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Convection Caused Symmetry Breaking of Azimuthal Magnetorotational Instability in a Liquid Metal Taylor Couette Flow

Stefani, F.; Seilmayer, M.

In the laboratory, the magnetorotational instability (MRI) can be observed in azimuthal (AMRI) or helical (HMRI) magnetic field configurations. In both variants, the shear flow between the two cylinders is operating in the hydrodynamically stable regime (Ωo∕Ωi >0.25). AMRI occurs then as an m=1 -symmetric wave with a characteristic drift and spatial frequency. First evidence of AMRI was obtained some years ago by Seilmayer et al. [1]. A Taylor Couette (TC) setup, filled with liquid metal (GaInSn), was exposed to a magnetic field Bφ∝r^(-1), which lead to instability of the flow. In that previous setup, the necessary current was supplied by a large frame of copper rods which also caused a residual m=1 magnetic field disturbance producing a stationary dominant background flow. Since then, several changes took place to circumvent external asymmetries and influences.
The main improvement was the symmetric current return path which eliminates the m=1 background flow and reduces stray fields. This optimized magnetic field system leads to a symmetric B_φ distribution. However, remaining mechanical misalignments of each axis (two cylinder axes, central rod axis) still impose a weak residual m=1 modulation of magnetic field with respect to the liquid metal flow. Nevertheless, the field displacement could be minimized to a value in the order of 1 mm by the present installation.
We observe a reasonable energy dependence of the dominant m=1 mode on the Hartmann number. But drift and spatial distribution differ from theory [2] and may depend on current and/or B_φ. The main feature is a symmetry breaking, which leads to an AMRI wave which is mainly located at the top of the cylinder. This is surprising since the theoretical prediction point to a symmetric wave with m=± 1 configuration. However, the wave component in the lower half of the cylindrical volume remained missing until now. The measured velocity in the range of v=O(1 mm/s) is inferred from an Ultrasound Doppler Velocimetry (UDV) system.
Recent observations indicate that thermal convection could be a possible source of symmetry breaking. It turns out that a minimal radial heat flux q ̇≈0.1 W⋅m^(-2) or a temperature difference of about Δϑ≈10^(-2) K across the cylindrical gap can cause a significant convection flow in the present TC-setup. Here, significant Rayleigh numbers Ra≈10^(4…5) can be achieved right from the beginning because of the liquid metal properties with a typically low Prandtl number of Pr=0.033 in conjunction with the low viscosity ν=3.4⋅10^(-7) m^2⋅s^(-1). As the driving heat source the radiation of the inner current carrying rod could be identified.
Figure 2 (left) summarizes different convective flow regimes, which occur for a hydrodynamic stable TC configuration with Ωi=0, Ωo≈0 and Irod=20 kA driving the convection due to radiation from the central rod. The thermal boundary condition is then defined by the vacuum insulation (Fig. 1 (1)) and the inner boundary of the vessel (Fig. 1 (8)) forming a small cylindrical gap with 3 mm in width and 0.4 m in height. The combinations of different insulation schemes (top/bottom/open chimney) indicate a connection between heat transport features and thermal convection. The solid line in Figure 2 (left) is the result of an axisymmetric MHD-simulation to verify the “convective” flow pattern, which was gained experimentally by UDV. Figure 2 (right) illustrates an ARMI run with Ω_o⁄Ω_i =0.26 and I=12.87 kA (Ha=100) when the yellow coil (see Fig. 1) heated the fluid to ϑ_Fluid≈30°C prior which also corresponds to a heat flux pointing radially inward. The AMRI wave then travels upwards as seen in the left part. Right after the switch off event at t=0 the hot copper coil starts to cool down. In the moment the heat flux points radially outwards again at t≈3000 s, the wave at the bottom is suppressed and the wave in the upper half starts to evolve as usual. Here convection reverses to normal operation which corresponds to a heated-from-inside regime.
We like to present experimental results giving evidence of the dependence of AMRI mode on thermal boundary conditions which affect the symmetry breaking of AMRI in a TC-setup.

[1] M. Seilmayer, V. Galindo, G. Gerbeth, T. Gundrum, F. Stefani, M. Gellert, G. Rüdiger, M. Schultz, and R. Hollerbach, Phys. Rev. Lett. 113, 024505 (2014).
[2] G. Rüdiger, R. Hollerbach, M. Gellert, and M. Schultz, Astron. Nachrichten 328, 1158 (2007).

Keywords: AMRI; magnetorotational instability; Taylor Couette

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Publ.-Id: 28445