Authors: Johnathan Stauffer (NRL), Mark Linton (NRL)

In magnetostatics, potential (i.e. curl-free) magnetic fields represent the minimum energy state for a given distribution of magnetic flux. Therefore, they are often chosen as a reference field for the calculation of the free magnetic energy in studies of solar active regions. However, the limitations of solar observing — namely, the discretization of the observed magnetic field and incomplete boundary information — break this uniqueness and necessitate the use of approximate numerical methods to compute the potential field. In this work, we present a novel Green’s function kernel for the calculation of potential fields in the local Cartesian approximation which outperforms the traditional monopole kernel. We apply this new Green’s function to re-calculate photospheric shear and excess energy in a sample of 166 active regions, finding that the use of an inaccurate potential field in the official SHARP data processing pipeline resulted in significant errors in the calculation of several SHARP parameters.