A Test on Two Codes for Extrapolating Solar Linear Force-free Magnetic Fields

We evaluate the performances of two newly-implemented codes for extrapolating the solar linear force-free magnetic fields, by measuring their quantified responses to the lower boundary vector field data on a finite region using analytical models. The codes are based on two boundary integral formulas with different mechanisms in utilizing the transverse boundary field: the first one only utilizes the transverse boundary field to derive the value of the force-free parameter, while the other one explicitly utilizes the whole transverse boundary field, in addition to the vertical field component. Studies on the test cases show that both of the codes could reproduce the analytical model fields with reasonable accuracy within the valid domain, provided a sufficient amount of data is available at the lower boundary. The code utilizing explicitly all three components of the boundary field shows generally better performances and requires a smaller boundary-data area in order to achieve the same degree of accuracy in the metric quantities such as the normalized vector error, vector correlation, vector angular difference, and magnetic energy; however, the accuracy in the divergence-free metric and especially the force-free metric are less ideal.