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

Journal Article · 01 July 2019 · Journal of Instrumentation

DOI: https://doi.org/10.1088/1748-0221/14/07/P07002 · OSTI ID:1559865

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

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

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.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: Alexander von Humboldt Foundation, Bonn (Germany); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1559865
• Alternate ID(s): OSTI ID: 22895944
• Journal Information: Journal of Instrumentation, Journal Name: Journal of Instrumentation Journal Issue: 07 Vol. 14; ISSN 1748-0221
• Publisher: Institute of Physics (IOP)Copyright Statement
• Country of Publication: United States
• Language: English