Although the magnetorotational instability (MRI) has been widely accepted a
s a powerful accretion mechanism in magnetized accretion discs, it has not
been realized in, the laboratory. The possibility of studying MRI in a rota
ting liquid metal annulus (Couette flow) is explored by local and global st
ability analysis. Stability diagrams are drawn in dimensionless parameters,
and also in terms of the-angular velocities at the inner and outer cylinde
rs. It is shown that MRI can be triggered in a moderately rapidly rotating
table-top apparatus, using easy-to-handle metals such as gallium. Practical
issues of this proposed experiment are discussed.