The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for various magnetic Prandtl numbers Pm .
The calculations are performed for a wide gap container with \hat { \eta } = 0.5 with an axial uniform magnetic field excluding counterrotating cylinders .
For both hydrodynamically stable and unstable flows the magnetorotational instability produces characteristic minima of the Reynolds number for certain ( low ) magnetic field amplitudes and Pm > 0.01 .
For Pm \buildrel < \over { \scriptstyle \sim } 1 there is a characteristic magnetic field amplitude beyond which the instability sets in in form of nonaxisymmetric spirals with the azimuthal number m = 1 .
Obviously , the magnetic field is able to excite nonaxisymmetric configurations despite of the tendency of differential rotation to favor axisymmetric magnetic fields which is known from the dynamo theory .
If Pm is too big or too small , however , the axisymmetric mode with m =0 appears to be the most unstable one possessing the lowest Reynolds numbers – as it is also true for hydrodynamic Taylor-Couette flow or for very weak fields .
That the most unstable mode for modest Pm proves to be nonaxisymmetric must be considered as a strong indication for the possibility of dynamo processes in connection with the magnetorotational instability .