ISSN:
1089-7674
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The nonlinear evolution of the kink instability of a plasma with an elliptic magnetic stagnation line is studied by means of an amplitude expansion of the ideal magnetohydrodynamic (MHD) equations. A cylindrically symmetric plasma with circular field lines is used to model the magnetic field geometry close to the stagnation line. Due to the symmetry with respect to ±z, the linear stability problem of such a system has a two-folded degeneracy, with equal eigenvalues for helical kink perturbations with positive and negative polarization. It is shown that, near marginal stability, the nonlinear evolution of the instability can be described in terms of a two-dimensional potential U(X,Y), where X and Y represent the amplitudes of the perturbations with positive and negative helical polarization. The potential U(X,Y) is found to be nonlinearly stabilizing for all values of the polarization. Furthermore, in addition to the equilibrium point (X,Y)=(0,0), the nonlinear potential has eight equilibrium points in the XY-plane, four corresponding to helical polarization (X or Y=0) and four to plane polarization (|X|=|Y|). The latter equilibria have the lowest energy, indicating that plane kinks preferably should be formed as the stagnation line instability evolves. The equilibria with helical polarization agree with the bifurcated Z-pinch equilibria obtained by means of a different method in a previous paper [Plasma Phys. Controlled Fusion 35, 551 (1993)]. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.872220
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