Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

Landreman, Matt; Medasani, Bharat; Zhu, Caoxiang

doi:10.1063/5.0061665

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

Journal Article · Wed Sep 08 00:00:00 EDT 2021 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0061665· OSTI ID:1823165

^[1]; ^[2]; ^[2]

Univ. of Maryland, College Park, MD (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1823165

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 28; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (29)

A criterion for the non-existence of invariant circles Mather, John Publications mathématiques de l'IHÉS, Vol. 63, Issue 1 https://doi.org/10.1007/BF02831625	journal	December 1986
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
Requirements for accuracy of superconducting coils in the Large Helical Device Yamazaki, K.; Yanagi, N.; Ji, H. Fusion Engineering and Design, Vol. 20 https://doi.org/10.1016/0920-3796(93)90027-F	journal	January 1993
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
Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000 Pedersen, T. Sunn; Otte, M.; Lazerson, S. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13493	journal	November 2016
SciPy 1.0: fundamental algorithms for scientific computing in Python Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E. Nature Methods https://doi.org/10.1038/s41592-019-0686-2	journal	February 2020
Reduction of islands in full-pressure stellarator equilibria Hudson, S. R.; Monticello, D. A.; Reiman, A. H. Physics of Plasmas, Vol. 8, Issue 7 https://doi.org/10.1063/1.1377614	journal	July 2001
Computation of multi-region relaxed magnetohydrodynamic equilibria Hudson, S. R.; Dewar, R. L.; Dennis, G. Physics of Plasmas, Vol. 19, Issue 11 https://doi.org/10.1063/1.4765691	journal	November 2012
A method for determining a stochastic transition Greene, John M. Journal of Mathematical Physics, Vol. 20, Issue 6 https://doi.org/10.1063/1.524170	journal	June 1979
Simple method for calculating island widths Cary, John R.; Hanson, James D. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 4 https://doi.org/10.1063/1.859829	journal	April 1991
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
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria Hirshman, S. P. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864116	journal	January 1983
Elimination of stochasticity in stellarators Hanson, James D.; Cary, John R. Physics of Fluids, Vol. 27, Issue 4 https://doi.org/10.1063/1.864692	journal	January 1984
Stochasticity reduction Cary, John R.; Hanson, James D. Physics of Fluids, Vol. 29, Issue 8 https://doi.org/10.1063/1.865539	journal	January 1986
Constructing integrable high-pressure full-current free-boundary stellarator magnetohydrodynamic equilibrium solutions Hudson, S. R.; Monticello, D. A.; Reiman, A. H. Nuclear Fusion, Vol. 43, Issue 10 https://doi.org/10.1088/0029-5515/43/10/004	journal	September 2003
Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS) Beidler, C. D.; Allmaier, K.; Isaev, M. Yu. Nuclear Fusion, Vol. 51, Issue 7 https://doi.org/10.1088/0029-5515/51/7/076001	journal	June 2011
Free-boundary full-pressure island healing in stellarator equilibria: coil-healing* Hudson, S. R.; Reiman, A.; Strickler, D. Plasma Physics and Controlled Fusion, Vol. 44, Issue 7 https://doi.org/10.1088/0741-3335/44/7/323	journal	June 2002
Performance and properties of the first plasmas of Wendelstein 7-X Klinger, T.; Alonso, A.; Bozhenkov, S. Plasma Physics and Controlled Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/0741-3335/59/1/014018	journal	October 2016
Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry Qu, Z. S.; Pfefferlé, D.; Hudson, S. R. Plasma Physics and Controlled Fusion, Vol. 62, Issue 12 https://doi.org/10.1088/1361-6587/abc08e	journal	November 2020
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
Eliminating Islands in High-Pressure Free-Boundary Stellarator Magnetohydrodynamic Equilibrium Solutions Hudson, S. R.; Monticello, D. A.; Reiman, A. H. Physical Review Letters, Vol. 89, Issue 27 https://doi.org/10.1103/PhysRevLett.89.275003	journal	December 2002
Symplectic maps, variational principles, and transport Meiss, J. D. Reviews of Modern Physics, Vol. 64, Issue 3 https://doi.org/10.1103/RevModPhys.64.795	journal	July 1992
Lessons Learned in Risk Management on NCSX Neilson, G. H.; Gruber, C. O.; Harris, J. H. IEEE Transactions on Plasma Science, Vol. 38, Issue 3 https://doi.org/10.1109/TPS.2009.2037889	journal	March 2010
Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow MacKay, Robert S. Regular and Chaotic Dynamics, Vol. 23, Issue 6 https://doi.org/10.1134/S1560354718060126	journal	November 2018
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
Magnetic Configuration and Modular Coil Design for the Chinese First Quasi-Axisymmetric Stellarator Liu, Haifeng; Shimizu, Akihiro; Isobe, Mitsutaka Plasma and Fusion Research, Vol. 13, Issue 0 https://doi.org/10.1585/pfr.13.3405067	journal	January 2018
SIMSOPT: A flexible framework for stellarator optimization Landreman, Matt; Medasani, Bharat; Wechsung, Florian Journal of Open Source Software, Vol. 6, Issue 65 https://doi.org/10.21105/joss.03525	journal	September 2021
Data for the paper "Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry" Landreman, Matt Zenodo https://doi.org/10.5281/zenodo.5035515	dataset	January 2021

Similar Records

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Part 2. Applications

Journal Article · Sun Jan 12 19:00:00 EST 2020 · Journal of Plasma Physics · OSTI ID:1597686

Constructing stellarators with quasisymmetry to high order

Journal Article · Thu Nov 14 19:00:00 EST 2019 · Journal of Plasma Physics · OSTI ID:1597688

Omnigenity as generalized quasisymmetry

Journal Article · Tue May 15 00:00:00 EDT 2012 · Physics of Plasmas · OSTI ID:22072381

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Magnetohydrodynamics
Optimization problems
Plasma codes
Plasma confinement
Programming languages
Stellarators

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

Citation Formats

References (29)

Similar Records

Related Subjects