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


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.


  • High energy physics
  • Magnetic fields
  • Numerical methods

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Instrumentation


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