Hessian matrix approach for determining error field sensitivity to coil deviations.
The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculations of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proofofprinciple example is given on a CNTlike configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.
 Authors:

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 Univ. of Science and Techology of China, Hefei (China)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Grant/Contract Number:
 No. 201506340040; AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 Plasma Physics and Controlled Fusion
 Additional Journal Information:
 Journal Volume: 60; Journal Issue: 5; Journal ID: ISSN 07413335
 Publisher:
 IOP Science
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
 OSTI Identifier:
 1429101
Zhu, Caoxiang, Hudson, Stuart R., Lazerson, Samuel A., Song, Yuntao, and Wan, Yuanxi. Hessian matrix approach for determining error field sensitivity to coil deviations.. United States: N. p.,
Web. doi:10.1088/13616587/aab6cb.
Zhu, Caoxiang, Hudson, Stuart R., Lazerson, Samuel A., Song, Yuntao, & Wan, Yuanxi. Hessian matrix approach for determining error field sensitivity to coil deviations.. United States. doi:10.1088/13616587/aab6cb.
Zhu, Caoxiang, Hudson, Stuart R., Lazerson, Samuel A., Song, Yuntao, and Wan, Yuanxi. 2018.
"Hessian matrix approach for determining error field sensitivity to coil deviations.". United States.
doi:10.1088/13616587/aab6cb.
@article{osti_1429101,
title = {Hessian matrix approach for determining error field sensitivity to coil deviations.},
author = {Zhu, Caoxiang and Hudson, Stuart R. and Lazerson, Samuel A. and Song, Yuntao and Wan, Yuanxi},
abstractNote = {The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculations of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proofofprinciple example is given on a CNTlike configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.},
doi = {10.1088/13616587/aab6cb},
journal = {Plasma Physics and Controlled Fusion},
number = 5,
volume = 60,
place = {United States},
year = {2018},
month = {3}
}