ABSTRACT
The azimuthal version of the magnetorotational instability (MRI) is a nonaxisymmetric instability of a hydrodynamically stable differentially rotating flow under the influence of a purely or predominantly azimuthal magnetic field. It may be of considerable importance for destabilizing accretion disks, and plays a central role in the concept of the MRI dynamo. We report the results of a liquid metal Taylor-Couette experiment that shows the occurrence of an azimuthal MRI in the expected range of Hartmann numbers.
ABSTRACT
We consider the linear stability of dissipative magnetic Taylor-Couette flow with imposed toroidal magnetic fields. The inner and outer cylinders can be either insulating or conducting; the inner one rotates, the outer one is stationary. The magnetic Prandtl number can be as small as 10(-5) , approaching realistic liquid-metal values. The magnetic field destabilizes the flow, except for radial profiles of B(phi)(R) close to the current-free solution. The profile with B(in)=B(out) (the most uniform field) is considered in detail. For weak fields the Taylor-Couette flow is stabilized, until for moderately strong fields the m=1 azimuthal mode dramatically destabilizes the flow again so that a maximum value for the critical Reynolds number exists. For sufficiently strong fields (as measured by the Hartmann number) the toroidal field is always unstable, even for the nonrotating case with Re=0 . The electric currents needed to generate the required toroidal fields in laboratory experiments are a few kA if liquid sodium is used, somewhat more if gallium is used. Weaker currents are needed for wider gaps, so a wide-gap apparatus could succeed even with gallium. The critical Reynolds numbers are only somewhat larger than the nonmagnetic values; hence such experiments would work with only modest rotation rates.
ABSTRACT
A recent Letter [R. Hollerbach and G. Rüdiger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability in a Taylor-Couette flow is dramatically reduced if both axial and azimuthal magnetic fields are imposed. In agreement with this prediction, we present results of a Taylor-Couette experiment with the liquid metal alloy GaInSn, showing evidence for the existence of the magnetorotational instability at Reynolds numbers of order 1000 and Hartmann numbers of order 10.
ABSTRACT
The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic Prandtl number Pm of order 10(-5). The calculations are performed for a container with R(out)=2R(in), with an axial uniform magnetic field and with boundary conditions for both vacuum and perfect conductions. For resting outer cylinder subcritical excitation in comparison to the hydrodynamical case occurs for large Pm but it disappears for small Pm. For rotating outer cylinder the Rayleigh line plays an exceptional role. The hydromagnetic instability exists with Reynolds numbers exactly scaling with Pm(-1/2) so that the moderate values of order 10(4) (for Pm=10(-5)) result. For the smallest step beyond the Rayleigh line, however, the Reynolds numbers scale as 1/Pm leading to much higher values of order 10(6). Then it is the magnetic Reynolds number Rm that directs the excitation of the instability. It results as lower for insulating than for conducting walls. The magnetic Reynolds number has to exceed here values of order 10 leading to frequencies of about 20 Hz for the rotation of the inner cylinder if containers with (say) 10 cm radius are considered. With vacuum boundary conditions the excitation of nonaxisymmetric modes is always more difficult than the excitation of axisymmetric modes. For conducting walls, however, crossovers of the lines of marginal stability exist for both resting and rotating outer cylinders, and this might be essential for future dynamo experiments. In this case the instability also can onset as an overstability.
