The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
Abstract
A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixedboundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a highorder complex system of ordinary differential equations, the EulerLagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straightfieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q(ψ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixedboundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixedboundary instabilities, an M × M plasma response matrix W_{P} with M the number of poloidal harmonics used, is constructed from the EulerLagrange solutions at the plasmavacuum boundary. This is added to amore »
 Authors:

 Fusion Theory and Computation, Inc., Kingston, WA (United States)
 Publication Date:
 Research Org.:
 Fusion Theory and Computation, Inc., Kingston, WA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 OSTI Identifier:
 1418989
 Grant/Contract Number:
 SC0016106; AC0209CH11466; W7405ENG36
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Eigenvalues; Toroidal plasma confinement; Plasma materials processing; Magnetohydrodynamics; Numerical solutions
Citation Formats
Glasser, A. H. The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma. United States: N. p., 2016.
Web. doi:10.1063/1.4958328.
Glasser, A. H. The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma. United States. doi:10.1063/1.4958328.
Glasser, A. H. Wed .
"The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma". United States. doi:10.1063/1.4958328. https://www.osti.gov/servlets/purl/1418989.
@article{osti_1418989,
title = {The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma},
author = {Glasser, A. H.},
abstractNote = {A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixedboundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a highorder complex system of ordinary differential equations, the EulerLagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straightfieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q(ψ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixedboundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixedboundary instabilities, an M × M plasma response matrix WP with M the number of poloidal harmonics used, is constructed from the EulerLagrange solutions at the plasmavacuum boundary. This is added to a vacuum response matrix WV to form a total response matrix WT. Finally, the existence of negative eigenvalues of WT indicates the presence of freeboundary instabilities. The method is implemented in the fast and accurate DCON code.},
doi = {10.1063/1.4958328},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = {2016},
month = {7}
}
Web of Science
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Works referencing / citing this record:
Noninductively driven tokamak plasmas at nearunity βt in the P egasus toroidal experiment
journal, May 2018
 Reusch, J. A.; Bodner, G. M.; Bongard, M. W.
 Physics of Plasmas, Vol. 25, Issue 5
A Riccati solution for the ideal MHD plasma response with applications to realtime stability control
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 Glasser, Alexander S.; Kolemen, Egemen; Glasser, A. H.
 Physics of Plasmas, Vol. 25, Issue 3
A Riccati solution for the ideal MHD plasma response with applications to realtime stability control
journal, March 2018
 Glasser, Alexander S.; Kolemen, Egemen; Glasser, A. H.
 Physics of Plasmas, Vol. 25, Issue 3
Noninductively driven tokamak plasmas at nearunity βt in the P egasus toroidal experiment
journal, May 2018
 Reusch, J. A.; Bodner, G. M.; Bongard, M. W.
 Physics of Plasmas, Vol. 25, Issue 5