Importance of Finite Thermal Energy Density and Singular Modes for the Transport of Angular Momentum in Accretion Disks

Coppi, B.; Coppi, P.

doi:10.1006/aphy.2001.6140

Cited by 3 publications

(5 citation statements)

References 23 publications

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“…We note that, as shown by Coppi & Coppi (2001a, 2001b,v v and the plasma displacement R do not vanish…”

Section: Mode Profile Equationmentioning

confidence: 91%

“…These modes, as was demonstrated by Coppi & Coppi (2001a, 2001b, are characterized by being evanescent in the vertical direction and oscillatory in the radial direction and are represented bỹ…”

Section: Contained Modesmentioning

confidence: 96%

“…The most immediate approach to this problem is that of considering modes that are axisymmetric and are of the same type as those found originally for a long cylindrical plasma (Velikhov 1959;Chandrasekhar 1960;Balbus & Hawley 1991). Coppi & Coppi (2001a, 2001b pointed out that these axisymmetric modes when applied to a thin-disk configuration become of the ballooning type (Coppi 1977) in the vertical direction; i.e., they cannot be represented by a single Fourier harmonic and acquire a characteristic oscillation in the radial direction. The radial wavelength is related to the distance over which the mode is localized vertically.…”

Section: Introductionmentioning

confidence: 98%

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Ballooning Modes in Thin Accretion Disks: Limits for Their Excitation

Coppi

Keyes

2003

ApJ

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The conditions that limit the possible excitation of ideal MHD axisymmetric ballooning modes in thin accretion disks are discussed. As shown in 2001 by Coppi & Coppi, these modes are well localized in the vertical direction but have characteristic oscillatory and nonlocalized profiles in the radial direction. A necessary condition for their excitation is that the magnetic energy be considerably lower than the thermal energy. Even when this is satisfied, there remains the problem of identifying the possible physical factors that can make the considered modes radially localized. The general solution of the normal mode equation describing the modes is given, showing that it is characterized by a discrete spectrum of eigensolutions. The growth rates are reduced and have a different scaling relative to that of the '' long-cylinder '' modes, commonly known as the magnetorotational instability, that have been previously studied.

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“…We note that, as shown by Coppi & Coppi (2001a, 2001b,v v and the plasma displacement R do not vanish…”

Section: Mode Profile Equationmentioning

confidence: 91%

Section: Contained Modesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

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Ballooning Modes in Thin Accretion Disks: Limits for Their Excitation

Coppi

Keyes

2003

ApJ

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“…It has been noted also that application of the MRI to astrophysical disks may require various extensions of the basic theoretical model beyond the simple magnetohydrodynamics ͑MHD͒, and, in particular, may require consideration of nonaxisymmetric modes and resonance effects. 5,6 Great potential importance of MRI-type instabilities for astrophysics and intensive theoretical studies naturally led to the efforts to simulate this instability in a laboratory experiment. 7,8 A number of experiments has been proposed and performed ͑in various stages͒ over the recent years.…”

Section: Introductionmentioning

confidence: 99%

Magnetorotational instability in electrically driven flow of liquid metal: Spectral analysis of global modes

et al. 2006

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The spectral stability of liquid metal differentially rotating in transverse magnetic field is studied numerically by solving the eigenvalue problem with rigid-wall boundary conditions. The equilibrium velocity profile used in calculations corresponds to the electrically driven flow in circular channel with the rotation law Ω(r) ∝ 1/r 2 . This type of flow profile is planned to be used in new experimental device to test the magnetorotational instability (MRI) in laboratory. Our analysis includes calculations of the eigen-frequency spectra for both axisymmetric and non-axisymmetric modes. It is found that for chosen device parameters the flow is always spectrally unstable due to MRI with the fastest growth rate corresponding to the axisymmetric mode.

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“…In ideal MHD, the MRI threshold to a significant degree is affected by singularities inherent in eigen-value problem [27]. In incompressible limit, the MRI of non-axisymmetric modes is associated with one set of these singularities -the so-called Alfven resonances [25].…”

mentioning

confidence: 99%

Magnetorotational instability in electrically driven fluids

Khalzov,

Smolyakov,

Ilgisonis

2007

Preprint

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Importance of Finite Thermal Energy Density and Singular Modes for the Transport of Angular Momentum in Accretion Disks

Cited by 3 publications

References 23 publications

Ballooning Modes in Thin Accretion Disks: Limits for Their Excitation

Ballooning Modes in Thin Accretion Disks: Limits for Their Excitation

Magnetorotational instability in electrically driven flow of liquid metal: Spectral analysis of global modes

Magnetorotational instability in electrically driven fluids

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