## The azimuthal magnetorotational instability (AMRI)    [PDF]

G. Ruediger, M. Gellert, M. Schultz, R. Hollerbach, F. Stefani
We consider the interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfven frequency of the field are of the same order almost independent of the magnetic Prandtl number Pm. For the very steep rotation law \Omega\propto R^{-2} (the Rayleigh limit) this Azimuthal MagnetoRotational Instability (AMRI) scales with the ordinary Reynolds number and the Hartmann number, which allows a laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container. The growth rate of AMRI scales with \Omega^2 in the low-conductivity limit and with \Omega in the high-conductivity limit. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers between 0.05 and unity. We find that the magnetic energy scales with the magnetic Reynolds number Rm, while the kinetic energy scales with Rm/\sqrt{Pm}. The resulting turbulent Schmidt number as the ratio of the diffusion coefficients of angular momentum and a passive scalar (such as lithium) is of order 20 for Pm=1, but for small Pm drops to order unity. Hence, in a stellar core with fossil fields and steep rotation law the transport of angular momentum by AMRI is always accompanied by an intense mixing of the plasma, until the rotation becomes rigid.
View original: http://arxiv.org/abs/1303.4621