Abstract
We present a novel open-source Python software package, bfieldtools, for magneto-quasistatic calculations using current densities on surfaces of arbitrary shape. The core functionality of the software relies on a stream-function representation of surface-current density and its discretization on a triangle mesh. Although this stream-function technique is well known in certain fields, to date, the related software implementations have not been published or have been limited to specific applications. With bfieldtools, we aimed to produce a general, easy-to-use, and well-documented open-source software. The software package is written purely in Python; instead of explicitly using lower-level languages, we address computational bottlenecks through extensive vectorization and use of the NumPy library. The package enables easy deployment, rapid code development, and facilitates application of the software to practical problems. In this paper, we describe the software package and give an extensive demonstration of its use with an emphasis on one of its main applications—coil design.
Highlights
Within many fields of engineering and science, there is a need for modeling the relationship between magnetic fields and surface currents in complex geometries
Pissanetzky17 introduced a general streamfunction representation of the surface-current density on arbitrary surfaces, which discretizes the current on triangle surface meshes in a manner similar to finite-element and boundary-element methods (FEM and BEM, respectively)
Within the field of magnetic resonance imaging (MRI), triangle mesh-based stream-function methods have been applied to the magnetic field modeling and coil design since the early 1990s
Summary
Within many fields of engineering and science, there is a need for modeling the relationship between magnetic fields and surface currents in complex geometries. To model eddy currents in conducting sheets, one needs to calculate the coupling between the external field and the currents as well as the inductive effects of the currents within the conductor.1,2 Such modeling is useful in computing the magnetic noise arising from thermal fluctuations and designing surface-current patterns that generate a desired magnetic field. Within the field of magnetic resonance imaging (MRI), triangle mesh-based stream-function methods have been applied to the magnetic field modeling and coil design since the early 1990s.1,17–20. COMPUTATIONS USING THE DISCRETE STREAM FUNCTION bfieldtools uses the scalar stream-function representation of a surface current density, which is discretized as a piecewise linear function onto a triangle mesh. The surface-current density is obtained as the rotated gradient of the piecewise linear stream function, which makes it constant on each triangle face. With the resistance matrix R, the quadratic expression sRs gives the Ohmic (heating) power of the surface current
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