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 ~20 Gauss and axial currents of \~1200 A. For gallium the numbers are ~50 Gauss and ~3200 A. The vertical cell size is about twice the cell size known for nonmagnetic experiments.