Magnetorotational instability in electrically driven flow of liquid metal : Spectral analysis of global modes

The spectral magnetohydrodynamics stability of liquid metal differentially rotating in transverse magnetic field is studied numerically by solving the eigenvalue problem with rigid-wall boundary conditions. The equilibrium velocity profile used in calculations corresponds to the electrically driven flow in circular channel with the rotation law Ω(r)∝1∕r2. This type of flow profile is planned to be used in new experimental devices to test the magnetorotational instability (MRI) in the laboratory. Our analysis includes calculations of the eigenfrequency spectra for both axisymmetric (with azimuthal wavenumber m=0) and nonaxisymmetric (m≠0) modes. It is shown that for certain parameters the flow is unstable with respect to MRI with the fastest growth rate corresponding to the axisymmetric mode. For other parameters, the axisymmetric MRI modes can be suppressed and the instability develops only for modes with m≠0.