The DESC stellarator code suite. Part 2. Perturbation and continuation methods

Conlin, Rory; Dudt, Daniel W.; Panici, Dario; Kolemen, Egemen

doi:10.1017/S0022377823000399

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

Journal Article · Wed May 24 00:00:00 EDT 2023 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/S0022377823000399· OSTI ID:1975156

; ; ;

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $$\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

View Journal Article

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0022005; AC02-09CH11466

OSTI ID:: 1975156

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 3 Vol. 89; ISSN 0022-3778

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (28)

Computation of viscoelastic fluid flows using continuation methods Howell, Jason S. Journal of Computational and Applied Mathematics, Vol. 225, Issue 1 https://doi.org/10.1016/j.cam.2008.07.033	journal	March 2009
Stellarator design Boozer, Allen H. Journal of Plasma Physics, Vol. 81, Issue 6 https://doi.org/10.1017/S0022377815001373	journal	December 2015
The DESC stellarator code suite Part 3: Quasi-symmetry optimization Dudt, D. W.; Conlin, R.; Panici, D. Journal of Plasma Physics, Vol. 89, Issue 2 https://doi.org/10.1017/S0022377823000235	journal	April 2023
The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations Panici, D.; Conlin, R.; Dudt, D. W. Journal of Plasma Physics, Vol. 89, Issue 3 https://doi.org/10.1017/S0022377823000272	journal	May 2023
Array programming with NumPy Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J. Nature, Vol. 585, Issue 7825 https://doi.org/10.1038/s41586-020-2649-2	journal	September 2020
Computation of three-dimensional tokamak and spherical torus equilibria Park, Jong-kyu; Boozer, Allen H.; Glasser, Alan H. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2732170	journal	May 2007
Poloidal motion of trapped particle orbits in real-space coordinates Nemov, V. V.; Kasilov, S. V.; Kernbichler, W. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2912456	journal	May 2008
Importance of plasma response to nonaxisymmetric perturbations in tokamaks Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E. Physics of Plasmas, Vol. 16, Issue 5 https://doi.org/10.1063/1.3122862	journal	May 2009
The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma Glasser, A. H. Physics of Plasmas, Vol. 23, Issue 7 https://doi.org/10.1063/1.4958328	journal	July 2016
A Riccati solution for the ideal MHD plasma response with applications to real-time stability control Glasser, Alexander S.; Kolemen, Egemen; Glasser, A. H. Physics of Plasmas, Vol. 25, Issue 3 https://doi.org/10.1063/1.5007042	journal	March 2018
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
Transport and isomorphic equilibria Boozer, Allen H. Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.864166	journal	January 1983
J* optimization of small aspect ratio stellarator/tokamak hybrid devices Spong, D. A.; Hirshman, S. P.; Whitson, J. C. Physics of Plasmas, Vol. 5, Issue 5 https://doi.org/10.1063/1.872844	journal	May 1998
DESC: A stellarator equilibrium solver Dudt, D. W.; Kolemen, E. Physics of Plasmas, Vol. 27, Issue 10 https://doi.org/10.1063/5.0020743	journal	October 2020
On Halley's Iteration Method Gander, Walter The American Mathematical Monthly, Vol. 92, Issue 2 https://doi.org/10.1080/00029890.1985.11971554	journal	February 1985
On large-scale unconstrained optimization problems and higher order methods Gundersen, Geir; Steihaug, Trond Optimization Methods and Software, Vol. 25, Issue 3 https://doi.org/10.1080/10556780903239071	journal	June 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
Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions Hudson, S. R.; Dewar, R. L.; Hole, M. J. Plasma Physics and Controlled Fusion, Vol. 54, Issue 1 https://doi.org/10.1088/0741-3335/54/1/014005	journal	December 2011
Stellarator and tokamak plasmas: a comparison Helander, P.; Beidler, C. D.; Bird, T. M. Plasma Physics and Controlled Fusion, Vol. 54, Issue 12 https://doi.org/10.1088/0741-3335/54/12/124009	journal	November 2012
Hessian matrix approach for determining error field sensitivity to coil deviations Zhu, Caoxiang; Hudson, Stuart R.; Lazerson, Samuel A. Plasma Physics and Controlled Fusion, Vol. 60, Issue 5 https://doi.org/10.1088/1361-6587/aab6cb	journal	April 2018
New method to design stellarator coils without the winding surface Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao Nuclear Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/1741-4326/aa8e0a	journal	November 2017
Optimisation of stellarator equilibria with ROSE Drevlak, M.; Beidler, C. D.; Geiger, J. Nuclear Fusion, Vol. 59, Issue 1 https://doi.org/10.1088/1741-4326/aaed50	journal	November 2018
Optimized finite-build stellarator coils using automatic differentiation McGreivy, N.; Hudson, S. R.; Zhu, C. Nuclear Fusion, Vol. 61, Issue 2 https://doi.org/10.1088/1741-4326/abcd76	journal	January 2021
A model for the fast evaluation of prompt losses of energetic ions in stellarators Velasco, J. L.; Calvo, I.; Mulas, S. Nuclear Fusion, Vol. 61, Issue 11 https://doi.org/10.1088/1741-4326/ac2994	journal	October 2021
An energy principle for hydromagnetic stability problems Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40 https://doi.org/10.1098/rspa.1958.0023	journal	February 1958
The NumPy Array: A Structure for Efficient Numerical Computation van der Walt, Stéfan; Colbert, S. Chris; Varoquaux, Gaël Computing in Science & Engineering, Vol. 13, Issue 2 https://doi.org/10.1109/MCSE.2011.37	journal	March 2011
Continuation methods: Theory and applications Richter, Stephen L.; Decarlo, Raymond A. IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-13, Issue 4 https://doi.org/10.1109/TSMC.1983.6313131	journal	July 1983
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

Similar Records

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

Journal Article · Sun Jan 31 23:00:00 EST 2021 · Journal of Plasma Physics · OSTI ID:1850057

Internal wave energy flux from density perturbations in nonlinear stratifications

Journal Article · Fri Oct 12 00:00:00 EDT 2018 · Journal of Fluid Mechanics · OSTI ID:1609566

Finite orbit width effects in large aspect ratio stellarators

Journal Article · Mon Oct 17 00:00:00 EDT 2022 · Journal of Plasma Physics · OSTI ID:1896539

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

Citation Formats

References (28)

Similar Records

Related Subjects