Some mathematics for quasi-symmetry

Burby, J. W.; Kallinikos, N.; MacKay, R. S.

doi:10.1063/1.5142487

Title: Some mathematics for quasi-symmetry

Journal Article · 09 September 2020 · Journal of Mathematical Physics

DOI: https://doi.org/10.1063/1.5142487 · OSTI ID:2564532

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Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-center motion by a spatial symmetry. Here, we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analog of the Grad–Shafranov equation for the flux function in a quasi-symmetric magnetohydrostatic field.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); Simons Foundation; USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2564532

Report Number(s):: LA-UR-19-32407; 093503

Journal Information:: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 61; ISSN 0022-2488

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

The geometry of cross sections to flows Fried, David Topology, Vol. 21, Issue 4 https://doi.org/10.1016/0040-9383(82)90017-9	journal	January 1982
A free boundary problem and a related semilinear equation Ambrosetti, Antonio; Mancini, Giovanni Nonlinear Analysis: Theory, Methods & Applications, Vol. 4, Issue 5 https://doi.org/10.1016/0362-546x(80)90004-8	journal	September 1980
On a free boundary problem arising in plasma physics Berestycki, Henri; Brezis, Haîm Nonlinear Analysis: Theory, Methods & Applications, Vol. 4, Issue 3 https://doi.org/10.1016/0362-546x(80)90083-8	journal	January 1980
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
Differential forms for plasma physics MacKay, R. S. Journal of Plasma Physics, Vol. 86, Issue 1 https://doi.org/10.1017/S0022377819000928	journal	January 2020
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
Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions Landreman, Matt; Sengupta, Wrick; Plunk, Gabriel G. Journal of Plasma Physics, Vol. 85, Issue 1 https://doi.org/10.1017/s0022377818001344	journal	January 2019
Some Stable Hydromagnetic Equilibria Johnson, J. L.; Oberman, C. R.; Kulsrud, R. M. Physics of Fluids, Vol. 1, Issue 4 https://doi.org/10.1063/1.1705886	journal	January 1958
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
Toroidal precession as a geometric phase Burby, J. W.; Qin, H. Physics of Plasmas, Vol. 20, Issue 1 https://doi.org/10.1063/1.4789377	journal	January 2013
Toroidal regularization of the guiding center Lagrangian Burby, J. W.; Ellison, C. L. Physics of Plasmas, Vol. 24, Issue 11 https://doi.org/10.1063/1.5004429	journal	November 2017
The relationship between flux coordinates and equilibrium-based frames of reference in fusion theory Kruger, S. E.; Greene, John M. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5098313	journal	August 2019
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
Hydromagnetic equilibria and their proper coordinates Hamada, Shigeo Nuclear Fusion, Vol. 2, Issue 1-2 https://doi.org/10.1088/0029-5515/2/1-2/005	journal	January 1962
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
Plasma rotation in a quasi-symmetric stellarator Simakov, Andrei N.; Helander, Per Plasma Physics and Controlled Fusion, Vol. 53, Issue 2 https://doi.org/10.1088/0741-3335/53/2/024005	journal	January 2011
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces Amann, Herbert SIAM Review, Vol. 18, Issue 4 https://doi.org/10.1137/1018114	journal	October 1976

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