Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T09:59:15.484Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetohydrodynamic plasma instability driven by Alfvén waves excited by cosmic rays

Published online by Cambridge University Press:  13 March 2009

J. F. McKenzie  and
G. M. Webb
J. F. McKenzie
Affiliation:
Department of Mathematics and Applied Mathematics, University of Natal, Durban, Natal, South Africa
G. M. Webb
Affiliation:
Max-Planck-Institut für Kernphysik, Heidelberg, W. Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Hydrodynamical equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves scattering the cosmic rays used in cosmic ray shock acceleration theory (e.g. McKenzie & Völk 1982; Drury 1983; Webb 1983) are analysed for long-wavelength linear compressive instabilities. The Alfvén wave field may contain a pre-existing component as well as a component excited by the cosmic ray streaming instability. In the case of no Alfvén wave damping, adiabatic wave growth and Alfvén wave generation by the cosmic ray streaming instability, it is found that the backward propagating slow magneto-acoustic mode is driven convectively unstable by the pressure of the self-excited Alfvén waves, provided the thermal plasma β is sufficiently large. The equations are also analysed for the case where the Alfvén wave growth is balanced by some nonlinear damping mechanisms. In the latter case both the forward and backward propagating slow magneto-acoustic modes may be driven unstable if the plasma β is sufficiently small. The conditions under which the instabilities occur are delineated, and sample calculations of growth rates given. Possible applications of the instabilities to astrophysical situations are briefly discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 31 , Issue 2 , April 1984 , pp. 275 - 299
Copyright
Copyright © Cambridge University Press 1984

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.)

References

REFERENCES

Achterberg, A. 1981 Astron. Astrophys. 98, 195.Google Scholar
Alazraki, G. & Couturier, P. 1971 Astron. Astrophys. 13, 380.Google Scholar
Axford, W. I. 1981 Proceedings of 17th International Conference on Cosmic Raya (Paris), 12, 155.Google Scholar
Axford, W. I., Leer, E. & McKenzie, J. F. 1982 Astron. Astrophys. 111, 317.Google Scholar
Barnes, A. 1966 Phys. Fluids, 9, 1483.CrossRefGoogle Scholar
Belcher, J. W. 1971 Astrophys. J. 168, 509.CrossRefGoogle Scholar
Bell, A. R. 1978 Mon. Not. Roy. Astron. Soc. 182, 147.CrossRefGoogle Scholar
Blandford, R. D. 1980 Astrophys. J. 238, 410.CrossRefGoogle Scholar
Dewar, R. L. 1970 Phys. Fluids, 13, 2710.CrossRefGoogle Scholar
Drury, L. O'C. & Völk, H. J. 1981 Astrophys. J. 248, 344.CrossRefGoogle Scholar
Drury, L. O'C. 1983 Rep. Prog. Phys. 46, 973.CrossRefGoogle Scholar
Ginzburg, V. L. & Ptuskin, V. S. 1976 Rev. Modern Phys. 48, 161.CrossRefGoogle Scholar
Ghosh, A. & Ptuskin, V. S. 1983 Astrophys. Space Sci. 92, 37.CrossRefGoogle Scholar
Lee, M. A. & Volk, H. J. 1973 Astrophys. Space Sci. 24, 31.CrossRefGoogle Scholar
Lerche, I. 1967 Astrophys. J. 147, 689.CrossRefGoogle Scholar
Lighthill, M. J. 1960 Phil. Trans. Roy. Soc. A 252, 397.Google Scholar
McKenzie, J. F. & Völk, H. J. 1982 Astron. Astrophys. 116, 191.Google Scholar
McKenzie, J. F. & Bond, R. A. B. 1983 Astron. Astrophys. 123, 111.Google Scholar
Owens, A. J. & Jokipii, J. R. 1977 a Astrophys. J. 215, 677.CrossRefGoogle Scholar
Owens, A. J. & Jokipii, J. R. 1977 b Astrophys. J. 215, 685.CrossRefGoogle Scholar
Parker, E. N. 1969 Space Sci. Rev. 9, 651.Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.Google Scholar
Skilling, J. A. 1975 Mon. Not. Roy. Astron. Soc. 173, 255.CrossRefGoogle Scholar
Völk, H. J. & McKenzie, J. F. 1981 Proceedings of 17th International Conference on Cosmic Rays (Paris), 9, 246.Google Scholar
Völk, H. J. & Cesarsky, C. J. 1982 Z. Naturforschung, 37a, 809.CrossRefGoogle Scholar
Völk, H. J., Drury, L. O'C. & McKenzie, J. F. 1983 Astron. Astrophys. 130, 19.Google Scholar
Webb, G. M. 1983 Astron. Astrophys. 127, 97.Google Scholar
Webb, G. M. & McKenzie, J. F. 1984 J. Plasma Phys. (To be published.)Google Scholar