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

Bodwin, G. T.; Chung, H. S.; Repond, J.

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 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.

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)

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.  https://doi.org/10.1088/1748-0221/14/07/P07002.

Copy to clipboard


                    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.  https://doi.org/10.1088/1748-0221/14/07/P07002

Copy to clipboard


                    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.  https://doi.org/10.1088/1748-0221/14/07/P07002.  https://www.osti.gov/servlets/purl/1559865.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1088/1748-0221/14/07/P07002

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Classification of Arnold-Beltrami flows and their hidden symmetries

Journal Article Fré, P., E-mail: fre@to.infn.it ; National Research Nuclear University MEPhI ; Sorin, A. S., E-mail: sorin@theor.jinr.ru ; ... - Physics of Particles and Nuclei

In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold’s theorem stating that, for flows taking place on compact three manifolds ℳ{sub 3}, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★{sub g }d, which canmore »« less
https://doi.org/10.1134/S1063779615040036
Kinetic stability properties of an intense relativistic electron ring in a high-current betatron accelerator

Journal Article Uhm, H S ; Davidson, R C ; Petillo, J J - Phys. Fluids; (United States)

The kinetic stability properties of an intense relativistic electron ringlocated at the midplane of an externally applied betatron field are investigatedwithin the framework of the linearized Vlasov--Maxwell equations, including the important influence of electromagnetic effects and surface-wave perturbations. Stability properties are calculated for eigenfrequency ..omega.. near harmonics of the relativistic cyclotron frequency ..omega../sub c/z in the applied betatron field. Making use of the large-aspect-ratio assumption (R/sub 0/>>a/sub c/), a closed algebraic dispersion relation is obtained for the longitudinal instability, assuming that the electron ring is located inside a perfectly conducting toroidal shell. Several points are noteworthy in this analysis. First,more »« less
https://doi.org/10.1063/1.865261
Finite difference solutions of Maxwell's equations in three dimensions

Thesis/Dissertation Cleveland, F H

The method of finite differences is used successfully to solve elliptic second-order partial differential equations. For Laplace's equation (..delta..E = 0) and Poisson's equation (..delta..E = G(x,y,z)), there is little difficulty in applying finite difference equations. However, for the Helmholz equation (..delta..E + k/sup 2/E = 0), which is derived from Maxwell's equations, there has arisen problems which have limited application of this method. This dissertation investigates these problems and suggest ways to alleviate them. Included is an analysis of the numerical errors, an example of an application to microwave circuits, a discussion of other applications to specific problems andmore »« less
Theoretical Model for the EM Effects Induced by High-Energy Photons (Gamma, X-ray) in Dielectric Materials and Electronic Systems

Technical Report Yee, J H ; Mayhall, D J ; Bland, M F

During last twenty years, a number of models have been used to calculate the change of conductivity and dielectric strength in materials caused by the passage of high-energy photons, such as Gamma-rays and X-rays. In these models, the electromagnetic fields generated in the electronic system created by the high-energy photons have not been investigated. That is, the solution of Maxwell's equations has not been obtained for these kinds of problems. We constructed a theoretical model, described by a set of equations to solve such a problem. The model includes the equations that describe the physics of the recombination and generationmore »« less
https://doi.org/10.2172/15004648

Full Text Available
Electric and magnetic losses modeled by a stable hybrid with explicit-implicit time-stepping for Maxwell's equations

Journal Article Halleroed, Tomas ; Rylander, Thomas - Journal of Computational Physics

A stable hybridization of the finite-element method (FEM) and the finite-difference time-domain (FDTD) scheme for Maxwell's equations with electric and magnetic losses is presented for two-dimensional problems. The hybrid method combines the flexibility of the FEM with the efficiency of the FDTD scheme and it is based directly on Ampere's and Faraday's law. The electric and magnetic losses can be treated implicitly by the FEM on an unstructured mesh, which allows for local mesh refinement in order to resolve rapid variations in the material parameters and/or the electromagnetic field. It is also feasible to handle larger homogeneous regions with lossesmore »« less
https://doi.org/10.1016/j.jcp.2008.01.007

Similar Records

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