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

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:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1];  [2];  [2]; ORCiD logo [3]; ORCiD logo [3]
  1. Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.
  2. Southwest Jiaotong Univ., Chengdu (China). Inst. of Fusion Science
  3. National Inst. for Fusion Science, National Inst. of Natural Sciences, Toki (Japan)
Publication Date:
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.
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.
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.
@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}
}

Journal Article:
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This content will become publicly available on September 20, 2020
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