Measures of quasisymmetry for stellarators

Rodríguez, E.; Paul, E. J.; Bhattacharjee, A.

doi:10.1017/S0022377821001331

Measures of quasisymmetry for stellarators

Journal Article · Thu Jan 27 23:00:00 EST 2022 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/S0022377821001331· OSTI ID:1880376

; ; Bhattacharjee, A.

Quasisymmetric stellarators are an attractive class of optimised magnetic confinement configurations. The property of quasisymmetry (QS) is in practice limited to be approximate, and thus the construction requires measures that quantify the deviation from the exact property. In this paper we study three measure candidates used in the literature, placing the focus on their origin and a comparison of their forms. The analysis shows clearly the lack of universality in these measures. As these metrics do not directly correspond to any physical property (except when exactly quasisymmetric), optimisation should employ additional physical metrics for guidance. It is suggested that close to QS minima, one should treat QS metrics through inequality constraints so that additional physics metrics dominate optimisation. The impact of different quasisymmetric measures on optimisation is presented through an example, for which the standard metric that weights the asymmetric Fourier modes of the field magnitude appears to perform best.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1880376

Alternate ID(s):: OSTI ID: 1887974

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 1 Vol. 88; ISSN 0022-3778

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (51)

ESTELL: A Quasi-Toroidally Symmetric Stellarator Drevlak, M.; Brochard, F.; Helander, P. Contributions to Plasma Physics, Vol. 53, Issue 6 https://doi.org/10.1002/ctpp.201200055	journal	March 2013
Quasi-helically symmetric toroidal stellarators Nührenberg, J.; Zille, R. Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90080-1	journal	May 1988
Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method Dekeyser, W.; Reiter, D.; Baelmans, M. Journal of Computational Physics, Vol. 278 https://doi.org/10.1016/j.jcp.2014.08.023	journal	December 2014
Variational principles of guiding centre motion Littlejohn, Robert G. Journal of Plasma Physics, Vol. 29, Issue 1 https://doi.org/10.1017/S002237780000060X	journal	February 1983
Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum Plunk, G. G.; Helander, Per Journal of Plasma Physics, Vol. 84, Issue 2 https://doi.org/10.1017/S0022377818000259	journal	April 2018
Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001289	journal	December 2018
Stellarator equilibria with reactor relevant energetic particle losses Bader, Aaron; Drevlak, M.; Anderson, D. T. Journal of Plasma Physics, Vol. 85, Issue 5 https://doi.org/10.1017/S0022377819000680	journal	October 2019
Constructing stellarators with quasisymmetry to high order Landreman, Matt; Sengupta, Wrick Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S0022377819000783	journal	November 2019
Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Part 2. Applications Paul, Elizabeth J.; Antonsen, Thomas; Landreman, Matt Journal of Plasma Physics, Vol. 86, Issue 1 https://doi.org/10.1017/S0022377819000916	journal	January 2020
Impurity temperature screening in stellarators close to quasisymmetry Martin, Mike F.; Landreman, Matt Journal of Plasma Physics, Vol. 86, Issue 3 https://doi.org/10.1017/S0022377820000574	journal	June 2020
On quasisymmetric plasma equilibria sustained by small force Constantin, Peter; Drivas, Theodore D.; Ginsberg, Daniel Journal of Plasma Physics, Vol. 87, Issue 1 https://doi.org/10.1017/S0022377820001610	journal	February 2021
Representing the boundary of stellarator plasmas Henneberg, S. A.; Helander, P.; Drevlak, M. Journal of Plasma Physics, Vol. 87, Issue 5 https://doi.org/10.1017/S0022377821000891	journal	September 2021
