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:
-
- 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:
- 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
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
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. https://doi.org/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. https://doi.org/10.1088/1741-4326/ab3a7c. https://www.osti.gov/servlets/purl/1567254.
@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}
}
Web of Science
Works referenced in this record:
Coil tolerance impact on plasma surface quality for NCSX
conference, January 2003
- Brooks, A.; Reiersen, W.
- 20th IEEE/NPSS Symposium onFusion Engineering, 2003.
Accuracy of the Construction of the Superconducting Coils for WENDELSTEIN 7-X
journal, June 2004
- Rummel, T.; Risse, K.; Viebke, H.
- IEEE Transactions on Appiled Superconductivity, Vol. 14, Issue 2
Lessons Learned in Risk Management on NCSX
journal, March 2010
- Neilson, G. H.; Gruber, C. O.; Harris, J. H.
- IEEE Transactions on Plasma Science, Vol. 38, Issue 3
Engineering cost & schedule lessons learned on NCSX
conference, June 2009
- Strykowsky, R. L.; Brown, T.; Chrzanowski, J.
- 2009 23rd IEEE/NPSS Symposium on Fusion Engineering - SOFE
Methods for measuring 1/1 error field in Wendelstein 7-X stellarator
journal, June 2016
- Bozhenkov, S. A.; Lazerson, S.; Otte, M.
- Nuclear Fusion, Vol. 56, Issue 7
Quasi-helically symmetric toroidal stellarators
journal, May 1988
- Nührenberg, J.; Zille, R.
- Physics Letters A, Vol. 129, Issue 2
Requirements for accuracy of superconducting coils in the Large Helical Device
journal, January 1993
- Yamazaki, K.; Yanagi, N.; Ji, H.
- Fusion Engineering and Design, Vol. 20
Non-axisymmetric magnetic fields and toroidal plasma confinement
journal, January 2015
- Boozer, Allen H.
- Nuclear Fusion, Vol. 55, Issue 2
Modular coil design developments for the National Compact Stellarator Experiment (NCSX)
journal, November 2005
- Williamson, D.; Brooks, A.; Brown, T.
- Fusion Engineering and Design, Vol. 75-79
Physics of the compact advanced stellarator NCSX
journal, November 2001
- Zarnstorff, M. C.; Berry, L. A.; Brooks, A.
- Plasma Physics and Controlled Fusion, Vol. 43, Issue 12A
Transport and isomorphic equilibria
journal, January 1983
- Boozer, Allen H.
- Physics of Fluids, Vol. 26, Issue 2
Three-dimensional free boundary calculations using a spectral Green's function method
journal, December 1986
- Hirshman, S. P.; van RIJ, W. I.; Merkel, P.
- Computer Physics Communications, Vol. 43, Issue 1
SOL studies for W7-X based on the island divertor concept
journal, July 1996
- Strumberger, E.
- Nuclear Fusion, Vol. 36, Issue 7
Properties of a new quasi-axisymmetric configuration
journal, January 2019
- Henneberg, S. A.; Drevlak, M.; Nührenberg, C.
- Nuclear Fusion, Vol. 59, Issue 2
Influence of construction errors on Wendelstein 7-X magnetic configurations
journal, June 2009
- Andreeva, T.; Bräuer, T.; Endler, M.
- Fusion Engineering and Design, Vol. 84, Issue 2-6
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
Ballooning stability optimization of low-aspect-ratio stellarators*
journal, May 2000
- Sanchez, R.; Hirshman, S. P.; Ware, A. S.
- Plasma Physics and Controlled Fusion, Vol. 42, Issue 6
Critical error fields for locked mode instability in tokamaks
journal, March 1992
- La Haye, R. J.; Fitzpatrick, R.; Hender, T. C.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7
Computing local sensitivity and tolerances for stellarator physics properties using shape gradients
journal, June 2018
- Landreman, Matt; Paul, Elizabeth
- Nuclear Fusion, Vol. 58, Issue 7
Theory and observations of magnetic islands
journal, September 2009
- Waelbroeck, F. L.
- Nuclear Fusion, Vol. 49, Issue 10
Stellarator design
journal, December 2015
- Boozer, Allen H.
- Journal of Plasma Physics, Vol. 81, Issue 6
Construction of an integrable field close to any non-integrable toroidal magnetic field
journal, October 1998
- Hudson, S. R.; Dewar, R. L.
- Physics Letters A, Vol. 247, Issue 3
Differentiating the shape of stellarator coils with respect to the plasma boundary
journal, September 2018
- Hudson, S. R.; Zhu, C.; Pfefferlé, D.
- Physics Letters A, Vol. 382, Issue 38
Quasi-axially symmetric stellarators
journal, August 1998
- Garabedian, P. R.
- Proceedings of the National Academy of Sciences, Vol. 95, Issue 17
Experimental and numerical study of error fields in the CNT stellarator
journal, May 2016
- Hammond, K. C.; Anichowski, A.; Brenner, P. W.
- Plasma Physics and Controlled Fusion, Vol. 58, Issue 7
Correction possibilities of magnetic field errors in WENDELSTEIN 7-X
journal, November 2005
- Kißlinger, J.; Andreeva, T.
- Fusion Engineering and Design, Vol. 74, Issue 1-4
Magnetic Configuration and Modular Coil Design for the Chinese First Quasi-Axisymmetric Stellarator
journal, January 2018
- Liu, Haifeng; Shimizu, Akihiro; Isobe, Mitsutaka
- Plasma and Fusion Research, Vol. 13, Issue 0
Eliminating Islands in High-Pressure Free-Boundary Stellarator Magnetohydrodynamic Equilibrium Solutions
journal, December 2002
- Hudson, S. R.; Monticello, D. A.; Reiman, A. H.
- Physical Review Letters, Vol. 89, Issue 27
Destruction of magnetic surfaces by magnetic field irregularities
journal, December 1966
- Rosenbluth, M. N.; Sagdeev, R. Z.; Taylor, J. B.
- Nuclear Fusion, Vol. 6, Issue 4
Configuration Property of the Chinese First Quasi-Axisymmetric Stellarator
journal, January 2018
- Shimizu, Akihiro; Liu, Haifeng; Isobe, Mitsutaka
- Plasma and Fusion Research, Vol. 13, Issue 0
The Helically Symmetric Experiment, (HSX) Goals, Design and Status
journal, April 1995
- Anderson, F. Simon B.; Almagri, Abdulgader F.; Anderson, David T.
- Fusion Technology, Vol. 27, Issue 3T
Lessons learned in risk management on NCSX
conference, June 2009
- Neilson, G. H.; Gruber, C. O.; Harris, J. H.
- 2009 23rd IEEE/NPSS Symposium on Fusion Engineering - SOFE
Experimental and numerical study of error fields in the CNT stellarator
text, January 2016
- Hammond, K. C.; Anichowski, A.; Brenner, P. W.
- arXiv