Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T17:59:52.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly multi-dimensional cosmic-ray-modified MHD shocks

Published online by Cambridge University Press:  13 March 2009

G. P. Zank  and
G. W. Webb
G. P. Zank
Affiliation:
Bartol Research Institute, The University of Delaware, Newark, Delaware 19716, U.S.A.
G. W. Webb
Affiliation:
Department of Planetary Sciences, University of Arizona, Tucson, Arizona 85721, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modelling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.

Type
Research Article
Information
Journal of Plasma Physics , Volume 44 , Issue 1 , August 1990 , pp. 91 - 101
Copyright
Copyright © Cambridge University Press 1990

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. 1965 Planet. Space Sci. 13, 115.CrossRefGoogle Scholar
Axford, W. I., Leer, E. & McKenzie, J. F. 1982 Astron Astrophys. 111, 317.Google Scholar
Bartucelli, M., Pantano, P. & Brugartno, T. 1983 Lett. Nuovo Єim. 37, 433.CrossRefGoogle Scholar
Blandford, R. D. & Eichler, D. 1987 Phys. Rep. 154, 1.CrossRefGoogle Scholar
Drury, L. O'C. 1983 Rep. Prog. Phys. 46, 973.CrossRefGoogle Scholar
Drury, L. O'C. & Völk, H. J. 1981 Astrophys. J. 248, 344.CrossRefGoogle Scholar
Forman, M. A. & Webb, G. M. 1985 Collisionless Shocks in the Heliosphere: A Tutorial Review (ed. R. G. Stone & B. T. Tsurutani), p. 91. American Geophysical Union: Geophysical Monograph 34.Google Scholar
Frenzen, C. L. & Kevorkian, J. 1985 Wave Motion, 7, 25.CrossRefGoogle Scholar
Gleeson, L. J. & Axford, W. I. 1967 Astrophys. J. Lett. 149, L115.CrossRefGoogle Scholar
Hirota, R. 1971 Phys. Rev. Lett. 27, 1192.CrossRefGoogle Scholar
Jokipii, J. R. 1982 Astrophys. J. 255, 716.CrossRefGoogle Scholar
Jokipii, J. R. 1987 Proceedings of 6th International Solar Wind Conference (ed. V. J. Pizzo, T. E. Holzer & D. G. Sime), p. 481.Google Scholar
Kang, H. & Jones, T. W. 1990 Astrophys. J. 353, 149.CrossRefGoogle Scholar
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.CrossRefGoogle Scholar
Lagage, P. O. & Cesarsky, C. J. 1983 Astron. Astrophys. 125, 249.Google Scholar
Segur, H. 1986 Physica, 18D, 1.Google Scholar
Steeb, W.-H. & Eitler, N. 1988 Nonlinear Evolution Equations and the Painlevé Test. World Scientific.CrossRefGoogle Scholar
Su, C. H. & Gardner, C. S. 1969 J. Math. Phys. 10, 536.CrossRefGoogle Scholar
Taniuti, T. & Wet, C. 1968 J. Phys. Soc. Japan, 24, 941.CrossRefGoogle Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.Google Scholar
Webb, G. M. 1983 Astron. Astrophys. 127, 97.Google Scholar
Webb, G. M. & Gleeson, L. J. 1979 Astrophys. Space Sci. 60, 335.CrossRefGoogle Scholar
Webb, G. M. & Mckenzie, J. F. 1984 J. Plasma Phys. 31, 337.CrossRefGoogle Scholar
Webb, G. M. & Zank, G. P. 1990 Physica D in press.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Zank, G. P. 1988 Astrophys. Space Sci. 140, 301.CrossRefGoogle Scholar
Zank, G. P., Webb, G. M. & McKenzie, J. F. 1988 Astron. Astrophys. 189, 338.Google Scholar