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Morphology of two-dimensional MRI in axial symmetry

Part of: Complex Plasma Phenomena

Published online by Cambridge University Press:  03 November 2015

G. Montani  and
D. Pugliese
G. Montani*
Affiliation:
ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Roma), Italy Physics Department, ‘Sapienza’ University of Rome, P.le Aldo Moro 5, 00185 (Roma), Italy
D. Pugliese
Affiliation:
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava, Czech Republic
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we analyse the linear stability of a stellar accretion disk having a stratified morphology. The study is performed in the framework of ideal magneto-hydrodynamics and therefore results in a characterization of the linear unstable magneto-rotational modes. The peculiarity of the present scenario consists of adopting the magnetic flux function as the basic dynamical variable. Such a representation of the dynamics allows us to take account of the co-rotation theorem as a fundamental feature of the ideal plasma equilibrium and to evaluate its impact on the perturbation evolution. According to the Alfvenic nature of the magneto-rotational instability, we consider an incompressible plasma profile and perturbations propagating along the background magnetic field. Furthermore, we develop a local perturbation analysis around fiducial coordinates of the background configuration and deal with very small-scale linear dynamics in comparison to the background inhomogeneity size. The main issue of the present study is that the condition for the emergence of unstable modes is the same in the stratified plasma disk as in the case of a thin configuration. Such a feature is the result of the cancellation of the vertical derivative of the disk angular frequency from the dispersion relation, which implies that only the radial profile of the differential rotation is responsible for the trigger of the growing modes.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 495810604
Copyright
© Cambridge University Press 2015 

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References

Balbus, S. A. 1995 General local stability criteria for stratified, weakly magnetized rotating systems. Astrophys. J. 453, 380.Google Scholar
Balbus, S. A. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I. Linear analysis. II. Nonlinear evolution. Astrophys. J. 376, 214–233.Google Scholar
Balbus, S. A. & Hawley, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1–53.Google Scholar
Bisnovatyi-Kogan, G. S. & Lovelace, R. V. E. 2001 Advective accretion disks and related problems including magnetic fields. New Astron. Rev. 45, 663–742; arXiv:astro-ph/0207625.Google Scholar
Chandrasekhar, S. 1960 The stability of non-dissipative Couette flow in hydromagnetics. Proc. Natl Acad. Sci. USA 46 (1), 253–257.Google Scholar
Coppi, B. 2005 Crystal magnetic structure in axisymmetric plasma accretion disks. Phys. Plasmas 12 (5), 11002.CrossRefGoogle Scholar
Ferraro, V. C. A. 1937 The non-uniform rotation of the Sun and its magnetic field. Mon. Not. R. Astron. Soc. 97, 458–462.Google Scholar
Ogilvie, G. I. 1997 The equilibrium of a differentially rotating disc containing a poloidal magnetic field. Mon. Not. R. Astron. Soc. 288, 63–77.Google Scholar
Shakura, N. I. 1973 Disk model of gas accretion on a relativistic star in a close binary system. Sov. Astron. 16, 756.Google Scholar
Shakura, N. I. & Sunyaev, R. A. 1973 Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355.Google Scholar
Velikhov, E. P. 1959 A powerful local shear instability in weakly magnetized disks. I. Linear analysis. II. Nonlinear evolution. Sov. Phys. JETP 36, 1398.Google Scholar