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Title: 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 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.

Authors:
 [1];  [2]; ORCiD logo [1];  [3]; ORCiD logo [1]
  1. Northwestern U.
  2. Trinity Coll., Hartford
  3. 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) (SC-25)
OSTI Identifier:
1557467
Report Number(s):
arXiv:1901.02498; Report-no: FERMILAB-PUB-19-006-TD; FERMILAB-PUB-19-006-TD; NUHEP-EXP/19-02
1712857
DOE Contract Number:  
AC02-07CH11359
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 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.},
doi = {},
journal = {TBD},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {1}
}