Magnetorotational instability in a short Couette flow of liquid gallium

A concise review is given of an experimental project to study magnetorotational instability (MRI) in a short Couette geometry using liquid gallium. Motivated by the astrophysical importance and lack of direct observation of MRI in nature and in the laboratory, a theoretical stability analysis was performed to predict the required experimental parameters. Despite the long-wavelength nature of MRI, local analysis agrees excellently with global eigenmode calculations when periodic boundary conditions are used in the axial direction. To explore the effects of rigidly rotating vertical boundaries (endcaps), a prototype water experiment was conducted using dimensions and rotation rates favored by the above analysis. Significant deviations from the expected Couette flow profiles were found. The cause of the discrepancy was investigated by nonlinear hydrodynamic simulations using realistic boundary conditions. It was found that Ekman circulation driven by the endcaps transports angular momentum and qualitatively modifies the azimuthal flow. Based on this new understanding, a new design was made to incorporate two independently driven rings at each endcap. Simulations were used to optimize the design by minimizing Ekman circulation while remaining within engineering capabilities. The new apparatus, which has been constructed and assembled, is currently being tested with water and will be ready for the MRI experiment with gallium soon. This development process illustrates the value of interplay between experiment, simulation, and analytic insight.