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The role of a density jump in the Kelvin—Helmholtz instability of compressible plasma

Published online by Cambridge University Press:  13 March 2009

A. G. González  and
J. Gratton
A. G. González
Affiliation:
INFIP–Laboratorio Física del Plasma, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
J. Gratton
Affiliation:
INFIP–Laboratorio Física del Plasma, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
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Abstract

The hydromagnetic Kelvin–Helmholtz instability is relevant in many complex situations in astrophysical and laboratory plasmas. Many cases of interest are very complicated, since they involve the combined role of velocity shear, of density and magnetic field stratification, and of various geometries in compressible plasmas. In the present work we continue investigating the influence of various physical and geometrical parameters of the plasma on the Kelvin–Helmholtz modes. We use the general dispersion relation for the ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas. We study analytically the existence and properties of the modes and their stability, for a velocity jump combined with a density jump, and for any relative orientation of B, u and k (B is continuous). Stability is analysed by means of a general procedure that allows discussion of any configuration and all kinds of perturbations. The boundaries between modes of different kinds are discussed. In contrast to the case of uniform density, for a density jump there are no monotonically unstable modes, only overstabilities. The unstable modes belong to two types. Those with the largest growth rates tend to monotonically unstable modes in the limit of uniform density, and are related to the torsional Alfvén mode. The other overstable modes have no analogue among the purely incompressible modes, and occur in a range of U that is stable in the incompressible limit. We derive bounds for the growth rate of the instability. The present results may serve as a guide to interpret results in more complicated and realistic situations as those occurring in laboratory and natural plasmas.

Type
Research Article
Information
Journal of Plasma Physics , Volume 52 , Issue 2 , October 1994 , pp. 223 - 244
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

Adam, J. A. 1978 J. Plasma Phys. 19, 77.CrossRefGoogle Scholar
Axford, W. I. 1960 Q. J. Mech. Appl. Maths 13, 314.CrossRefGoogle Scholar
Axford, W. I. 1962 Can. J. Phys. 40, 654.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press (reprinted 1981 Dover).Google Scholar
Duhau, S. & Gratton, J. 1973 Phys. Fluids 16, 150.CrossRefGoogle Scholar
Fejer, J. A. 1964 Phys. Fluids 7, 499.CrossRefGoogle Scholar
Ferrari, A. & Trussoni, E. 1983 Mon. Not. R. Astron. Soc. 205, 515.CrossRefGoogle Scholar
Gerwin, R. A. 1968 Rev. Mod. Phys. 40, 652.CrossRefGoogle Scholar
González, A. G. & Gratton, J. 1994 J. Plasma Phys. 51, 43.CrossRefGoogle Scholar
Gratton, J., Gratton, F. T. & González, A. G. 1988 Plasma Phys. Contr. Fusion 31, 435.CrossRefGoogle Scholar
Landau, L. 1944 C. R. Acad. Sci. USSR 44, 139.Google Scholar
Mikhailovskii, A. B. 1992 Electromagnetic Instabilities in an Inhomogeneous Plasma. IOP.Google Scholar
Miura, A. & Pritchett, P. L. 1982 J. Geophys. Res. 87, 7431.CrossRefGoogle Scholar
Prialnik, D., Eviatar, A. & Ershkovich, A. I. 1986 J. Plasma Phys. 35, 209.CrossRefGoogle Scholar
Sen, A. K. 1964 Phys. Fluids 7, 1293.CrossRefGoogle Scholar
Southwood, D. J. 1968 Planet. Space Sci. 16, 587.CrossRefGoogle Scholar
Southwood, D. J. 1979 Magnetospheric Boundary Layers (ed. Battrick, B. & Mort, J.), p. 357. ESA.Google Scholar
Wang, Z. & Pritchett, P. L. 1989 Phys. Fluids B 1, 1767.CrossRefGoogle Scholar