Magnetic-field modeling with surface currents: Physical and computational principles of bfieldtools

TL;DR

This paper introduces bfieldtools, a Python package for modeling static magnetic fields using surface currents, with advanced discretization and expansion techniques for efficient and flexible magnetic field analysis.

Contribution

It presents a comprehensive set of computational tools and physical principles for surface current modeling, including novel surface-harmonic expansion methods.

Findings

Effective discretization of surface currents on triangle meshes.

Implementation of analytical integral equations for magnetic field computation.

Introduction of surface-harmonic expansion for efficient magnetic field representation.

Abstract

Surface currents provide a general way to model static magnetic fields in source-free volumes. To facilitate the use of surface currents in magneto-quasistatic problems, we have implemented a set of computational tools in a Python package named bfieldtools. In this work, we describe the physical and computational principles of this toolset. To be able to work with surface currents of arbitrary shape, we discretize the currents on triangle meshes using piecewise-linear stream functions. We apply analytical discretizations of integral equations to obtain the magnetic field and potentials associated with the discrete stream function. In addition, we describe the computation of the spherical multipole expansion and a novel surface-harmonic expansion for surface currents, both of which are useful for representing the magnetic field in source-free volumes with a small number of parameters. Last, we share examples related to magnetic shielding and surface-coil design using the presented tools.