Instabilities of highly-resistive rotating liquids in helical magnetic fields

The instabilities of differential rotation of highly-resistive liquids with Pm≪1 in the presence of axial and azimuthal components of magnetic field are considered. The dispersion relation for axisymmetric perturbations in a local (short-wave) approximation (kRR≫1) is derived. It is found that the axisymmetric modes of perturbations in such a helical magnetic field are oscillating modes. In agreement with the results by Hollerbach and Rüdiger the modes have much lower thresholds than in the case of axial magnetic field. It is shown that the low-threshold instability is mainly caused by the radial inhomogeneity of B0ϕ/R and can hardly be called the magnetorotational instability (MRI). At the Rayleigh line (Ω∝R−2) far above the instability threshold the mode frequency is equal to its growth rate, and both are proportional to Ω. Away from the Rayleigh line (in the case of flatter rotation laws) the unstable mode is the weakly destabilized inertial oscillation mode. Its growth rate is small and does not exceed the value of the order of the viscous frequency.