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Standard and Helical Magnetorotational Instability

How Singularities Create Paradoxical Phenomena in MHD

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Abstract

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus explain several paradoxes in the theory of MRI that were poorly understood since the 1950s.

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Correspondence to Oleg N. Kirillov.

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Financial support from the Alexander von Humboldt Foundation and the DFG in frame of STE 991/1-1 and of SFB 609 is gratefully acknowledged.

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Kirillov, O.N., Stefani, F. Standard and Helical Magnetorotational Instability. Acta Appl Math 120, 177–198 (2012). https://doi.org/10.1007/s10440-012-9689-z

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