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Azimuthal magnetorotational instability with super-rotation

Part of: 50 years of Mean Field Electrodynamics

Published online by Cambridge University Press:  25 January 2018

G. Rüdiger ,
M. Schultz ,
M. Gellert  and
F. Stefani
G. Rüdiger*
Affiliation:
Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
M. Schultz
Affiliation:
Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
M. Gellert
Affiliation:
Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
F. Stefani
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, PF 510119, 01314 Dresden, Germany
*
†Email address for correspondence: gruediger@aip.de
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Abstract

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

Keywords

astrophysical plasmasplasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 1 , February 2018 , 735840101
Copyright
© Cambridge University Press 2018 

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