# 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:

- 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:

- 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.
```

```
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.
```

```
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.
```

```
@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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