The Stellarator Concept Spitzer, Lyman Physics of Fluids, Vol. 1, Issue 4 https://doi.org/10.1063/1.1705883	journal	January 1958
Transport optimization in stellarators Mynick, H. E. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2177643	journal	May 2006
Omnigenity as generalized quasisymmetry Landreman, Matt; Catto, Peter J. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3693187	journal	May 2012
Plasma flow healing of magnetic islands in stellarators Hegna, C. C. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3694042	journal	May 2012
Collisionless high energy particle losses in optimized stellarators calculated in real-space coordinates Nemov, V. V.; Kasilov, S. V.; Kernbichler, W. Physics of Plasmas, Vol. 21, Issue 6 https://doi.org/10.1063/1.4876740	journal	June 2014
Some mathematics for quasi-symmetry Burby, J. W.; Kallinikos, N.; MacKay, R. S. Journal of Mathematical Physics, Vol. 61, Issue 9 https://doi.org/10.1063/1.5142487	journal	September 2020
Existence of quasihelically symmetric stellarators Garren, D. A.; Boozer, A. H. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859916	journal	October 1991
Plasma equilibrium with rational magnetic surfaces Boozer, Allen H. Physics of Fluids, Vol. 24, Issue 11 https://doi.org/10.1063/1.863297	journal	January 1981
Transport and isomorphic equilibria Boozer, Allen H. Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.864166	journal	January 1983
Island formation and destruction of flux surfaces in three-dimensional MHD equilibria Reiman, A.; Boozer, Allen H. Physics of Fluids, Vol. 27, Issue 10 https://doi.org/10.1063/1.864526	journal	January 1984
Isodynamical (omnigenous) equilibrium in symmetrically confined plasma configurations Bernardin, M. P.; Moses, R. W.; Tataronis, J. A. Physics of Fluids, Vol. 29, Issue 8 https://doi.org/10.1063/1.865501	journal	January 1986
Neoclassical transport in stellarators Ho, Darwin D. -M.; Kulsrud, Russell M. Physics of Fluids, Vol. 30, Issue 2 https://doi.org/10.1063/1.866395	journal	January 1987
Hamiltonian approach to the magnetostatic equilibrium problem Tessarotto, Massimo; Johnson, John L.; Zheng, Lin Jin Physics of Plasmas, Vol. 2, Issue 12 https://doi.org/10.1063/1.871008	journal	December 1995
Theory of pressure‐induced islands and self‐healing in three‐dimensional toroidal magnetohydrodynamic equilibria Bhattacharjee, A.; Hayashi, T.; Hegna, C. C. Physics of Plasmas, Vol. 2, Issue 3 https://doi.org/10.1063/1.871369	journal	March 1995
Quasi‐helical magnetohydrodynamic equilibria in the presence of flow Tessarotto, M.; Johnson, J. L.; White, R. B. Physics of Plasmas, Vol. 3, Issue 7 https://doi.org/10.1063/1.871522	journal	July 1996
Physics of compact stellarators Hirshman, S. P.; Spong, D. A.; Whitson, J. C. Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873489	journal	May 1999
Evaluation of 1/ν neoclassical transport in stellarators Nemov, V. V.; Kasilov, S. V.; Kernbichler, W. Physics of Plasmas, Vol. 6, Issue 12 https://doi.org/10.1063/1.873749	journal	December 1999
Necessary and sufficient conditions for quasisymmetry Rodríguez, E.; Helander, P.; Bhattacharjee, A. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/5.0008551	journal	June 2020
Solving the problem of overdetermination of quasisymmetric equilibrium solutions by near-axis expansions. I. Generalized force balance Rodríguez, E.; Bhattacharjee, A. Physics of Plasmas, Vol. 28, Issue 1 https://doi.org/10.1063/5.0027574	journal	January 2021
Solving the problem of overdetermination of quasisymmetric equilibrium solutions by near-axis expansions. II. Circular axis stellarator solutions Rodríguez, E.; Bhattacharjee, A. Physics of Plasmas, Vol. 28, Issue 1 https://doi.org/10.1063/5.0027575	journal	January 2021
Islands and current singularities in quasisymmetric toroidal plasmas Rodríguez, E.; Bhattacharjee, A. Physics of Plasmas, Vol. 28, Issue 9 https://doi.org/10.1063/5.0057186	journal	September 2021
