Flow shear stabilization of rotating plasmas due to the Coriolis effect

Haverkort, J.W.; Blank, H. J. de

doi:10.1103/physreve.86.016411

“…, and this for all poloidal-toroidal mode number pairs. At the same time, Haverkort & de Blank (2012) clearly showed that in such 2D equilibrium settings as valid for accretion tori, a radially decreasing toroidal rotation frequency can be stabilizing for nonaxisymmetric MHD modes, by a Coriolis pressure effect. This finding is relevant both for accretion disks and for rotating, toroidally confined laboratory plasmas (which are known to feature transport barriers).…”

Section: Cylindrical Versus Toroidal Analysismentioning

confidence: 91%

The Super-Alfvénic Rotational Instability in Accretion Disks about Black Holes

Goedbloed

¹

,

Keppens

²

2022

ApJS

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The theory of instability of accretion disks about black holes, neutron stars, or protoplanets is revisited by means of the recent method of the Spectral Web. The cylindrical accretion disk differential equation is shown to be governed by the forward and backward Doppler-shifted continuous Alfvén spectra Ω A ± ≡ m Ω ± ω A , where ω A is the static Alfvén frequency. It is crucial to take nonaxisymmetry (m ≠ 0) and super-Alfvénic rotation of the Doppler frames (∣mΩ∣ ≫ ∣ω A∣) into account. The continua Ω A + and Ω A − then overlap, ejecting a plethora of super-Alfvénic rotational instabilities (SARIs). In-depth analysis for small inhomogeneity shows that the two Alfvén singularities reduce the extent of the modes to sizes much smaller than the width of the accretion disk. Generalization for large inhomogeneity leads to the completely unprecedented result that, for mode numbers ∣k∣ ≫ ∣m∣, any complex ω in a wide neighborhood of the real axis is an approximate “eigenvalue.” The difference with genuine eigenmodes is that the amount of complementary energy to excite the modes is tiny, ∣W com∣ ≤ c, with c the machine accuracy of the computation. This yields a multitude of two-dimensional continua of quasi-discrete modes: quasi-continuum SARIs. We conjecture that the onset of 3D turbulence in magnetized accretion disks is governed not by the excitation of discrete axisymmetric magnetorotational instabilities but by the excitation of modes from these two-dimensional continua of quasi-discrete nonaxisymmetric SARIs.

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“…The approach presented in [7] has been extensively employed for the study of highly localised (Suydam-like) modes in cylindrical and toroidal ideal plasmas [8][9][10]. Various stability criteria have been derived with both poloidal and toroidal rotation [8][9][10]. Global m=1 modes, i.e.…”

Section: Introductionmentioning

confidence: 99%

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis

Brunetti

¹

,

Lazzaro

²

,

Nowak

³

2017

Plasma Phys. Control. Fusion

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The problem of the linear stability of internal magnetohydrodynamic modes in a cylindrical plasma with a sheared longitudinal flow is addressed. A Newcomb-like equation describing the perturbation is derived and exactly solved for a class of analytic profiles for rotational transform, equilibrium flow and pressure. A dispersion relation for ideal modes is then derived and analysed for different limits of the poloidal mode number (viz. m = 1, > m 1 and  m 1). In the resistive case, a simple and exact expression for the tearing stability index D¢ is derived using the same class of equilibrium profiles. It is found that a small flow shear has a destabilising effect, while if the flow shear is dominant over the magnetic shear the tearing mode is stabilised. Implications on the stability of the m=1 resistive mode are also discussed.

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“…The same is true for the TSAC modes, since in the strong field limit β 1 of magnetically dominated thick accretion tori, this continuum instability switches on whenever the squared poloidal Alfvén Mach number exceeds a value of about 1 2 γβ, and this for all poloidal-toroidal mode numbers pairs. At the same time, Haverkort & de Blank (2012) clearly showed that in such 2D equilibrium settings as valid for accretion tori, a radially decreasing toroidal rotation frequency can act stabilizing for non-axisymmetric MHD modes, by a Coriolis-pressure effect. This finding is relevant for both accretion disks and for rotating, toroidally confined, laboratory plasmas (which are known to feature transport barriers).…”

Section: Cylindrical Versus Toroidal Analysismentioning

confidence: 93%

The Super-Alfvénic Rotational Instability in accretion disks about black holes

Goedbloed,

Keppens

2022

Preprint

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The theory of instability of accretion disks about black holes, neutron stars or protoplanets, is revisited by means of the recent method of the Spectral Web. The cylindrical accretion disk differential equation is shown to be governed by the forward and backward Doppler-shifted continuous Alfvén spectra Ω ± A ≡ mΩ ± ω A , where ω A is the static Alfvén frequency. It is crucial to take non-axisymmetry (m = 0) and super-Alfvénic rotation of the Doppler frames (|mΩ|A and Ω − A then overlap, ejecting a plethora of Super-Alfvénic Rotational Instabilities (SARIs). Indepth analysis for small inhomogeneity shows that the two Alfvén singularities reduce the extent of the modes to sizes much smaller than the width of the accretion disk. Generalization for large inhomogeneity leads to the completely unprecedented result that, for mode numbers |k| |m|, any complex ω in a wide neighborhood of the real axis is an approximate 'eigenvalue'. The difference with genuine eigenmodes is that the amount of complementary energy to excite the modes is tiny, |W com | ≤ c, with c the machine accuracy of the computation. This yields a multitude of two-dimensional continua of quasi-discrete modes: quasi-continuum SARIs. We conjecture that the onset of 3D turbulence in magnetized accretion disks is governed, not by the excitation of discrete axisymmetric Magneto-Rotational Instabilities, but by the excitation of modes from these two-dimensional continua of quasidiscrete non-axisymmetric Super-Alfvénic Rotational Instabilities.

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Flow shear stabilization of rotating plasmas due to the Coriolis effect

Cited by 6 publications

References 44 publications

The Super-Alfvénic Rotational Instability in Accretion Disks about Black Holes

The Super-Alfvénic Rotational Instability in Accretion Disks about Black Holes

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis

The Super-Alfvénic Rotational Instability in accretion disks about black holes

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