Modeling magnetic fields with helical solutions to Laplace's equation

Brian Pollack*, Ryan Pellico, Cole Kampa, Henry Glass, Michael Schmitt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 motivated by geometry, a small number of free parameters, and sparse input data can lead to highly accurate, fine-grained 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.

Keywords

  • High energy physics
  • Magnetic fields
  • Numerical methods

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Instrumentation

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