Nonlinear kink mode dynamics in circular and noncircular pinches

Journal Article · Mon Jun 01 00:00:00 EDT 1992 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860065· OSTI ID:7043115

Wahlberg, C ^[1]

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1. Department of Technology, Uppsala University, Box 534, S-751 21 Uppsala (Sweden)

It is shown that the global (free-boundary) {ital m}=1 kink instability of the ideal, magnetohydrodynamic (MHD) sharp boundary (surface current) pinch is stabilized by nonlinear effects, provided {ital B}{sub {ital e}}{approx lt}1 and {beta}{sub {ital p}}{lt}1, where {beta}{sub {ital p}}=1+{ital B}{sup 2}{sub {ital e}}{minus}{ital B}{sup 2}{sub {ital i}} and {ital B}{sub {ital i}} and {ital B}{sub {ital e}} denote, respectively, the internal and external axial magnetic fields of the pinch, normalized to the poloidal magnetic field. The stabilization has to do with the bending of the interior, frozen'' field lines and associated volume currents induced in the pinch, and does not occur in a pure surface current model, which neglects these currents and only conserves the total magnetic flux through the pinch. It is suggested that the global, helical {ital m}=1 structures observed in various pinch experiments may have to do with the stabilizing mechanism above. The nonlinear stability has been calculated by means of a new approach to the bifurcated equilibria of the helical {ital m}=1 mode, and the method should also be useful in connection with other nonlinear, ideal MHD phenomena. The regime of nonlinear stability above corresponds to intermediate or short wavelengths of the marginal mode ({ital ka}{approx gt}1). In the opposite, long-wavelength regime, the ideal MHD model and the pure surface current model give similar results, predicting nonlinear instability for, e.g., the nearly marginal Kruskal--Shafranov mode in tokamaks, in agreement with previous theories. Effects of mode rotation as well as of a noncircular cross section of the pinch, modeling the Extrap (Fusion Technol. {bold 16}, 7 (1989)) configuration, have also been considered, extending the results of a previous, linear investigation (Phys. Fluids B {bold 2}, 1601 (1990)) to the nonlinear regime.

• OSTI ID: 7043115
• Journal Information: Physics of Fluids B; (United States), Vol. 4:6; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
KINK INSTABILITY
PINCH EFFECT
CIRCULAR CONFIGURATION
MAGNETOHYDRODYNAMICS
MHD EQUILIBRIUM
PLASMA CONFINEMENT
PLASMA MACROINSTABILITIES
STABILIZATION
CONFIGURATION
CONFINEMENT
EQUILIBRIUM
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
MECHANICS
PLASMA INSTABILITY
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