Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section
For designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest fo...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | Nuclear Fusion |
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| Online Access: | https://doi.org/10.1088/1741-4326/adb04e |
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| author | Matt Landreman Siena Hurwitz Thomas M. Antonsen |
| author_facet | Matt Landreman Siena Hurwitz Thomas M. Antonsen |
| author_sort | Matt Landreman |
| collection | DOAJ |
| description | For designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest for computing stress and strain, and due to superconducting quench limits. For these force, inductance, energy, and internal field calculations, the coils cannot be naively approximated as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables the internal magnetic field vector, self-force, and self-inductance to be computed rapidly and accurately within a 1D filament model. The method is applicable to coils for which the curve center-line can have general noncircular shape, as long as the conductor width is small compared to the radius of curvature. This paper extends a previous calculation for circular-cross-section conductors (Hurwitz et al 2024 IEEE Trans. Magn. ) to consider the case of rectangular cross-section. The reduced model is derived by rigorous analysis of the singularity, regularizing the filament integrals such that they match the true high-dimensional integrals at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce full finite-cross-section calculations for a non-planar coil of a stellarator magnetic fusion device. Due to the efficiency of the model here, it is well suited for use inside design optimization. |
| format | Article |
| id | doaj-art-256fad7f2a064a30a8529db61efdc794 |
| institution | Kabale University |
| issn | 0029-5515 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Nuclear Fusion |
| spelling | doaj-art-256fad7f2a064a30a8529db61efdc7942025-02-10T09:06:59ZengIOP PublishingNuclear Fusion0029-55152025-01-0165303600810.1088/1741-4326/adb04eEfficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-sectionMatt Landreman0https://orcid.org/0000-0002-7233-577XSiena Hurwitz1https://orcid.org/0000-0001-6659-9659Thomas M. Antonsen2Institute for Research in Electronics and Applied Physics , University of Maryland, College Park, MD 20740, United States of AmericaInstitute for Research in Electronics and Applied Physics , University of Maryland, College Park, MD 20740, United States of AmericaInstitute for Research in Electronics and Applied Physics , University of Maryland, College Park, MD 20740, United States of AmericaFor designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest for computing stress and strain, and due to superconducting quench limits. For these force, inductance, energy, and internal field calculations, the coils cannot be naively approximated as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables the internal magnetic field vector, self-force, and self-inductance to be computed rapidly and accurately within a 1D filament model. The method is applicable to coils for which the curve center-line can have general noncircular shape, as long as the conductor width is small compared to the radius of curvature. This paper extends a previous calculation for circular-cross-section conductors (Hurwitz et al 2024 IEEE Trans. Magn. ) to consider the case of rectangular cross-section. The reduced model is derived by rigorous analysis of the singularity, regularizing the filament integrals such that they match the true high-dimensional integrals at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce full finite-cross-section calculations for a non-planar coil of a stellarator magnetic fusion device. Due to the efficiency of the model here, it is well suited for use inside design optimization.https://doi.org/10.1088/1741-4326/adb04eelectromagnetic coilself-inductancemagnetic energyself-forceLorentz forcestellarator |
| spellingShingle | Matt Landreman Siena Hurwitz Thomas M. Antonsen Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section Nuclear Fusion electromagnetic coil self-inductance magnetic energy self-force Lorentz force stellarator |
| title | Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section |
| title_full | Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section |
| title_fullStr | Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section |
| title_full_unstemmed | Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section |
| title_short | Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section |
| title_sort | efficient calculation of self magnetic field self force and self inductance for electromagnetic coils with rectangular cross section |
| topic | electromagnetic coil self-inductance magnetic energy self-force Lorentz force stellarator |
| url | https://doi.org/10.1088/1741-4326/adb04e |
| work_keys_str_mv | AT mattlandreman efficientcalculationofselfmagneticfieldselfforceandselfinductanceforelectromagneticcoilswithrectangularcrosssection AT sienahurwitz efficientcalculationofselfmagneticfieldselfforceandselfinductanceforelectromagneticcoilswithrectangularcrosssection AT thomasmantonsen efficientcalculationofselfmagneticfieldselfforceandselfinductanceforelectromagneticcoilswithrectangularcrosssection |