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arXiv · 2105.12522

Computation of the Biot-Savart line integral with higher-order convergence using straight segments

Nick McGreivy·Caoxiang Zhu·Lee Gunderson·Stuart R. Hudson
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Abstract

One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot-Savart field from each straight segment is known analytically. However, if the endpoints of the straight segments are chosen to lie on the coil, then the accuracy of the Biot-Savart computation is generally only second-order in the number of endpoints. We propose a simple modification: shift each endpoint off the coil in the outwards normal direction by an amount proportional to the local curvature. With this modification, the Biot-Savart accuracy increases to fourth order and the numerical error is dramatically reduced for a given number of discretization points.

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Nick McGreivy, Caoxiang Zhu, Lee Gunderson, Stuart R. Hudson. 2021-07-27. Computation of the Biot-Savart line integral with higher-order convergence using straight segments. https://doi.org/10.1063/5.0058014

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