Abstract
Surface currents provide a general way to model 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 the 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. Lastly, we share examples related to magnetic shielding and the surface-coil design using the presented tools.
Highlights
Modeling magnetic phenomena with surface currents has various applications in physics and engineering.[1,2,3,4,5] One large field of applications is the surface-coil design, where continuous surface currents are used to design coil winding patterns
By taking a line integral of ψ from ~r0 to ~r on the surface, we find that the difference in the stream function between the two ends of the path equals the flux of surface current ~j(~r) passing the curve[2] ð~r ψ(~r) À ψ(~r0) 1⁄4 ~j(~r 0) Á (d~l 0 Â n^0), (2)
We have introduced a set of tools for static and quasistatic modeling of divergence-free surface currents and their fields
Summary
Modeling magnetic phenomena with surface currents has various applications in physics and engineering.[1,2,3,4,5] One large field of applications is the surface-coil design, where continuous surface currents are used to design coil winding patterns. To facilitate surface-current-based methods, we introduce a novel Python software package bfieldtools (available at https://bfieldtools.github.io) This package provides tools for representing currents on arbitrarily shaped surfaces and calculating the associated magnetic field and potentials. As in many preceding works,[1,2,4,8,9,10,14] in bfieldtools, we model divergence-free surface currents with scalar stream functions. We discretize these functions on a triangle mesh using piecewise-linear basis functions equivalent to piecewise-constant surface-current density. More applications are described in Part II,[30] including references to the software implementation
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