A local-frame approach to three-dimensional analysis of magnetospheric magnetic fields

Understanding the three-dimensional geometric structure of the Earth’s magnetospheric magnetic field is crucial for analyzing plasma physics phenomena. However, conventional methods often overlook geometric properties orthogonal to magnetic field lines. To address this, we adopted a local-frame approach that extends the Frenet–Serret system, enabling the quantification of curvature and torsion in directions both parallel and perpendicular to the field lines. We developed an open-source Python library, geopack-vectorize , featuring the Mageometry component as the analysis framework, and leveraged NumPy-based vectorization to enable high-speed execution across multiple points. Performance benchmarks demonstrate that the vectorized implementation achieves speedups ranging from approximately 30 to 116 times compared to conventional scalar processing for Tsyganenko models when processing 1,000 points. Through application to dipole and Tsyganenko 96 models, we demonstrated that the spatial distributions of the eight independent derivative coefficients can be efficiently derived. Consequently, this library enables the quantitative and visual assessment of magnetic field curvature and torsion—properties that were previously understood only qualitatively through field-line tracing. This library provides a standard, efficient tool for the quantitative analysis of complex magnetic field configurations, facilitating large-scale simulations and data analysis in magnetospheric physics.