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, a small number of free parameters and sparse input data can lead to highly accurate, finegrained 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.
 Authors:

 Northwestern U.
 Trinity Coll., Hartford
 Fermilab
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1557467
 Report Number(s):
 arXiv:1901.02498; Reportno: FERMILABPUB19006TD; FERMILABPUB19006TD; NUHEPEXP/1902
1712857
 DOE Contract Number:
 AC0207CH11359
 Resource Type:
 Journal Article
 Journal Name:
 TBD
 Additional Journal Information:
 Journal Name: TBD
 Country of Publication:
 United States
 Language:
 English
 Subject:
 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Pollack, Brian, Pellico, Ryan, Kampa, Cole, Glass, Henry, and Schmitt, Michael. Modeling Magnetic Fields with Helical Solutions to Laplace's Equation. United States: N. p., 2019.
Web.
Pollack, Brian, Pellico, Ryan, Kampa, Cole, Glass, Henry, & Schmitt, Michael. Modeling Magnetic Fields with Helical Solutions to Laplace's Equation. United States.
Pollack, Brian, Pellico, Ryan, Kampa, Cole, Glass, Henry, and Schmitt, Michael. Tue .
"Modeling Magnetic Fields with Helical Solutions to Laplace's Equation". United States. https://www.osti.gov/servlets/purl/1557467.
@article{osti_1557467,
title = {Modeling Magnetic Fields with Helical Solutions to Laplace's Equation},
author = {Pollack, Brian and Pellico, Ryan and Kampa, Cole and Glass, Henry and Schmitt, Michael},
abstractNote = {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, a small number of free parameters and sparse input data can lead to highly accurate, finegrained 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.},
doi = {},
journal = {TBD},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {1}
}
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