun, PFSS performs well at large scales and is computationally efficient. The PFSS approach, however, fails when electric currents distort the coronal field from its potential state. More advanced extrapolation techniques, such as nonlinear force-free field (NLFFF) models, can capture non-potential effects but are significantly more computationally demanding for global studies. Observational techniques enable the reconstruction of the 3D geometry of coronal loops, which trace the magnetic field in the corona. The goal of this work is to develop a new implementation to multi-constrain the global PFSS model by incorporating 3D coronal loop information, thereby improving its consistency with observations while preserving its computational efficiency. Although the model remains constrained by the PFSS field derived from photospheric observations, it allows the magnetic field to deviate from the potential, minimum-energy state within the loop influence regions, while maintaining control over its divergence and force-freeness. We adapted the NLFFF optimization formalism to the PFSS framework, enabling the inclusion of multiple physical constraints. Up to three terms were considered in the functional: a divergence-free term, a loop term, and a force-free term. The newly developed second-order finite-difference Python algorithm was tested with synthetic coronal loop data, using Carrington rotation 2284 as the lower boundary condition. The method produces magnetic field solutions that are more consistent with the geometry of the included coronal loops, controlling the divergence and force-freeness levels associated with the coronal loop inclusion. Our method shows that 3D coronal loop information can be consistently incorporated into the PFSS, while largely preserving its computational efficiency, even when a substantial number of loops is considered.