Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow

Abstract

This paper presents the analysis of axisymmetric helical magnetorotational instability (HMRI) in the inviscid limit, which is relevant for astrophysical conditions. The inductionless approximation defined by zero magnetic Prandtl number is adopted to distinguish the HMRI from the standard MRI in the cylindrical Taylor-Couette flow subject to a helical magnetic field. Using a Chebyshev collocation method convective and absolute instability thresholds are computed in terms of the Elsasser number for a fixed ratio of inner and outer radii λ=2 and various ratios of rotation rates and helicities of the magnetic field. It is found that the extension of self-sustained HMRI modes beyond the Rayleigh limit does not reach the astrophysically relevant Keplerian rotation profile not only in the narrow- but also in the finite-gap approximation. The Keppler limit can be attained only by the convective HMRI mode provided that the boundaries are perfectly conducting. However, this mode requires not only a permanent external excitation to be observable but also has a long axial wave length, which is not compatible with limited thickness of astrophysical accretion disks.

12 pages, 9 figures, published version with a few typos corrected

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• Destabilization of rotating flows with positive shear by azimuthal magnetic fields
• Generalised quasi-linear approximation of the HMRI
• Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Inconsistency in the Standard Model for Thin Accretion Disks
• Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
• Metamorphosis of helical magnetorotational instability in the presence axial electric current
• Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• High-speed standard magneto-rotational instability
• The inviscid instability in an electrically conducting fluid affected by a parallel magnetic field