Astrophysical and experimental implications from the magnetorotational instability of toroidal fields

Abstract

The interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders is considered. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfvén frequency of the field are of the same order, almost independent of the magnetic Prandtl number Pm. For the very steep rotation law Ω\propto R^{-2} (the Rayleigh limit) and for small Pm the threshold values of rotation and field for this Azimuthal MagnetoRotational Instability (AMRI) scale with the ordinary Reynolds number and the Hartmann number, resp. A laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container has been designed on the basis of this finding. For fluids with more flat rotation laws the Reynolds number and the Hartmann number are no longer typical quantities for the instability. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers \leq 1. We find that the magnetic energy grows monotonically with the magnetic Reynolds number Rm, while the kinetic energy grows with Rm/\sqrt{Pm}. The resulting turbulent Schmidt number, as the ratio of the `eddy' viscosity and the diffusion coefficient of a passive scalar (such as lithium) is of order 20 for Pm=1, but for small Pm it 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.

8 pages, 11 figures

References in corpus (5)

• Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants
• Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
• Energy distribution in nonaxisymmetric magnetic Taylor-Couette flow

Cited by in corpus (15)

• Experimental evidence for non-axisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field
• The angular momentum transport by unstable toroidal magnetic fields
• Stability and instability of hydromagnetic Taylor-Couette flows
• Characterization of Quasi-Keplerian, Differentially Rotating, Free-Boundary Laboratory Plasmas
• Fossil field decay due to nonlinear tides in massive binaries
• Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone
• Destabilization of rotating flows with positive shear by azimuthal magnetic fields
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum. V. Efficiency of the transport on the red giant branch and in the red clump
• Subcritical excitation of the current-driven Tayler instability by super-rotation
• Asteroseismology of evolved stars to constrain the internal transport of angular momentum. VI. Testing a parametric formulation for the azimuthal magneto-rotational instability
• Diffusive MHD Instabilities: Beyond the Chandrasekhar Theorem
• Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry
• Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• Mixing of a passive scalar by the instability of a differentially rotating axial pinch