Linear stability analysis of the Hall magnetorotational instability in a spherical domain

Kondić, Todor; Rüdiger, G.; Arlt, R.

doi:10.1002/asna.201211675

Cited by 3 publications

(3 citation statements)

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“…With spherical models it has been shown that the growth rates of SHI scale with the rotation rate and not with the rather long Hall time [191,192]. The dispersion relation (126) leads to the same conclusion.…”

Section: The Shear-hall Instability (Shi)mentioning

confidence: 79%

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Stability and instability of hydromagnetic Taylor–Couette flows

et al. 2018

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Decades ago S. Lundquist, S. Chandrasekhar, P. H. Roberts and R. J. Tayler first posed questions about the stability of Taylor-Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number Pm on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number Rm = √Re · Rm (with Re the Reynolds number of rotation, Rm its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for Pm 1 while for Pm 1 the instability instead sets in for supercritical Rm at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields, those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For Pm 1 the onset of the instability scales with Re while it scales with Rm for Pm 1. Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding Pm = 1. It scales with Re for Pm → 0 and with Rm for Pm → ∞.The presented results allow the construction of several new experiments with liquid metals as the conducting fluid. Some of them are described here and their results will be discussed together with relevant diversifications of the magnetic instability theory including nonlinear numerical studies of the kinetic and magnetic energies, the azimuthal spectra and the influence of the Hall effect.

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Section: The Shear-hall Instability (Shi)mentioning

confidence: 79%

“…It is then easy to calculate the magnetic Mach number as Mm = Rm/S. In all cases with Pm < ∼ 1 the instability exists for rapid rotation with Mm > 1.With spherical models it has been shown that the growth rates of SHI scale with the rotation rate and not with the rather long Hall time[191,192]. The dispersion relation(126) leads to the same conclusion.…”

mentioning

confidence: 82%

Stability and instability of hydromagnetic Taylor–Couette flows

et al. 2018

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“…They showed that the MRI of a Kepler flow is significantly modified by the Hall effect depending on the orientation of the magnetic field in relation to the rotation axis. Kondić et al (2012Kondić et al ( , 2011 investigated the stability of the Hall-MHD system for a spherical shell and determined its importance for newborn neutron stars. Similarly, their re-sults differ for magnetic fields aligned with the rotation axis and anti-parallel magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

Magnetic field gradient effects on the magnetorotational instability

Doğan

2017

Astron Nachr

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The magnetorotational instability (MRI), also known as the Balbus -Hawley instability, is thought to have an important role on the initiation of turbulence and angular momentum transport in accretion discs. In this work, we investigate the effect of the magnetic field gradient in the azimuthal direction on MRI. We solve the magnetohydrodynamic equations by including the azimuthal component of the field gradient. We find the dispersion relation and calculate the growth rates of the instability numerically. The inclusion of the azimuthal magnetic field gradient produces a new unstable region on wavenumber space. It also modifies the growth rate and the wavelength range of the unstable mode: the higher the magnitude of the field gradient, the greater the growth rate and the wider the unstable wavenumber range. Such a gradient in the magnetic field may be important in T Tauri discs where the stellar magnetic field has an axis which is misaligned with respect to the rotation axis of the disc.

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2013

Magnetic Processes in Astrophysics

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Linear stability analysis of the Hall magnetorotational instability in a spherical domain

Cited by 3 publications

References 25 publications

Stability and instability of hydromagnetic Taylor–Couette flows

Stability and instability of hydromagnetic Taylor–Couette flows

Magnetic field gradient effects on the magnetorotational instability

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