Bifurcations of tokamak equilibria at high. beta. associated with ideal n = 0 n = infinity mode stabilization

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1983

OSTI ID:5746550

Elkin, D J

The bifurcation theory of elastic structures is applied to two analagous problems in ideal magnetohydrodynamics. In a tokamak or similar toroidal plasma confinement machine, stable bifurcations of an axisymmetric equilibrium are associated with instabilities having a toroidal model number of n = 0 or n = infinity. The former, the axisymmetric mode, as well as the latter, the ballooning mode, have a regime of second stability at high ..beta... A method for crossing the linearly unstable regime, granting sufficient energy deposition, is brought to light through use of the stable bifurcations. The Lyapunov-Schmidt expansion for solutions of nonlinear equilibrium equations at a critical point highlights the analysis. From it, a potential energy function possessing all the bifurcation information is obtained as a projection of the energy functional for the plasma. This function reveals the connection between equilibrium and stability. The bifurcation point is simultaneously the critical value for instability. Elementary catastrophe surfaces arise for various choices of a nonlinear current density profile in the axisymmetric mode problem. For the ballooning mode, a variation of the procedure is used to derive the cusp catastrophe surface as the pertinent model.

• Research Organization: Columbia Univ., New York (USA)
• OSTI ID: 5746550
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
700107* -- Fusion Energy-- Plasma Research-- Instabilities
CLOSED PLASMA DEVICES
EQUILIBRIUM
FLUID MECHANICS
HIGH-BETA PLASMA
HYDRODYNAMICS
INSTABILITY
LYAPUNOV METHOD
MAGNETOHYDRODYNAMICS
MECHANICS
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
STABILITY
THERMONUCLEAR DEVICES
TOKAMAK DEVICES