Nonlinear behavior of magnetohydrodynamic modes near marginally stable states. I. General formulation and application to the nonresonant kink modes in a reversed field pinch and to the quasi-interchange modes in a tokamak

Journal Article · Fri Jun 01 00:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859253· OSTI ID:6804794

Nakajima, N ^[1]

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1. Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (USA)

Two types of nonlinear equations describing the time development of modes near marginally stable states in an inhomogeneous medium are obtained through a general formulation that employs a perturbation expansion around the marginally stable state under the assumption of a single helicity. One type of nonlinear equation has a Hamiltonian form that may be interpreted as the equation of motion for a particle in the potential field of a central force; the other type leads to the Landau equation, which is well known in fluid dynamics. The former equation is obtained when the linear operator is degenerate at the marginally stable state, which corresponds to the case when the linear dispersion relation has a double root for the frequency at the marginally stable state, whereas the latter is obtained when the linear operator is nondegenerate, i.e., the linear dispersion relation has a single root. In the framework of magnetohydrodynamics, the former corresponds to the nonresonant ideal modes, and the latter to the resistive modes. The nonlinear behavior of the nonresonant kink modes in a reversed field pinch and of the quasi-interchange modes in a tokamak are examined with the application of the general formulation. It is shown that new stable helical equilibria bifurcate near the initial axisymmetric equilibrium, so that the plasma nonlinearly oscillates around the new bifurcated equilibrium, which leads to nonlinear saturation of the nonresonant kink modes in a reversed field pinch and of the quasi-interchange mode in a tokamak. The nonlinear stabilizing effects causing bifurcation of the equilibrium are interpreted as quasilinear effects. Compressibility reduces the nonlinear stabilizing effects through changing the quasilinear components and is important even when the modes are near marginally stable states.

• OSTI ID: 6804794
• Journal Information: Physics of Fluids B; (USA), Vol. 2:6; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
MAGNETOHYDRODYNAMICS
NONLINEAR PROBLEMS
REVERSE-FIELD PINCH
PLASMA MACROINSTABILITIES
TOKAMAK DEVICES
DISPERSION RELATIONS
EQUATIONS OF MOTION
FLUTE INSTABILITY
HAMILTONIANS
HELICITY
INHOMOGENEOUS PLASMA
KINK INSTABILITY
OSCILLATION MODES
PERTURBATION THEORY
SERIES EXPANSION
TIME DEPENDENCE
CLOSED PLASMA DEVICES
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
PINCH EFFECT
PLASMA
PLASMA INSTABILITY
QUANTUM OPERATORS
THERMONUCLEAR DEVICES
640430* - Fluid Physics- Magnetohydrodynamics
700108 - Fusion Energy- Plasma Research- Wave Phenomena