Helical magnetorotational instability of Taylor-Couette flows in the Rayleigh limit and for quasi-Kepler rotation

Abstract

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current-free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short-wave approximation. All the solutions are overstable for B_z \cdot B_ϕ\neq 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor-Couette flows between rotating cylinders. -- With B_phi and B_z of the same order the traveling-mode solutions are also prefered for flat rotation laws such as the quasi-Kepler rotation. For magnetic Prandtl number Pm\to 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. -- Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_ϕ/B_z only for the extrema. For B_ϕ>> B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z >> B_ϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered.

arXiv comment8 pages, 12 figures, accepted for publication in Astron. Nachr

References in corpus (5)

• Magnetorotational Instability in a Rotating Liquid Metal Annulus
• New type of magneto-rotational instability in cylindrical Taylor-Couette flow
• MHD instability in differentially rotating cylindric flows
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• Magneto-rotational overstability in accretion disks

Cited by in corpus (7)

• Stability and instability of hydromagnetic Taylor-Couette flows
• On the relation of standard and helical magnetorotational instability
• Paradoxes of magnetorotational instability and their geometrical resolution
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields