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Dissipative instability of the MHD tangential discontinuity in magnetized plasmas with anisotropic viscosity and thermal conductivity

Published online by Cambridge University Press:  13 March 2009

M. S. Ruderman ,
E. Verwichte ,
R. Erdélyi  and
M. Goossens
M. S. Ruderman
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium
E. Verwichte
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium
R. Erdélyi
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium
M. Goossens
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, B-3001 Heverlee, Belgium
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Abstract

The stability of the MHD tangential discontinuity is studied in compressible plasmas in the presence of anisotropic viscosity and thermal conductivity. The general dispersion equation is derived, and solutions to this dispersion equation and stability criteria are obtained for the limiting cases of incompressible and cold plasmas. In these two limiting cases the effect of thermal conductivity vanishes, and the solutions are only influenced by viscosity. The stability criteria for viscous plasmas are compared with those for ideal plasmas, where stability is determined by the Kelvin—Helmholtz velocity VKH as a threshold for the difference in the equilibrium velocities. Viscosity turns out to have a destabilizing influence when the viscosity coefficient takes different values at the two sides of the discontinuity. Viscosity lowers the threshold velocity V below the ideal Kelvin—Helmholtz velocity VKH, so that there is a range of velocities between V and VKH where the overstability is of a dissipative nature.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 2 , October 1996 , pp. 285 - 306
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

Braginskii, S.I. 1965 Transport processes in plasma. Reviews of Plasma Physics (ed. Leontovich, M.A.), Vol. 1, pp. 205–309. Consultants Bureau, New York.Google Scholar
Chandarsekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford.Google Scholar
Duhau, S. & Gratton, J. 1973 Effect of compressibility on the stability of a vortex sheet in an ideal magnetofluid. Phys. Fluids 16, 150–152.CrossRefGoogle Scholar
Duhau, S., Gratton, F. & Gratton, J. 1970 Hydromagnetic oscillations of a tangential discontinuity in the Chew, Goldberger, and Low approximation. Phys. Fluids 13, 1503–1509.Google Scholar
Duhau, S., Gratton, F. & Gratton, J. 1971 Radiation of hydromagnetic waves from a tangential velocity discontinuity. Phys. Fluids 14, 2067–2068.CrossRefGoogle Scholar
Fejer, J.A. 1964 Hydromagnetic stability at a fluid velocity discontinuity between compressible fluids. Phys. Fluids 7, 499–503.CrossRefGoogle Scholar
Gerwin, 1968 Stability of interface between two fluids in relative motion. Rev. Mod. Phys. 40, 652–658.CrossRefGoogle Scholar
González, A.G. & Gratton, J. 1994 a The Kelvin-Helmholtz instability in a compressible plasma: the role of orientation of the magnetic field with respect to the flow. J. Plasma Phys. 51, 43–60.CrossRefGoogle Scholar
González, A.G. & Gratton, J. 1994 b The role of density jump in the Kelvin-Helmholtz instability of a compressible plasma. J. Plasma Phys. 52, 223–244.Google Scholar
Hollweg, J.V. 1985 Viscosity in magnetized plasma: physical interpretation. J. Geophys. Res. 90, 7620–7622.Google Scholar
Mckenzie, J.F. 1970 Hydromagnetic wave interaction with the magnetopanse and the bow shock. Planet. Space Sci. 18, 1–23.CrossRefGoogle Scholar
Mitnitskiiˇ, V. Ya. 1984 Ob ustoiˇchivosti magnitogazodinamicheskih tangentsialnych razryvov. Zh. Vych. Mat. i Mat. Fiz. 24, 124–131.Google Scholar
Ostrovskiiˇ, L.A., Rybak, S.A. & Tsimring, L. Sh. 1986 Volny otritsatelnoiˇ energii v gidrodinamike. Usp. Fiz. Nauk 150, 417–437. [Negative energy waves in hydrodynamics. Soviet Phys. Usp. 29, 1040–1052.]Google Scholar
Roy, Choudhury S. 1986 An analytical study of the Kelvin-Helmholtz instabilities of compressible, magnetized, anisotropic, and isotropic tangential velocity discontinuities. Phys. Fluids 29, 1509–1519.Google Scholar
Roy, Choudhury S. & Patel, V.L. 1985 Kelvin-Helmholtz instabilities of high-velocity magnetized, anisotropic shear layers. Phys. Fluids 28, 3292–3301.Google Scholar
Ruderman, M.S. & Fahr, H.J. 1993 The effect of magnetic fields on the macroscopic instability of the heliopause. I. Parallel interstellar magnetic fields. Astron. Astrophys. 275, 635–644.Google Scholar
Ruderman, M.S. & Fahr, H.J. 1995 The effect of magnetic fields on the macroscopic instability of the heliopause. II. Inclusion of solar wind magnetic fields. Astron. Astrophys.. 299, 258–266.Google Scholar
Ruderman, M.S. & Goossens, M. 1995 Surface Alfvén waves of negative energy. J. Plasma Phys. 54, 149–155.Google Scholar
Syrovatskiiˇ, S.I. 1957 Magnitnaya gidrodinamika. Usp. Fiz. Nauk 62, 247–303.Google Scholar