Generalized Boozer coordinates: A natural coordinate system for quasisymmetry Rodríguez, E.; Sengupta, W.; Bhattacharjee, A. Physics of Plasmas, Vol. 28, Issue 9 https://doi.org/10.1063/5.0060115	journal	September 2021
Three-dimensional analysis of tokamaks and stellarators Garabedian, P. R. Proceedings of the National Academy of Sciences, Vol. 105, Issue 37 https://doi.org/10.1073/pnas.0806354105	journal	September 2008
Interaction of tearing modes with external structures in cylindrical geometry (plasma) Fitzpatrick, R. Nuclear Fusion, Vol. 33, Issue 7 https://doi.org/10.1088/0029-5515/33/7/I08	journal	July 1993
Design studies of low aspect ratio quasi-omnigenous stellarators Spong, D. A.; Hirshman, S. P.; Whitson, J. C. Nuclear Fusion, Vol. 40, Issue 3Y https://doi.org/10.1088/0029-5515/40/3Y/317	journal	March 2000
Improved -particle confinement in stellarators with poloidally closed contours of the magnetic field strength Mikhailov, M. I.; Shafranov, V. D.; Subbotin, A. A. Nuclear Fusion, Vol. 42, Issue 11 https://doi.org/10.1088/0029-5515/42/11/102	journal	October 2002
New classes of quasi-helically symmetric stellarators Ku, L. P.; Boozer, A. H. Nuclear Fusion, Vol. 51, Issue 1 https://doi.org/10.1088/0029-5515/51/1/013004	journal	December 2010
Theory of plasma confinement in non-axisymmetric magnetic fields Helander, Per Reports on Progress in Physics, Vol. 77, Issue 8 https://doi.org/10.1088/0034-4885/77/8/087001	journal	July 2014
Ballooning stability optimization of low-aspect-ratio stellarators* Sanchez, R.; Hirshman, S. P.; Ware, A. S. Plasma Physics and Controlled Fusion, Vol. 42, Issue 6 https://doi.org/10.1088/0741-3335/42/6/303	journal	May 2000
Physics of the compact advanced stellarator NCSX Zarnstorff, M. C.; Berry, L. A.; Brooks, A. Plasma Physics and Controlled Fusion, Vol. 43, Issue 12A https://doi.org/10.1088/0741-3335/43/12A/318	journal	November 2001
3D toroidal geometry of currentless magnetic configurations with improved confinement Skovoroda, A. A. Plasma Physics and Controlled Fusion, Vol. 47, Issue 11 https://doi.org/10.1088/0741-3335/47/11/004	journal	October 2005
Kinetic shielding of magnetic islands in 3D equilibria Hegna, C. C. Plasma Physics and Controlled Fusion, Vol. 53, Issue 2 https://doi.org/10.1088/0741-3335/53/2/024003	journal	January 2011
Flow damping in stellarators close to quasisymmetry Calvo, Iván; Parra, Felix I.; Velasco, José Luis Plasma Physics and Controlled Fusion, Vol. 57, Issue 1 https://doi.org/10.1088/0741-3335/57/1/014014	journal	November 2014
Properties of a new quasi-axisymmetric configuration Henneberg, S. A.; Drevlak, M.; Nührenberg, C. Nuclear Fusion, Vol. 59, Issue 2 https://doi.org/10.1088/1741-4326/aaf604	journal	January 2019
Intrinsic Ambipolarity and Rotation in Stellarators Helander, P.; Simakov, A. N. Physical Review Letters, Vol. 101, Issue 14 https://doi.org/10.1103/PhysRevLett.101.145003	journal	September 2008
Transport Optimization and MHD Stability of a Small Aspect Ratio Toroidal Hybrid Stellarator Hirshman, S. P.; Spong, D. A.; Whitson, J. C. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevLett.80.528	journal	January 1998
The ARIES-CS Compact Stellarator Fusion Power Plant Najmabadi, F.; Raffray, A. R.; Abdel-Khalik, S. I. Fusion Science and Technology, Vol. 54, Issue 3 https://doi.org/10.13182/FST54-655	journal	October 2008
The Helically Symmetric Experiment, (HSX) Goals, Design and Status Anderson, F. Simon B.; Almagri, Abdulgader F.; Anderson, David T. Fusion Technology, Vol. 27, Issue 3T https://doi.org/10.13182/FST95-A11947086	journal	April 1995
Design of the DEMO Fusion Reactor Following ITER Garabedian, Paul R.; McFadden, Geoffrey B. Journal of Research of the National Institute of Standards and Technology, Vol. 114, Issue 4 https://doi.org/10.6028/jres.114.016	journal	July 2009

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