Abstract
The eigenvalue problem for linear stability of concentric radial profiles of current and vorticity in reduced forms of three-dimensional magnetohydrodynamics is solved numerically. Arbitrary relative amplitudes of the velocity and magnetic fields are considered. Vorticity profiles are unstable if nonmonotonic, but are stabilized by a poloidal magnetic field when the on-axis vertical current is at least as large as the on-axis vertical vorticity. Nonmonotonic current profiles are less efficient at stabilization. When the neutral modes have vertical structure, an added poloidal magnetic field does not stabilize the mode unless the vertical field is also moderately strong. Current profiles in which the integrated current changes sign, although spectrally stable, are shown to be nonlinearly unstable via both numerical solution and Lyapunov techniques.
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