Resistive instability in the absence of critical levels

Publisher Website
Google Scholar
Abstract
Fearn and Weiglhofer (1992) identified and investigated an instability of the magnetic field B 0 = B 0(s)1 φ that is resistive in character but which is unstable when the condition usually associated with resistive instability k·B 0 = 0 is not satisfied. The instability is not present when the (cylindrical) container boundaries are perfect conductors. Fearn and Weiglhofer tried to determine what other conditions, particularly on the choice of B 0, are required for instability, but they could find no simple condition. Here we adopt a simpler plane-layer model in which the z-direction is normal to the plane, B 0 = B 0(z)1 y, and the rotation vector Ω lies in the x-z plane, making an angle θ with the z-direction. The case θ = π/2, with ω parallel to the boundaries, corresponds most closely to Fearn and Weiglhofer's (1992) cylindrical model, but is a singular case in the magnetostrophic approximation. We show that the instability exists in the plane-layer model, for all values of θ. The simpler geometry permits some analytical progress. This establishes some necessary conditions for instability.