Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Generalized Mercier stability criterion for stellarators

Journal Article · · Physics of Plasmas
DOI:https://doi.org/10.1063/5.0144211· OSTI ID:2420468

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

Research Organization:
Fusion Theory and Computation Inc., Kingston, WA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0016106
OSTI ID:
2420468
Journal Information:
Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 30; ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (8)

Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point journal January 1955
Hydromagnetic stability of a diffuse linear pinch journal June 1960
Stability Criterion for Arbitrary Hydromagnetic Equilibria journal January 1962
The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma journal July 2016
Ideal magnetohydrodynamics: Global mode analysis of three‐dimensional plasma configurations journal September 1993
Resistive instabilities in general toroidal plasma configurations journal January 1975
Overview of first Wendelstein 7-X high-performance operation journal June 2019
An energy principle for hydromagnetic stability problems
  • Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40 https://doi.org/10.1098/rspa.1958.0023
journal February 1958

Similar Records

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
Journal Article · Tue Jul 12 20:00:00 EDT 2016 · Physics of Plasmas · OSTI ID:1418989

Finite Larmor radius modification of the Mercier criterion
Technical Report · Sat Mar 31 23:00:00 EST 1984 · OSTI ID:6821877

Mercier criterion modified by kinetic effects
Conference · Mon Dec 30 23:00:00 EST 1996 · OSTI ID:489473

Related Subjects