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arXiv · 1901.02498

Modeling Magnetic Fields with Helical Solutions to Laplace's Equation

Brian Pollack·Ryan Pellico·Cole Kampa·Henry Glass·Michael Schmitt
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Abstract

The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via linear, multidimensional curve-fitting. A judicious choice of functional forms, a small number of free parameters and sparse input data can lead to highly accurate, fine-grained modeling of solenoidal magnetic fields, including helical features arising from the winding of the solenoid, with overall field accuracy at better than one part per million.

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Brian Pollack, Ryan Pellico, Cole Kampa, Henry Glass, Michael Schmitt. 2019-01-08. Modeling Magnetic Fields with Helical Solutions to Laplace's Equation. https://doi.org/10.1016/j.nima.2020.164303

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