TY - JOUR
T1 - Modeling magnetic fields with helical solutions to Laplace's equation
AU - Pollack, Brian
AU - Pellico, Ryan
AU - Kampa, Cole
AU - Glass, Henry
AU - Schmitt, Michael
N1 - Funding Information:
The authors would like to thank Matt Bonakdarpour for helpful discussions. 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. We thank the reviewers for providing helpful comments on earlier drafts of the manuscript.
Funding Information:
The authors would like to thank Matt Bonakdarpour for helpful discussions. 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 . We thank the reviewers for providing helpful comments on earlier drafts of the manuscript.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/10/11
Y1 - 2020/10/11
N2 - 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.
AB - 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.
KW - High energy physics
KW - Magnetic fields
KW - Numerical methods
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U2 - 10.1016/j.nima.2020.164303
DO - 10.1016/j.nima.2020.164303
M3 - Article
AN - SCOPUS:85087509918
VL - 977
JO - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
JF - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
SN - 0168-9002
M1 - 164303
ER -