A recent paper [R. Hollerbach and G. Rüdiger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability (MRI) 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 MRI at Reynolds numbers of order 1000 and Hartmann numbers of order 10.The role of magnetic fields in the cosmos is two-fold: First, planetary, stellar and galactic fields are a product of the homogeneous dynamo effect in electrically conducting fluids. Second, magnetic fields are also believed to play an active role in cosmic structure formation, by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI) [1]. Considerable theoretical and computational progress has been made in understanding both processes. The dynamo effect has even been verified experimentally, in large-scale liquid sodium facilities in Riga and Karlsruhe, and continues to be studied in laboratories around the world [2]. In contrast, obtaining the MRI experimentally has been less successful thus far [3]. ([4] claim to have observed it, but their background state was already fully turbulent, thereby defeating the original idea that the MRI would destabilize an otherwise stable flow.)If only an axial magnetic field is externally applied, the azimuthal field that is necessary for the occurrence of the MRI must be produced by induction effects, which are proportional to the magnetic Reynolds number (Rm) of the flow. But why not substitute this induction process simply by externally applying an azimuthal magnetic field as well ? This question was at the heart of the paper [5], where it was shown that the MRI is then possible with far smaller Reynolds (Re) and Hartmann (Ha) numbers. In this paper we report experimental verification of this idea, presenting evidence of the MRI in a liquid metal Taylor-Couette (TC) flow with externally imposed axial and azimuthal (i.e., helical) magnetic fields.

Abstract. We present shell dynamo models for the solar convection zone with positive α-effect in the northern hemisphere and a meridional circulation which is directed equatorward at the bottom and poleward at the top of the convection zone. Two different rotation patterns are used: a simple variation of the rotation rate with depth and the rotation law as derived by helioseismology. Depending on the Reynolds number associated with the meridional flow, the dynamo shows a whole "zoo" of solutions. For sufficiently small values of the eddy magnetic diffusivity (10 11 cm 2 /s), field advection by the meridional flow becomes dominant and even changes the character of the butterfly diagram. Flow amplitudes of a few m/s are then sufficient to turn the originally "wrong" butterfly diagram into a "solar-type" butterfly diagram, i.e. with activity belts drifting equatorward. This effect can easily be demonstrated with a super-rotation law (∂Ω/∂r > 0) with Ω independent of the latitude. The situation is much more complicated for the "real" rotation law with the observed strong negative shear at high latitudes. With zero meridional flow, oscillating solutions are found without any latitudinal migration of the toroidal field belts, neither poleward nor equatorward. Small but finite flow amplitudes cause the magnetic field belts to drift poleward while in case of fast flow they move equatorward.

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.

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.

We consider the effect of toroidal magnetic fields on hydrodynamically stable Taylor–Couette differential rotation flows. For current‐free magnetic fields a non‐axisymmetric m= 1 magnetorotational instability arises when the magnetic Reynolds number exceeds O(100). We then consider how this ‘azimuthal magnetorotational instability’ (AMRI) is modified if the magnetic field is not current‐free, but also has an associated electric current throughout the fluid. This gives rise to current‐driven Tayler instabilities (TIs) that exist even without any differential rotation at all. The interaction of the AMRI and the TI is then considered when both electric currents and differential rotation are present simultaneously. The magnetic Prandtl number Pm turns out to be crucial in this case. Large Pm have a destabilizing influence, and lead to a smooth transition between the AMRI and the TI. In contrast, small Pm have a stabilizing influence, with a broad stable zone separating the AMRI and the TI. In this region the differential rotation is acting to stabilize the TIs, with possible astrophysical applications (Ap stars). The growth rates of both the AMRI and the TI are largely independent of Pm, with the TI acting on the time‐scale of a single rotation period, and the AMRI slightly slower, but still on the basic rotational time‐scale. The azimuthal drift time‐scale is ∼20 rotations, and may thus be a (flip‐flop) time‐scale of stellar activity between the rotation period and the diffusion time.