Modeling Magnetic Fields with Helical Solutions to Laplace's Equation
Instrumentation and Detectors
2020-07-10 v2 High Energy Physics - Experiment
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.
Cite
@article{arxiv.1901.02498,
title = {Modeling Magnetic Fields with Helical Solutions to Laplace's Equation},
author = {Brian Pollack and Ryan Pellico and Cole Kampa and Henry Glass and Michael Schmitt},
journal= {arXiv preprint arXiv:1901.02498},
year = {2020}
}
Comments
22 pages, 16 figures