Hostname: page-component-89b8bd64d-z2ts4 Total loading time: 0 Render date: 2026-05-10T01:54:35.971Z Has data issue: false hasContentIssue false
  • English
  • Français

The Kelvin–Helmholtz instability in a compressible plasma: the role of the orientation of the magnetic field with respect to the flow

Published online by Cambridge University Press:  13 March 2009

A. G. Gozález  and
J. Gratton
A. G. Gozález
Affiliation:
INFIP–Labratorio 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–Labratorio Física del Plasma, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Get access Rights & Permissions [Opens in a new window]

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 roles of velocity shear, density and magnetic field stratification, and various geometries in compressible plasmas. The present work is part of a systematic investigation of the influence of the various physical and geometrical parameters characterizing the plasmas on the Kelvin–Helmholtz modes. The general dispersion relation for ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas is derived. The existence and characteristics of the modes and their stability are studied analytically for any relative orientation of B, u and k, for continuous B and ρ. It is shown that the stability of a given configuration cannot be determined by considering only special orientations of k (say flute or parallel modes). The results obtained here may serve as a guide to interpret results in more complicated and realistic situations, such as those occurring in experiments and natural plasmas.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 1 , February 1994 , pp. 43 - 60
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Adam, J. A. 1978 J. Plasma Phys. 19, 77.CrossRefGoogle Scholar
Bhattacharyya, B. 1986 Phys. Fluids 29, 2210.CrossRefGoogle Scholar
Bodo, G., Massaglia, S., Rossi, P., Trussoni, E. & Ferrari, A. 1993 Phys. Fluids A 5, 405.CrossRefGoogle Scholar
Cairns, R. A. 1979 J. Fluid Mech. 92, 1.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press. (Reprinted 1981 by Dover.)Google Scholar
Chen, X. L. & Morrison, P. J. 1991 Phys. Fluids B 3, 863.CrossRefGoogle Scholar
Chew, G. F., Goleberger, M. L. & Low, F. E. 1956 Proc. R. Soc. Lond. A 236, 112.Google Scholar
Dobrowolny, M. 1972 Phys. Fluids 15, 2263.CrossRefGoogle Scholar
Duhau, S. & Gartton, J. 1975 J. Plasma Phys. 13, 451.CrossRefGoogle Scholar
Duhau, S., Gratton, F. T. & Gratton, J. 1970 Phys. Fluids 13, 1503.CrossRefGoogle Scholar
Duhau, S., Gratton, F. T. & Gratton, J. 1971 Phys. Fluids 14, 2067.CrossRefGoogle Scholar
Duha, 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. B. Astron. Soc. 205, 515.CrossRefGoogle Scholar
Field, A. R., Fussmann, G. & Hofmann, J. V. 1992 Nucl. Fusion 32, 1191.CrossRefGoogle Scholar
Gerwin, R. A. 1968 Rev. Mod. Phys. 40, 652.CrossRefGoogle Scholar
González, A. G. & Gratton, J. 1991 Solar Phys. 134, 211.CrossRefGoogle Scholar
Gratton, F. T., Gratton, J. & Sánchez, J. 1971 Nucl. Fusion 11, 25.CrossRefGoogle Scholar
Gratton, J. & Gratton, F. T. 1971 Plasma Phys. 13, 567.CrossRefGoogle Scholar
Gratton, J., Gratton, F. T. & González, A. G. 1988 Plasma Phys. Contr. Fusion 31, 435.CrossRefGoogle Scholar
Groebner, R. J., Burrell, K. H. & Seraydarian, N. P. 1990 Phys. Rev. Lett. 64, 3015.CrossRefGoogle Scholar
Ida, K., Hidekuma, S., Miura, Y., Fujita, T., Mori, M., Hoshino, K., Suzuki, N. & Yamauchi, T. 1990 Phys. Rev. Lett.. 65, 1364.CrossRefGoogle Scholar
Landau, L. 1944 C. R. Acad. Sci. USSR 44, 139.Google Scholar
McKenzie, J. F. 1970 Planet. Space Sci. 18, 1.CrossRefGoogle Scholar
McKenzie, J. F. 1971 J. Plasma Phys. 5, 275.CrossRefGoogle Scholar
Michael, D. H. 1955 Proc. Camb. Phil. Soc. 51, 528.CrossRefGoogle Scholar
Mikhailovskii, A. B. 1982 J. Plasma Phys. 28, 1.CrossRefGoogle Scholar
Mikhailovskii, A. B. 1992 Electromagnetic Inst abilities in an Inhomogeneous Plasma. IOP.Google Scholar
Miura, A. 1982 Phys. Rev. Lett. 49, 779.CrossRefGoogle Scholar
Miura, A. 1992 J. Geophys. Res. 97, 10655.CrossRefGoogle Scholar
Ohsawa, Y., Nosaki, K. & Hasegawa, A. 1976 Phys. Fluids 19, 1139.CrossRefGoogle Scholar
Parhi, S. 1992 Phys. Fluids B 4, 1589.CrossRefGoogle Scholar
Prialnik, D., Eviatar, A. & Ershovich, A. I. 1986 J. Plasma Phys. 35, 209.CrossRefGoogle Scholar
Rogister, A., Hasselberg, G., Li, D. & Khalil, S. M. 1992 Plasma Phys. Contr. Fusion 34, 1265.CrossRefGoogle Scholar
Roy, Choudhury S. 1986 Phys. Fluids 29, 1509.Google Scholar
Roy, Choudhury S. & Patel, V. L. 1985 Phys. Fluids 28, 3292.Google Scholar
Sánnchez, H. R., Gaska, P. & Gratton, J. 1984 Radiation inPlasnias (ed. MeNainara, B.), vol. II, p. 998. World Scientific.Google Scholar
Satyanarayana, P., Guzdar, P. N., Huba, J. D. & Ossakow, S. L. 1984 J. Geophys. Res. 89, 2945CrossRefGoogle Scholar
Satyanarayana, P. & Lee, Y. C. 1987 Phys. Fluids 30, 81.CrossRefGoogle Scholar
Sen, A. K. 1964 Phys. Fluids 7, 1293.CrossRefGoogle Scholar
Southwood, D. J. 1968 Planet. Space Sci. 16, 587.CrossRefGoogle Scholar
Tajima, T., Horton, W., Morrison, P. J., Schutkeker, J., Kamimura, T., Mima, K. & Abe, Y. 1991 Phys. Fluids B 3, 938.CrossRefGoogle Scholar
Tajima, T. & Leboeuf, J. N. 1980 Phys. Fluids 23, 884.CrossRefGoogle Scholar
Wang, Z. & Pritchett, P. L. 1989 Phys. Fluids B 1, 1767.CrossRefGoogle Scholar