Nonaxisymmetric magnetorotational instabilities in cylindrical Taylor-Couette flow.

We study the stability of cylindrical Taylor-Couette flow in the presence of azimuthal magnetic fields, and show that one obtains nonaxisymmetric magnetorotational instabilities, having azimuthal wave number m=1. For Omega{o}/Omega{i} only slightly greater than the Rayleigh value (r{i}/r{o}){2}, the critical Reynolds and Hartmann numbers are Re{c} approximately 10{3} and Ha{c} approximately 10{2}, independent of the magnetic Prandtl number Pm. These values are sufficiently small that it should be possible to obtain these instabilities in the Potsdam Rossendorf Magnetic Instability Experiment.