Particle accelerators use powerful and complex magnetic fields to turn, shape, and eventually collide beams of near-light-speed particles, yet the fundamental magnetic principles behind the accelerator magnets can be understood by undergraduate students. In this paper, we use small-scale accelerator magnet analogs in a multi-faceted, low-cost exploration of the magnetic field exterior to accelerator magnets. These fields are best understood using the multipole expansion of the field. If we assume that the magnetic field is created by ideal magnetic dipoles, we can derive a theoretical model that shows that each accelerator magnet configuration is dominated by a single multipole moment and obeys , where l is the multipole order (with for the dipole, quadrupole, octopole, and hexadecapole moments, respectively). Using commercially available NdFeB magnets and the magnetic field sensor inside a smartphone, we experimentally verify the power-law dependence of the accelerator magnet configurations. Finally, we use the open-source Python library Magpylib to simulate the magnetic field of the permanent magnet configurations, showing good agreement among theory, experiment, and simulation.
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Investigating the magnetic field outside small accelerator magnet analogs via
experiment, simulation, and theory
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June 2023
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June 01 2023
Investigating the magnetic field outside small accelerator magnet analogs via
experiment, simulation, and theory
Kelley D. Sullivan
;
Kelley D. Sullivan
a)
Department of Physics & Astronomy, Ithaca College
,
Ithaca, New York 14850
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Antara Sen
;
Antara Sen
b)
Department of Physics & Astronomy, Ithaca College
,
Ithaca, New York 14850
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M. C. Sullivan
M. C. Sullivan
c)
Department of Physics & Astronomy, Ithaca College
,
Ithaca, New York 14850
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a)
ORCID: 0000-0003-2379-0132.
b)
ORCID: 0000-0002-0999-9370.
c)
Electronic mail: [email protected], ORCID: 0000-0002-3782-835X.
Am. J. Phys. 91, 432–439 (2023)
Article history
Received:
August 26 2021
Accepted:
March 25 2023
Citation
Kelley D. Sullivan, Antara Sen, M. C. Sullivan; Investigating the magnetic field outside small accelerator magnet analogs via experiment, simulation, and theory. Am. J. Phys. 1 June 2023; 91 (6): 432–439. https://doi.org/10.1119/5.0068701
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