Modeling magnetic fields with helical solutions to Laplace's equation
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 curvefitting. A judicious choice of functional forms motivated by geometry, a small number of free parameters, and sparse input data can lead to highly accurate, finegrained modeling of solenoidal magnetic fields. These models capture the helical features arising from the winding of the solenoid, with overall field accuracy at better than one part per million.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 October 2020
 DOI:
 10.1016/j.nima.2020.164303
 arXiv:
 arXiv:1901.02498
 Bibcode:
 2020NIMPA.97764303P
 Keywords:

 High energy physics;
 Magnetic fields;
 Numerical methods;
 Physics  Instrumentation and Detectors;
 High Energy Physics  Experiment
 EPrint:
 22 pages, 16 figures