Magnetorotational Instability in a Couette Flow of Plasma

Abstract

All experiments, which have been proposed so far to model the magnetorotational instability (MRI) in the laboratory, involve a Couette flow of liquid metals in a rotating annulus. All liquid metals have small magnetic Prandtl numbers, Pm, of about 10^{-6} (the ratio of kinematic viscosity to magnetic diffusivity). With plasmas both large and small Pm are achievable by varying the temperature and the density of plasma. Compressibility and fast rotation of the plasma result in radial stratification of the equilibrium plasma density. Evolution of perturbations in radially stratified viscous and resistive plasma permeated by an axial uniform magnetic field is considered. The differential rotation of the plasma is induced by the ExB drift in applied radial electric field. Global unstable eigenmodes are calculated by our newly developed matrix code. The plasma is shown to be MRI unstable for parameters easily achievable in experimental setup.Comment: 6 pages, 2 figures; to be published in the Proceedings of the 3d Workshop on Non-Neutral Plasmas, July 2003, Santa Fe, US

Equilibrium magnetohydrodynamic flows of liquid metals in magnetorotational instability experiments

“…This results in different phenomena such as enhanced angular momentum transport and magnetic dynamo (Balbus & Hawley 1998;Balbus 2003;Silk & Langer 2006). Because of the role played by MRI in astrophysics, a number of experiments have been initiated in recent years to test this instability in the laboratories (Noguchi et al 2002;Noguchi & Pariev 2003;Ji et al 2004;Sisan et al 2004;Stefani et al 2006;Velikhov et al 2006b). The idea of these experiments is to drive the rotation of a conducting fluid (liquid metal or plasma) and investigate its stability in an external magnetic field.…”

“…Two different mechanisms of fluid rotation have been proposed for MRI experiments: mechanical drive by virtue of the viscous drag force acting on the fluid between rotating coaxial cylinders -the so-called Taylor-Couette flow or TCF (figure 1; Noguchi et al 2002;Ji et al 2004;Stefani et al 2006), and electrical drive by the Ampere force arising when an electric current is passed through the fluid, which is in a transverse magnetic field -electrically driven flow or EDF (figure 2; Noguchi & Pariev 2003;Velikhov et al 2006b). In most of the existing MRI experiments TCF is used.…”

Prospects for observing the magnetorotational instability in the plasma Couette experiment

“…Analysis of EDF in relation to the MRI has been presented in various parameter regimes using dissipative single-fluid MHD (Noguchi & Pariev 2003;Khalzov et al 2006Khalzov et al , 2010. In this analysis Hall and neutral collision terms are included to reflect the regime of weakly-ionized sparse plasmas.…”