A new continuous optimization method of standardized cubic permanent magnets for stellarators
Stellarator configurations can be realized using permanent magnets in combination with tokamak-like planar coils. From the perspective of engineering feasibility and cost-effectiveness, using standardized cubic permanent magnets with a finite number of magnetization directions is particularly advant...
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| Main Authors: | , , , , , , , |
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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/adab06 |
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| _version_ | 1832582517248491520 |
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| author | Xiangyu Zhang Dehong Chen Guosheng Xu Zhiyuan Lu Caoxiang Zhu Liang Chen Minyou Ye Baonian Wan |
| author_facet | Xiangyu Zhang Dehong Chen Guosheng Xu Zhiyuan Lu Caoxiang Zhu Liang Chen Minyou Ye Baonian Wan |
| author_sort | Xiangyu Zhang |
| collection | DOAJ |
| description | Stellarator configurations can be realized using permanent magnets in combination with tokamak-like planar coils. From the perspective of engineering feasibility and cost-effectiveness, using standardized cubic permanent magnets with a finite number of magnetization directions is particularly advantageous. However, optimizing the discrete magnetization directions of tens of thousands of cubic magnets poses a significant challenge. This paper introduces a novel method that converts the discrete optimization problem into a continuous nonlinear optimization problem, enabling the direct application of well-established nonlinear optimization algorithms. This approach leverages a specially tailored continuous function to represent the magnetization moment and incorporates a penalty term to ensure the direction vector converges to one of the discrete points. Subsequently, a discrete solution for the magnetization direction distribution is derived by truncating the continuous solution and eliminating adjacent magnets with opposing magnetization directions. The proposed optimization method is validated using the ESTELL stellarator configuration as a case study. The results demonstrate that the designed distribution of cubic permanent magnets can accurately reproduce the intended magnetic field configuration. |
| format | Article |
| id | doaj-art-6f8ca80c33df4bff8bce51d06be36c44 |
| institution | Kabale University |
| issn | 0029-5515 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Nuclear Fusion |
| spelling | doaj-art-6f8ca80c33df4bff8bce51d06be36c442025-01-29T15:22:35ZengIOP PublishingNuclear Fusion0029-55152025-01-0165202606010.1088/1741-4326/adab06A new continuous optimization method of standardized cubic permanent magnets for stellaratorsXiangyu Zhang0Dehong Chen1https://orcid.org/0000-0003-3655-1819Guosheng Xu2https://orcid.org/0000-0001-8495-8678Zhiyuan Lu3https://orcid.org/0000-0002-6860-3831Caoxiang Zhu4https://orcid.org/0000-0003-2337-3232Liang Chen5https://orcid.org/0000-0002-7176-4978Minyou Ye6https://orcid.org/0000-0002-9055-1476Baonian Wan7Institute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, China; University of Science and Technology of China , Hefei 230026, ChinaInstitute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, ChinaInstitute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, ChinaInstitute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, ChinaUniversity of Science and Technology of China , Hefei 230026, ChinaInstitute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, ChinaUniversity of Science and Technology of China , Hefei 230026, ChinaInstitute of Plasma Physics , Chinese Academy of Sciences, Hefei 230031, ChinaStellarator configurations can be realized using permanent magnets in combination with tokamak-like planar coils. From the perspective of engineering feasibility and cost-effectiveness, using standardized cubic permanent magnets with a finite number of magnetization directions is particularly advantageous. However, optimizing the discrete magnetization directions of tens of thousands of cubic magnets poses a significant challenge. This paper introduces a novel method that converts the discrete optimization problem into a continuous nonlinear optimization problem, enabling the direct application of well-established nonlinear optimization algorithms. This approach leverages a specially tailored continuous function to represent the magnetization moment and incorporates a penalty term to ensure the direction vector converges to one of the discrete points. Subsequently, a discrete solution for the magnetization direction distribution is derived by truncating the continuous solution and eliminating adjacent magnets with opposing magnetization directions. The proposed optimization method is validated using the ESTELL stellarator configuration as a case study. The results demonstrate that the designed distribution of cubic permanent magnets can accurately reproduce the intended magnetic field configuration.https://doi.org/10.1088/1741-4326/adab06stellaratorpermanent magnetnumerical optimizationpolarization function |
| spellingShingle | Xiangyu Zhang Dehong Chen Guosheng Xu Zhiyuan Lu Caoxiang Zhu Liang Chen Minyou Ye Baonian Wan A new continuous optimization method of standardized cubic permanent magnets for stellarators Nuclear Fusion stellarator permanent magnet numerical optimization polarization function |
| title | A new continuous optimization method of standardized cubic permanent magnets for stellarators |
| title_full | A new continuous optimization method of standardized cubic permanent magnets for stellarators |
| title_fullStr | A new continuous optimization method of standardized cubic permanent magnets for stellarators |
| title_full_unstemmed | A new continuous optimization method of standardized cubic permanent magnets for stellarators |
| title_short | A new continuous optimization method of standardized cubic permanent magnets for stellarators |
| title_sort | new continuous optimization method of standardized cubic permanent magnets for stellarators |
| topic | stellarator permanent magnet numerical optimization polarization function |
| url | https://doi.org/10.1088/1741-4326/adab06 |
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