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University of Wisconsin Physics Department Department of Energy National Science Foundation


Accretion is a fundamental process in astrophysics by which virtually all astrophysical bodies are formed. Due to gravity, the interstellar gas and plasma collapses into rotating disks around the central, point-like accreting objects such as protostars, collapsed stars in binary systems, and supermassive black holes in active galactic nuclei. Accretion disks power many of the most luminous astrophysical objects, including X-ray binaries, probably quasars, and perhaps even gamma-ray bursts. Accretion around young stars, though less luminous, is of great interest for its role in planet formation.

For a long time it was unclear what causes the disk matter to loose its orbital energy and transport angular momentum outward to fall on the central object; the dissipation mechanism has been an area of active debate for many decades as the molecular viscosity is negligibly small, and the disks are linearly stable according to Rayleigh's criterion. The current working hypothesis, put forth in the early 1990's, is that a weak magnetic field, generated somewhere outside the disk and frozen into the highly conducting plasma that make up the accretion disk, might lead to a quickly growing magnetic instability, rendering the disks turbulent and tremendously increasing the effective viscosity. 3D numerical simulations based upon one-fluid MHD equations have shown that the nonlinear outcome of the instability is turbulence of exactly the sort required for accretion.


MRI mechanism

The MRI instability only requires a weak magnetic seed field and Keplerian-like differential rotation, similar to that of accretion disks, with angular velocity greatest towards the center, and angular momentum increasing with radius. We imagine a weak magnetic field acting like a spring connecting two fluid elements. If one fluid element is displaced inward, it speeds up, and pulls the other fluid element along with it through magnetic tension. This transfers angular momentum to the outer fluid element. After losing angular momentum, the inner fluid element falls inward, while the outer fluid element moves further outward to a radius of matching angular momentum.  As two elements separate further, magnetic tension increases and the instability grows.


How is plasma different than liquid metal?

An experiment that uses plasma is challenging since some thermal confinement is necessary to keep the plasma away from the walls and hot enough to be a good conductor. The plasma needs to be continuously fueled and heated to overcome the losses, and a scheme is required to drive the flows.

This challenge of having good confinement without a magnetic field has been the
primary motivation for using liquid metals (either sodium or gallium) as a substitute for plasma in experimental investigations of the MRI and dynamos. Liquid metals are conducting, satisfy the MHD equations, and require no magnetic field to provide initial confinement

The Plasma Couette Experiment has several advantages over liquid metal experiments for investigating the MRI. These are:







Previous MRI experiments

Laboratory investigations of the MRI using liquid metals have also been proposed by Goodman and Ji [1], Rudiger et al. [2], Kageyama et al. [3], Willis and Barenghi [4], and Noguchi et al. [5]. These experiments use liquid-metals and have velocity fields similar to Keplerian flows generated in liquid sodium or gallium using the Taylor-Couette geometry (two differentially rotating cylindrical, or spherical shells). A seed magnetic field is applied to the flows from an external electromagnetic, and the MRI is observed on magnetic probes and torque measurements.

Signatures of the MRI have been observed in a sodium based spherical Couette flow experiment Maryland [6]. Strong magnetic fluctuations with spatial structures similar to those predicted for the MRI were observed when a sufficiently large magnetic field was applied to the flow. This experiment has been criticized for having a pre-existing turbulent background flow due to Eckman pumping in boundary layers. It seems plausible that the MRI is driven by the average flow, but clarifying work remains to be done.

A second experiment by the Potsdam-Dresden group has reported observing the MRI in a cylindrical Couette flow in which a helical rather than standard axial magnetic field was applied by external coils [7]. The relevance of this setting for Keplerian accretion disks may however be limited, as argued by Liu et al. [8].

The major difficulties of the liquid metal experiments is that the low conductivity of liquid metals imply that very high speed flows and strong magnetic fields are needed simply to observe the instability.


[1] J. Goodman and H. Ji. Magnetorotational instability of dissipative couette flow. J. Fluid Mech., 462:365, 2002.

[2] G. Rudiger, M. Schultz, and D. Shalybkov. Linear magnetohydrodynamic taylor-couette instability for liquid sodium. Phys. Rev. E, 67:046312, 2003.

[3] A. Kageyama, H. Ji, J. Goodman, F. Chen, and E. Shoshan. Numerical and experimental investigation of circulation in short cylinders. J. Phys. Soc. Japan, 73:2424, 2004.

[4] A.P. Willis and C.F. Barenghi. A taylor-couette dynamo. Astron. Astrophys., 393:339, 2002.

[5] K. Noguchi, I.V. Pariev, S.A. Colgate, and J. Nordhaus. Magnetorotational instability in liquid metal couette  flow. Astrophys. J., 575:1151, 2002.

[6] D.R. Sisan, N. Mujica, W.A. Tillotson, Y.-M. Huang, W. Dorland, A.B. Hassam, T.M. Antonsen, and D.P. Lathrop. Experimental observation and characterization of the magnetorotational instability. Phys. Rev. Lett., 93:114502, 2004.

[7] F. Stefani, T. Gundrum, G. Gerbeth, Rüdiger G., M. Schultz, J. Szklarski, and R. Hollerbach.
Experimental evidence for magnetorotational instability in a taylor-couette flow under the influence
of a helical magnetic field. Phys. Rev. Lett, 97:184502, 2007.

[8] W. Liu, J. Goodman, I. Herron, and H. Ji. Helical magnetorotational instability in magnetized Taylor-Couette flow. Phys. Rev. E, 74:056302, 2006.