Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring

doi:10.1088/1748-0221/14/07/P07002

Title: Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring

Abstract

We present a method for implementing the constraints that are implied by Maxwell's equations in fits to measurements of the magnetic field in the muon storage ring of the $g - 2$ experiment. The method that we use makes use of toroidal-harmonic solutions of Laplace's equation. We point out that the fitting problem can be approximated well as a linear-algebra problem. We have devised an efficient algorithm for the linear-algebra problem that makes it possible to find a solution for 10 ⁵ data points and 10 ⁴ harmonics in less than an hour on a present-day desktop computer. We illustrate our method by applying it to some preliminary measurements of the magnetic field in the $g - 2$ storage ring.

Authors:

Bodwin, G. T. ^[1]; Chung, H. S. ^[2]; Repond, J. ^[3]

Argonne National Lab. (ANL), Argonne, IL (United States). Dept. of High Energy Physics
Technische Universität München, Garching (Germany). Physik-Dept.
European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Dept.

Publication Date:: 2019-07-02

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: Alexander von Humboldt Foundation, Bonn (Germany); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

OSTI Identifier:: 1559865

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Instrumentation

Additional Journal Information:: Journal Volume: 14; Journal Issue: 07; Journal ID: ISSN 1748-0221

Publisher:: Institute of Physics (IOP)

Country of Publication:: United States

Language:: English

Subject:: 43 PARTICLE ACCELERATORS; acceleration cavities and magnets superconducting (high-temperature superconductor; radiation hardened magnets; normal-conducting; permanent magnet devices; wigglers and undulators); instrumentation for particle accelerators and storage rings - low energy (linear accelerators, cyclotrons, electrostatic accelerators)

Citation Formats


                    Bodwin, G. T., Chung, H. S., and Repond, J. Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring.  United States: N. p., 2019. 
        Web.  doi:10.1088/1748-0221/14/07/P07002.

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                    Bodwin, G. T., Chung, H. S., & Repond, J. Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring.  United States.  doi:10.1088/1748-0221/14/07/P07002.

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                    Bodwin, G. T., Chung, H. S., and Repond, J. Tue .  
        "Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring".  United States.  doi:10.1088/1748-0221/14/07/P07002.  https://www.osti.gov/servlets/purl/1559865.

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@article{osti_1559865,

  title        = {Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring},

  author       = {Bodwin, G. T. and Chung, H. S. and Repond, J.},

  abstractNote = {We present a method for implementing the constraints that are implied by Maxwell's equations in fits to measurements of the magnetic field in the muon storage ring of the $g - 2$ experiment. The method that we use makes use of toroidal-harmonic solutions of Laplace's equation. We point out that the fitting problem can be approximated well as a linear-algebra problem. We have devised an efficient algorithm for the linear-algebra problem that makes it possible to find a solution for 105 data points and 104 harmonics in less than an hour on a present-day desktop computer. We illustrate our method by applying it to some preliminary measurements of the magnetic field in the $g - 2$ storage ring.},

  doi          = {10.1088/1748-0221/14/07/P07002},

  journal      = {Journal of Instrumentation},

  number       = 07,

  volume       = 14,

  place        = {United States},

  year         = {2019},

  month        = {7}

}

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Journal Article:

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DOI: 10.1088/1748-0221/14/07/P07002

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Works referenced in this record:

On Toroidal Functions
journal, October 1893

Basset, A. B.
American Journal of Mathematics, Vol. 15, Issue 4
DOI: 10.2307/2369515

Method of magnetic analysis for stellarator equilibria
journal, March 1997

Kuznetsov, A. B.; Shchepetov, S. V.
Nuclear Fusion, Vol. 37, Issue 3
DOI: 10.1088/0029-5515/37/3/I07

On best approximate solutions of linear matrix equations
journal, January 1956

Penrose, R.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 52, Issue 1
DOI: 10.1017/s0305004100030929

Expansion of vacuum magnetic fields in toroidal harmonics
journal, June 1994

van Milligen, B. Ph.; Lopez Fraguas, A.
Computer Physics Communications, Vol. 81, Issue 1-2
DOI: 10.1016/0010-4655(94)90112-0

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Title: Implementation of Maxwell's equations in the reconstruction of the magnetic field in the g -2 storage ring

Abstract

Citation Formats

On Toroidal Functions journal, October 1893

Method of magnetic analysis for stellarator equilibria journal, March 1997

On best approximate solutions of linear matrix equations journal, January 1956

Expansion of vacuum magnetic fields in toroidal harmonics journal, June 1994

On Toroidal Functions
journal, October 1893

Method of magnetic analysis for stellarator equilibria
journal, March 1997

On best approximate solutions of linear matrix equations
journal, January 1956

Expansion of vacuum magnetic fields in toroidal harmonics
journal, June 1994