Identification of important error fields in stellarators using the Hessian matrix method

doi:10.1088/1741-4326/ab3a7c

This content will become publicly available on September 20, 2020

Title: Identification of important error fields in stellarators using the Hessian matrix method

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Abstract

Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of the National Compact Stellarator Experiment and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming Chinese First Quasi-axisymmetric Stellarator configuration. Important perturbations that enlarge n/m = 4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to a substantial reduction in time and cost.

Authors:

^[1];

^[1]; Liu, Haifeng ^[2]; Xu, Yuhong ^[2];

^[3];

^[3]

Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.
Southwest Jiaotong Univ., Chengdu (China). Inst. of Fusion Science
National Inst. for Fusion Science, National Inst. of Natural Sciences, Toki (Japan)

Publication Date:: 2019-09-20

Research Org.:: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1567254

Grant/Contract Number:: AC02-09CH11466

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Fusion

Additional Journal Information:: Journal Volume: 59; Journal Issue: 12; Journal ID: ISSN 0029-5515

Publisher:: IOP Science

Country of Publication:: United States

Language:: English

Citation Formats


                    Zhu, Caoxiang, Gates, David A., Hudson, Stuart R., Liu, Haifeng, Xu, Yuhong, Shimizu, Akihiro, and Okamura, Shoichi. Identification of important error fields in stellarators using the Hessian matrix method.  United States: N. p., 2019. 
        Web.  doi:10.1088/1741-4326/ab3a7c.

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                    Zhu, Caoxiang, Gates, David A., Hudson, Stuart R., Liu, Haifeng, Xu, Yuhong, Shimizu, Akihiro, & Okamura, Shoichi. Identification of important error fields in stellarators using the Hessian matrix method.  United States.  doi:10.1088/1741-4326/ab3a7c.

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                    Zhu, Caoxiang, Gates, David A., Hudson, Stuart R., Liu, Haifeng, Xu, Yuhong, Shimizu, Akihiro, and Okamura, Shoichi. Fri .  
        "Identification of important error fields in stellarators using the Hessian matrix method".  United States.  doi:10.1088/1741-4326/ab3a7c.

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@article{osti_1567254,

  title        = {Identification of important error fields in stellarators using the Hessian matrix method},

  author       = {Zhu, Caoxiang and Gates, David A. and Hudson, Stuart R. and Liu, Haifeng and Xu, Yuhong and Shimizu, Akihiro and Okamura, Shoichi},

  abstractNote = {Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of the National Compact Stellarator Experiment and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming Chinese First Quasi-axisymmetric Stellarator configuration. Important perturbations that enlarge n/m = 4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to a substantial reduction in time and cost.},

  doi          = {10.1088/1741-4326/ab3a7c},

  journal      = {Nuclear Fusion},

  number       = 12,

  volume       = 59,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

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