skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
ORCiD logo [1];  [2]; ORCiD logo [2];  [1];  [1]
  1. Univ. of Science and Techology of China, Hefei (China)
  2. 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:
Journal Article: Accepted Manuscript
Journal Name:
Plasma Physics and Controlled Fusion
Additional Journal Information:
Journal Name: Plasma Physics and Controlled Fusion; 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. doi: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. doi:10.1088/1361-6587/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 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 = ,
volume = ,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2018},
month = {Thu Mar 15 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on March 15, 2019
Publisher's Version of Record

Save / Share: