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Title: The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma

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 W P with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added tomore » a vacuum response matrix W V to form a total response matrix W T. Finally, the existence of negative eigenvalues of W T indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.« less
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  1. Fusion Theory and Computation, Inc., Kingston, WA (United States)
Publication Date:
Grant/Contract Number:
SC0016106; AC02-09CH11466; W-7405-ENG-36
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070-664X
American Institute of Physics (AIP)
Research Org:
Fusion Theory and Computation, Inc., Kingston, WA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Country of Publication:
United States
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Eigenvalues; Toroidal plasma confinement; Plasma materials processing; Magnetohydrodynamics; Numerical solutions
OSTI Identifier: