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Title: 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 fixed-boundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline 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. Fixed-boundary 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 fixed-boundary instabilities, an M × M plasma response matrix WP with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added to amore » vacuum response matrix WV to form a total response matrix WT. Finally, the existence of negative eigenvalues of WT indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.« less

Authors:
ORCiD logo [1]
  1. 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) (SC-24)
OSTI Identifier:
1418989
Grant/Contract Number:  
SC0016106; AC02-09CH11466; W-7405-ENG-36
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070-664X
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 fixed-boundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline 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. Fixed-boundary 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 fixed-boundary instabilities, an M × M plasma response matrix WP with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum 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 free-boundary 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}
}

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Cited by: 12 works
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    Works referencing / citing this record:

    Non-inductively driven tokamak plasmas at near-unity 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
    • DOI: 10.1063/1.5017966

    A Riccati solution for the ideal MHD plasma response with applications to real-time stability control
    journal, March 2018

    • Glasser, Alexander S.; Kolemen, Egemen; Glasser, A. H.
    • Physics of Plasmas, Vol. 25, Issue 3
    • DOI: 10.1063/1.5007042

    A Riccati solution for the ideal MHD plasma response with applications to real-time stability control
    journal, March 2018

    • Glasser, Alexander S.; Kolemen, Egemen; Glasser, A. H.
    • Physics of Plasmas, Vol. 25, Issue 3
    • DOI: 10.1063/1.5007042

    Non-inductively driven tokamak plasmas at near-unity 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
    • DOI: 10.1063/1.5017966