The stability of MHD Taylor-Couette flow with current-free spiral magnetic fields between conducting cylinders

We study the magnetorotational instability in cylindrical Taylor-Couette flow, with the (vertically unbounded) cylinders taken to be perfect conductors, and with externally imposed spiral magnetic fields. The azimuthal component of this field is generated by an axial current inside the inner cylinder, and may be slightly stronger than the axial field. We obtain an instability beyond the Rayleigh line, for Reynolds numbers of order 1000 and Hartmann numbers of order 10, and independent of the (small) magnetic Prandtl number. For experiments with R-out = 2 R-in = 10 cm and Omega(out) = 0.27 Omega(in), the instability appears for liquid sodium for axial fields of similar to 20 Gauss and axial currents of 1200 A. For gallium the numbers are similar to 50 Gauss and 3200 A. The vertical cell size is about twice the cell size known for nonmagnetic experiments.