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Nonaxisymmetric patterns in the linear theory of MHD Taylor-Couette instability

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 \hatη=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 <~ 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.