Hessian matrix approach for determining error field sensitivity to coil deviations.
Abstract
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 proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.
- Authors:
-
[1];
[2];
- Univ. of Science and Techology of China, Hefei (China)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1429101
- Grant/Contract Number:
- No. 201506340040; AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Plasma Physics and Controlled Fusion
- Additional Journal Information:
- Journal Volume: 60; Journal Issue: 5; Journal ID: ISSN 0741-3335
- Publisher:
- IOP Science
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
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., 2018.
Web. doi:10.1088/1361-6587/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. https://doi.org/10.1088/1361-6587/aab6cb
Zhu, Caoxiang, Hudson, Stuart R., Lazerson, Samuel A., Song, Yuntao, and Wan, Yuanxi. Thu .
"Hessian matrix approach for determining error field sensitivity to coil deviations.". United States. https://doi.org/10.1088/1361-6587/aab6cb. https://www.osti.gov/servlets/purl/1429101.
@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 proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.},
doi = {10.1088/1361-6587/aab6cb},
journal = {Plasma Physics and Controlled Fusion},
number = 5,
volume = 60,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2018},
month = {Thu Mar 15 00:00:00 EDT 2018}
}
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Works referencing / citing this record:
Error fields in the Wendelstein 7-X stellarator
journal, November 2018
- Lazerson, Samuel A.; Bozhenkov, Sergey; Israeli, Ben
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 12