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Surface currents provide a general way to model static magnetic fields insource-free volumes. To facilitate the use of surface currents inmagneto-quasistatic problems, we have implemented a set of computational toolsin a Python package named bfieldtools. In this work, we describe the physicaland computational principles of this toolset. To be able to work with surfacecurrents of arbitrary shape, we discretize the currents on triangle meshesusing piecewise-linear stream functions. We apply analytical discretizations ofintegral equations to obtain the magnetic field and potentials associated withthe discrete stream function. In addition, we describe the computation of thespherical multipole expansion and a novel surface-harmonic expansion forsurface currents, both of which are useful for representing the magnetic fieldin source-free volumes with a small number of parameters. Last, we shareexamples related to magnetic shielding and surface-coil design using thepresented tools.

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