Modeling Magnetic Fields with Helical Solutions to Laplace’s Equation
ORAL
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.
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.
*We gratefully acknowledge the support provided by the Department of Energy under award number DE-SC0015910. This document was prepared by members of the Mu2e Collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359.
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Presenters
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Cole Kampa
- Northwestern University