The Tayler instability of toroidal magnetic fields in a columnar gallium experiment

Abstract

The nonaxisymmetric Tayler instability of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two coaxial cylinders without endplates. The inner cylinder is considered as so thin that even the limit of R_in \to 0 can be computed. The magnetic Prandtl number is varied over many orders of magnitudes but the azimuthal mode number of the perturbations is fixed to m=1. In the linear approximation the critical magnetic field amplitudes and the growth rates of the instability are determined for both resting and rotating cylinders. Without rotation the critical Hartmann numbers do {\em not} depend on the magnetic Prandtl number but this is not true for the growth rates. For given product of viscosity and magnetic diffusivity the growth rates for small and large magnetic Prandtl number are much smaller than those for Pm=1. For gallium under the influence of a magnetic field at the outer cylinder of 1 kG the resulting growth time is 5 s. The minimum electric current through a container of 10 cm diameter to excite the kink-type instability is 3.20 kA. For a rotating container both the critical magnetic field and the related growth times are larger than for the resting column.

7 pages, 9 figures, submitted to Astron. Nachr

References in corpus (5)

• Stellar evolution with rotation and magnetic fields:III: The interplay of circulation and dynamo
• The Stability of Magnetized Rotating Plasmas with Superthermal Fields
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• Theory of current instability experiments in magnetic Taylor-Couette flows
• Nonaxisymmetric patterns in the linear theory of MHD Taylor-Couette instability

Cited by in corpus (8)

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• Stability and instability of hydromagnetic Taylor-Couette flows
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Critical fields and growth rates of the Tayler instability as probed by a columnar gallium experiment
• Magnetic field dynamos and magnetically triggered flow instabilities
• Elementary model of internal electromagnetic pinch-type instability