  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.
