skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Modeling magnetic fields with helical solutions to Laplace’s equation

Journal Article · · Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment
 [1];  [2];  [1];  [3];  [1]
  1. Northwestern Univ., Evanston, IL (United States)
  2. Trinity College, Hartford, CT (United States)
  3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
+ Show Author Affiliations

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.

Research Organization:
Univ. of Pittsburgh, PA (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0015910; AC02-07CH11359
OSTI ID:
1637891
Alternate ID(s):
OSTI ID: 1557467; OSTI ID: 1637751
Report Number(s):
arXiv:1901.02498; Report-no: FERMILAB-PUB-19-006-TD; FERMILAB-PUB-19-006-TD; NUHEP-EXP/19-02; TRN: US2201675
Journal Information:
Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 977, Issue C; ISSN 0168-9002
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

References (10)

The CMS Magnetic Field Map Performance journal June 2010
Measurement of the ATLAS solenoid magnetic field journal April 2008
A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems journal January 1999
The effects of realistic pancake solenoids on particle transport
  • Gu, X.; Okamura, M.; Pikin, A.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 637, Issue 1 https://doi.org/10.1016/j.nima.2011.01.123
journal May 2011
Status of the ALICE magnet system journal March 2002
A Helical Coordinate System and its Applications in Electromagnetic Theory journal January 1958
Hall Probe Calibration System Design for the Mu2e Solenoid Field Mapping System journal April 2018
Comparison of magnetic field uniformities for discretized and finite-sized standard , solenoidal, and spherical coils journal September 2013
Helical harmonics for static fields journal August 2001
LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python software September 2014

Similar Records

Expansion solution of Laplace`s equation: Technique and application to hollow beam gun design
Conference · Tue Dec 31 00:00:00 EST 1996 · OSTI ID:1637891
Chiral charge erasure via thermal fluctuations of magnetic helicity
Journal Article · Wed May 11 00:00:00 EDT 2016 · Journal of Cosmology and Astroparticle Physics · OSTI ID:1637891
Analysis of magnetic measurement data by least squares fit to series expansion solution of 3-D Laplace equation
Technical Report · Sun Mar 01 00:00:00 EST 1992 · OSTI ID:1637891

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY
high energy physics
magnetic fields
numerical methods