Linear instability of magnetic Taylor-Couette flow with Hall effect

The influence of the Hall effect on the linear marginal stability of a molecular hydrodynamic Taylor-Couette flow in the presence of an axial uniform magnetic field is considered. The Hall effect leads to the situation that the Taylor-Couette flow becomes unstable for any ratio of the angular velocities of the inner and outer cylinders. The instability, however, does not exist for both signs of the axial magnetic field B0. For positive shear dOmega/dR the Hall instability exists for negative Hartmann number and for negative shear dOmega/dR the Hall instability exists for positive Hartmann number. For negative shear, of course, the Hall instability combines with the magnetorotational instability, resulting in a rather complex bifurcation diagram. In this case the critical magnetic Reynolds numbers with Hall effect are much lower than without Hall effect. In order to verify the presented shear-Hall instability at the laboratory with experiments using liquid metals, one would need rather large magnetic fields ( approximately 10(7) G).