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 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.
- Research Organization:
- Fusion Theory and Computation, Inc., Kingston, WA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- Grant/Contract Number:
- SC0016106; AC02-09CH11466; W-7405-ENG-36
- OSTI ID:
- 1418989
- Journal Information:
- Physics of Plasmas, Vol. 23, Issue 7; ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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