Constructing stellarators with quasisymmetry to high order
Abstract
Here, a method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren & Boozer’s expansion about the magnetic axis (Phys Fluids B, vol. 3, 1991, p. 2805), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landremanet al. (J. Plasma Phys., vol. 85, 2019, 905850103), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect-ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer’s ideal scaling of quasisymmetry breaking with the cube of the inverse aspect ratio. We also demonstrate a strongly non-axisymmetric configuration (vacuum rotational transform $$\unicode[STIX]{x1D704} >0.4$$) in which symmetry-breaking mode amplitudes throughout a finite volume are $${<}2\times 10^{-7}$$, the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. In conclusion, the approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization.
- Authors:
-
[1];
[2]
- Univ. of Maryland, College Park, MD (United States). Inst. for Research in Electronics and Applied Physics
- New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); Simons Foundation
- OSTI Identifier:
- 1597688
- Grant/Contract Number:
- FG02-93ER54197; FG02-86ER53223; 560651
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Plasma Physics
- Additional Journal Information:
- Journal Volume: 85; Journal Issue: 6; Journal ID: ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Landreman, Matt, and Sengupta, Wrick. Constructing stellarators with quasisymmetry to high order. United States: N. p., 2019.
Web. doi:10.1017/S0022377819000783.
Landreman, Matt, & Sengupta, Wrick. Constructing stellarators with quasisymmetry to high order. United States. https://doi.org/10.1017/S0022377819000783
Landreman, Matt, and Sengupta, Wrick. Fri .
"Constructing stellarators with quasisymmetry to high order". United States. https://doi.org/10.1017/S0022377819000783. https://www.osti.gov/servlets/purl/1597688.
@article{osti_1597688,
title = {Constructing stellarators with quasisymmetry to high order},
author = {Landreman, Matt and Sengupta, Wrick},
abstractNote = {Here, a method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren & Boozer’s expansion about the magnetic axis (Phys Fluids B, vol. 3, 1991, p. 2805), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landremanet al. (J. Plasma Phys., vol. 85, 2019, 905850103), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect-ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer’s ideal scaling of quasisymmetry breaking with the cube of the inverse aspect ratio. We also demonstrate a strongly non-axisymmetric configuration (vacuum rotational transform $\unicode[STIX]{x1D704} >0.4$) in which symmetry-breaking mode amplitudes throughout a finite volume are ${<}2\times 10^{-7}$, the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. In conclusion, the approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization.},
doi = {10.1017/S0022377819000783},
journal = {Journal of Plasma Physics},
number = 6,
volume = 85,
place = {United States},
year = {2019},
month = {11}
}
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Works referenced in this record:
Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction
journal, May 2019
- Landreman, Matt
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 7
Quasi-helically symmetric toroidal stellarators
journal, May 1988
- Nührenberg, J.; Zille, R.
- Physics Letters A, Vol. 129, Issue 2
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
journal, January 1998
- Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H.
- SIAM Journal on Optimization, Vol. 9, Issue 1
Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis
journal, November 2019
- Plunk, Gabriel G.; Landreman, Matt; Helander, Per
- Journal of Plasma Physics, Vol. 85, Issue 6
Existence of quasihelically symmetric stellarators
journal, October 1991
- Garren, D. A.; Boozer, A. H.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10
Magnetic field strength of toroidal plasma equilibria
journal, October 1991
- Garren, D. A.; Boozer, A. H.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10
Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum
journal, April 2018
- Plunk, G. G.; Helander, Per
- Journal of Plasma Physics, Vol. 84, Issue 2
Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)
journal, June 2011
- Beidler, C. D.; Allmaier, K.; Isaev, M. Yu.
- Nuclear Fusion, Vol. 51, Issue 7
Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates
journal, December 2018
- Landreman, Matt; Sengupta, Wrick
- Journal of Plasma Physics, Vol. 84, Issue 6
Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions
journal, January 2019
- Landreman, Matt; Sengupta, Wrick; Plunk, Gabriel G.
- Journal of Plasma Physics, Vol. 85, Issue 1
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
Optimisation of stellarator equilibria with ROSE
journal, November 2018
- Drevlak, M.; Beidler, C. D.; Geiger, J.
- Nuclear Fusion, Vol. 59, Issue 1
Transport and isomorphic equilibria
journal, January 1983
- Boozer, Allen H.
- Physics of Fluids, Vol. 26, Issue 2
Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis
journal, September 1964
- Mercier, Claude
- Nuclear Fusion, Vol. 4, Issue 3
Properties of a new quasi-axisymmetric configuration
journal, January 2019
- Henneberg, S. A.; Drevlak, M.; Nührenberg, C.
- Nuclear Fusion, Vol. 59, Issue 2
Stellarators with the magnetic symmetry of a tokamak
journal, July 1996
- Garabedian, P. R.
- Physics of Plasmas, Vol. 3, Issue 7
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
ESTELL: A Quasi-Toroidally Symmetric Stellarator
journal, March 2013
- Drevlak, M.; Brochard, F.; Helander, P.
- Contributions to Plasma Physics, Vol. 53, Issue 6
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983
- Hirshman, S. P.
- Physics of Fluids, Vol. 26, Issue 12
Quasi-helical symmetry in stellarators
journal, November 1995
- Boozer, A. H.
- Plasma Physics and Controlled Fusion, Vol. 37, Issue 11A
New classes of quasi-helically symmetric stellarators
journal, December 2010
- Ku, L. P.; Boozer, A. H.
- Nuclear Fusion, Vol. 51, Issue 1
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
J* optimization of small aspect ratio stellarator/tokamak hybrid devices
journal, May 1998
- Spong, D. A.; Hirshman, S. P.; Whitson, J. C.
- Physics of Plasmas, Vol. 5, Issue 5
Physics design of a high-bbeta quasi-axisymmetric stellarator
journal, December 1999
- Reiman, A.; Fu, G.; Hirshman, S.
- Plasma Physics and Controlled Fusion, Vol. 41, Issue 12B
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
Equilibrium and Stability of a Three-Dimensional Toroidal MHD Configuration Near its Magnetic Axis
journal, November 1976
- Lortz, D.; Nührenberg, J.
- Zeitschrift für Naturforschung A, Vol. 31, Issue 11
Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum
text, January 2018
- Plunk, G. G.; Helander, P.
- arXiv