Full analytical solution for the magnetic field of uniformly magnetized cylinder tiles

F. Slanovc; M. Ortner; M. Moridi; C. Abert; D. Suess

doi:10.1016/j.jmmm.2022.169482

Full analytical solution for the magnetic field of uniformly magnetized cylinder tiles

F. Slanovc (Corresponding author)
, M. Ortner
, M. Moridi
, C. Abert
, D. Suess

Physics of Functional Materials

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments r∈R³. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder and a rotation sensor system.

Original language	English
Article number	169482
Number of pages	19
Journal	Journal of Magnetism and Magnetic Materials
Volume	559
DOIs	https://doi.org/10.1016/j.jmmm.2022.169482
Publication status	Published - 1 Oct 2022

Funding

This project has been supported by the COMET K1 center ASSIC Austrian Smart Systems Integration 100 Research Center. The COMET — Competence Centers for Excellent Technologies — Program is supported by BMVIT, 101 BMDW and the federal provinces of Carinthia and Styria. Financial support by the Vienna Doctoral School in Physics (VDSP) is also acknowledged.

Austrian Fields of Science 2012

103017 Magnetism

Keywords

Analytical expression
Cylinder
Cylinder tile
Halbach
Magnetic field
Surface charge
Surface integral
Uniformly magnetized

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10.1016/j.jmmm.2022.169482Licence: CC BY 4.0

https://phaidra.univie.ac.at/o:1637840Licence: CC BY 4.0

Cite this

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abstract = "We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments r∈R3. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder and a rotation sensor system.",

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AU - Slanovc, F.

AU - Ortner, M.

AU - Moridi, M.

AU - Abert, C.

AU - Suess, D.

PY - 2022/10/1

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N2 - We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments r∈R3. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder and a rotation sensor system.

AB - We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments r∈R3. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder and a rotation sensor system.

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KW - Cylinder

KW - Cylinder tile

KW - Halbach

KW - Magnetic field

KW - Surface charge

KW - Surface integral

KW - Uniformly magnetized

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JO - Journal of Magnetism and Magnetic Materials

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M1 - 169482

ER -

Full analytical solution for the magnetic field of uniformly magnetized cylinder tiles

Abstract

Funding

Austrian Fields of Science 2012

Keywords

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