Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T14:09:39.800Z Has data issue: false hasContentIssue false
  • English
  • Français

The interaction of long-wavelength compressive waves with a cosmic ray shock

Published online by Cambridge University Press:  13 March 2009

G. P. Zank  and
J. F. Mckenzie
G. P. Zank
Affiliation:
Department of Mathematics and Applied Mathematics, University of Natal, Durban, 4001, South Africa
J. F. Mckenzie
Affiliation:
Department of Mathematics and Applied Mathematics, University of Natal, Durban, 4001, South Africa
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the stability of a cosmic ray shock to long-wavelength perturbations. The problem is formulated in terms of finding the transmission coefficient for compressive waves across a cosmic ray shock by solving the generalized, two-fluid Rankine-Hugoniot relations. For strong shocks, the transmission coefficient confirms that compressive waves can undergo considerable amplification on passage through such shocks. The resonances of the transmission coefficient provides us with the dispersion equation governing the stability of the shock to long-wavelength ripple-like distortions. By using the principle of the argument method, it is established that cosmic ray shocks are stable.

Type
Research Article
Information
Journal of Plasma Physics , Volume 37 , Issue 3 , June 1987 , pp. 363 - 372
Copyright
Copyright © Cambridge University Press 1987

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

Axford, W. I., Leer, E. & Skadron, G. 1977 Proceedings of 15th International Cosmic Ray Conference, Plovdiv, vol. 11, p. 132.Google Scholar
Axford, W. I., Leer, E. & McKenzie, J. F. 1982 Astron. Astrophys. 111, 317.Google Scholar
Bell, A. R. 1978 M.N.R.A.S. 182, 147.Google Scholar
Blandford, R. D. & Ostriker, J. P. 1978 Ap. J. 221, L29.Google Scholar
Blokhintzev, D. I. 1945 Akad. Nauk SSSR, 47, 22.Google Scholar
Burgers, J. M. 1946 Koninkl. Ned. Akad. Wetenschap. Proc. 49, 273.Google Scholar
Copson, E. T. 1935 Theory of Functions of a Complex Variable. Oxford University Press.Google Scholar
D'iakov, S. P. 1958 Soviet Phys. JETP, 6, 729.Google Scholar
Dorfi, E. A. & Dhury, L. O'C. 1985 Proceedings of 15th International Cosmic Ray Conference, La Jolla, vol. 3, p. 121.Google Scholar
Drury, L. O'C. 1984 Adv. Space Res. 4, 185.Google Scholar
Drury, L. O'C. & Völk, H. J. 1981 Ap. J. 248, 344.Google Scholar
Erpenbeck, J. J. 1962 a Phys. Fluids, 5, 604.Google Scholar
Erpenbeck, J. J. 1962 b Phys. Fluids, 5, 1181.Google Scholar
Kontorovich, V. M. 1960 Soviet Phys. Acoustics, 5, 320.Google Scholar
Krimsky, G. F. 1977 Doklady Akad. Nauk SSSR, 234, 1306.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1966 Fluid Mechanics. Pergamon.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
McKenzie, J. F. & Bornatici, M. 1974 J. Geophys. Res. 79, 4589.Google Scholar
McKenzie, J. F. & Völk, H. J. 1981 Proceedings of 17th International Cosmic Ray Conference, Paris, vol. 9, p. 242.Google Scholar
McKenzie, J. F. & Völk, H. J. 1982 Astron. Astrophys. 116, 191.Google Scholar
McKenzie, J. F. & Webb, G. M. 1984 J. Plasma Phys. 31, 275.Google Scholar
McKenzie, J. F. & Westphal, K. O. 1968 Phys. Fluids, 11, 2350.Google Scholar
Völk, H. J., Drury, L. O'C. & McKenzie, J. F. 1984 Astron. Astrophys. 130, 19.Google Scholar
Zank, G. P. & McKenzie, J. F. 1985 Proceedings of 19th International Cosmic Ray Conference, La Jolla, vol. 3, p. 111.Google Scholar
Zank, G. P. & McKenzie, J. F. 1987 J. Plasma Phys. 37, 347.Google Scholar