Magnetorotational instability in a rotating liquid metal annulus

Ji, Hantao; Goodman, P Jeremy; Kageyama, Akira

doi:10.1046/j.1365-8711.2001.04647.x

Cited by 172 publications

(161 citation statements)

References 32 publications

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“…Here we generalize the derivation of the MRI dispersion equation (1) given in Kato, Fukue & Mineshige (1998) for the case of nonideal plasma with arbitrary kinetic coefficients ν and η (see also Ji, Goodman & Kageyama (2001)). …”

Section: Appendix A: Derivation Of the Dispersion Equation For Non-idmentioning

confidence: 88%

“…This problem has been addressed previously by different authors (see, e.g. Balbus & Hawley (1998); Sano & Miyama (1999); Ji, Goodman & Kageyama (2001); Balbus (2004); Islam & Balbus (2005); Pessah & Chan (2008), among others), aimed at studying various aspects of the MRI physics and applications. To keep the paper self-contained, we re-derive the basic dispersion relation in the general case and investigate its behaviour for different values of the magnetic Prandtl number P m = ν/η and the kinematic vicosity ν.…”

Section: Introductionmentioning

confidence: 99%

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On properties of Velikhov–Chandrasekhar MRI in ideal and non-ideal plasma

Шакура¹,

Постнов²

2015

Monthly Notices of the Royal Astronomical Society

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Conditions of Velikhov-Chandrasekhar magneto-rotational instability in ideal and non-ideal plasmas are examined. Linear WKB analysis of hydromagnetic axially symmetric flows shows that in the Rayleigh-unstable hydrodynamic case where the angular momentum decreases with radius, the MRI branch becomes stable, and the magnetic field suppresses the Rayleigh instability at small wavelengths. We investigate the limiting transition from hydromagnetic flows to hydrodynamic flows. The Rayleigh mode smoothly transits to the hydrodynamic case, while the Velikhov-Chandrasekhar MRI mode completely disappears without the magnetic field. The effects of viscosity and magnetic diffusivity in plasma on the MRI conditions in thin accretion discs are studied. We find the limits on the mean free-path of ions allowing MRI to operate in such discs.

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Section: Appendix A: Derivation Of the Dispersion Equation For Non-idmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

On properties of Velikhov–Chandrasekhar MRI in ideal and non-ideal plasma

Шакура¹,

Постнов²

2015

Monthly Notices of the Royal Astronomical Society

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“…2. The experiment was designed to produce quasi-Keplerian flows of a liquid gallium alloy, GaInSn (Morley et al 2008) which would become unstable to the MRI in the presence of an applied solenoidal magnetic field (Ji et al 2001). To minimize the volume of GaInSn required for the MRI studies, the height of the cylinders is only twice the gap width between them, h/Δr = h/ (r 2 − r 1 ) ≈ 2.…”

Section: Methodsmentioning

confidence: 99%

“…It is worth noting that the β prescription by Richard & Zahn (1999), even if valid for the cyclonic evidence on which they based it, may not be valid for anti-cyclonic flow, in particular Keplerian flow. The Princeton MRI experiment is a Taylor-Couette device developed (Schartman et al 2009) to produce quasi-Keplerian flows in both water and a liquid gallium alloy to look for evidence of both SHI using water and the MRI using alloy (Ji et al 2001;Goodman & Ji 2002). The flows of interest are diagrammed in Fig.…”

Section: Introductionmentioning

confidence: 99%

Stability of quasi-Keplerian shear flow in a laboratory experiment

Schartman

Burin

et al. 2012

A&A

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Context. Subcritical transition to turbulence has been proposed as a source of turbulent viscosity required for the associated angular momentum transport for fast accretion in Keplerian disks. Previously cited laboratory experiments in supporting this hypothesis were performed either in a different type of flow than Keplerian or without quantitative measurements of angular momentum transport and mean flow profile, and all of them appear to suffer from Ekman effects, secondary flows induced by nonoptimal axial boundary conditions. Such Ekman effects are expected to be absent from astronomical disks, which probably have stress-free vertical boundaries unless strongly magnetized. Aims. To quantify angular momentum transport due to subcritical hydrodynamic turbulence, if exists, in a quasi-Keplerian flow with minimized Ekman effects. Methods. We perform a local measurement of the azimuthal-radial component of the Reynolds stress tensor in a novel laboratory apparatus where Ekman effects are minimized by flexible control of axial boundary conditions. Results. We find significant Ekman effects on angular momentum transport due to nonoptimal axial boundary conditions in quasiKeplerian flows. With the optimal control of Ekman effects, no statistically meaningful angular momentum transport is detected in such flows at Reynolds number up to two millions. Conclusions. Either a subcritical transition does not occur, or, if a subcritical transition does occur, the associated radial transport of angular momentum in optimized quasi-Keplerian laboratory flows is too small to directly support the hypothesis that subcritical hydrodynamic turbulence is responsible for accretion in astrophysical disks. Possible limitations in applying laboratory results to astrophysical disks due to experimental geometry are discussed.

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“…Because of the simplicity of this geometry, much work has been done to study the MRI for fluids between cylinders rotating with different angular velocities. Theory (Rüdiger & Zhang 2001;Ji et al 2001) and experiments (see Stefani et al 2009) revealed the possibilities to realize the MRI even in the laboratory.…”

Section: The Modelmentioning

confidence: 99%

The angular momentum transport by standard MRI in quasi-Kepler cylindrical Taylor-Couette flows

Gellert¹,

Rüdiger²,

Schultz³

2012

A&A

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We studied the instability of a dissipative quasi-Keplerian flow influenced by a homogeneous axial magnetic field in the geometry of a Taylor-Couette system. Especially we focus on the excitation of nonaxisymmetric modes and the resulting angular momentum transport, not on dynamo action. The excitation of nonaxisymmetric modes requires higher rotation rates than the excitation of the axisymmetric mode and this the more the higher the azimuthal mode number m is. We find that the weak-field branch in the instability map of the nonaxisymmetric modes always has a positive slope (in contrast to the axisymmetric modes) so that for given magnetic field the modes with m > 0 always have an upper limit of the supercritical Reynolds number. To excite a nonaxisymmetric mode at 1 AU in a Kepler disk, a minimum field strength of about 1 Gauss is necessary. For weaker magnetic field the nonaxisymmetric modes decay. The angular momentum transport of the nonaxisymmetric modes is always positive and depends linearly on the Lundquist number of the background field. The molecular viscosity and the basic rotation rate do not influence the related α-parameter. We did not find any indication that the magnetorotational instability decays for small magnetic Prandtl numbers as was found by using shearing-box codes. At 1 AU in a Kepler disk and with a field strength of about 1 Gauss α proves to be (only) about 0.005.

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Magnetorotational instability in a rotating liquid metal annulus

Cited by 172 publications

References 32 publications

On properties of Velikhov–Chandrasekhar MRI in ideal and non-ideal plasma

On properties of Velikhov–Chandrasekhar MRI in ideal and non-ideal plasma

Stability of quasi-Keplerian shear flow in a laboratory experiment

The angular momentum transport by standard MRI in quasi-Kepler cylindrical Taylor-Couette flows

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