Hostname: page-component-68945f75b7-72kh6 Total loading time: 0 Render date: 2024-08-06T01:36:29.749Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence conditions for collisionless hydromagnetic shock waves along the magnetic field

Published online by Cambridge University Press:  13 March 2009

Yusuke Kato† ,
Masayoshi Tajiri  and
Tosiya Taniuti
Yusuke Kato†
Affiliation:
Institute of Plasma Physics, Nagoya University, Nagoya, Japan
Masayoshi Tajiri
Affiliation:
Department of Mathematical Sciences, College of Engineering, University of Osaka Prefecture, Sakai, Osaka, Japan
Tosiya Taniuti
Affiliation:
Department of Physics, Nagoya University, Nagoya, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with existence conditions for steady hydromagnetic shock waves propagating in a collisionless plasma along an applied magnetic field. The electrostatic waves are excluded. The conditions are based on the requirement that solutions of the Vlasov-Maxwell equations deviate from a uniform state ahead of a wave. They are given as the conditions on the upstream flow velocity in the wave frame (i.e. in the form of inequalities among the upstream flow velocity and some critical velocities). The conditions crucially depend on the pressure anisotropy, and demonstrate possibilities of exacting collisionless shock waves for high β plasmas.

Type
Research Article
Information
Journal of Plasma Physics , Volume 6 , Issue 3 , December 1971 , pp. 467 - 493
Copyright
Copyright © Cambridge University Press 1971

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

Akhiezer, A. I., Lubarski, G. La & Polovin, R. V. 1958 Zh. Eksp. Teor. Fiz. 35, 731. (Also 1959 Sov. Phys., JETP, 8, 507.)Google Scholar
Gardner, C. S., Geortzel, H., Grad, H., Morawetz, C. S., Rose, M. H. & Rubin, H. 1959 Proc. 2nd Int. Conf. on the Peaceful Uses of Atomic Energy, Geneva, 31, 230. United Nations.Google Scholar
Gardner, C. S. & Morikawa, G. K. 1965 Commun. Pure Appl. Math. 18, 35.CrossRefGoogle Scholar
Gintzburg, M. A. 1967 J. Geophys. Res. 72, 2749.CrossRefGoogle Scholar
Kazantsev, A. P. 1963 Zh. Eksp. Teor. Fiz. 34, 1283. (Also 1963 Sov. Phys., JETP, 17, 865.)Google Scholar
Kennel, C. F. & Sagdeev, R. Z. 1967 J. Geophys. Res. 72, 3302.Google Scholar
Kever, H. & Morikawa, G. K. 1966 Phys. Fluids, 9, 2180.CrossRefGoogle Scholar
Mizutani, A. & Taniuti, T. 1969 Phys. Fluids, 12, 1167.CrossRefGoogle Scholar
Montgomery, M. D., Bames, S. J. & Hundhausen, A. J. 1968 J. Geophys. Res. 73, 4999.CrossRefGoogle Scholar
Montgomery, M. D., Ashbridge, J. R. & Bame, S. J. 1970 J. Geophys. Res. 75, 1217.Google Scholar
Morawetz, C. S. 1961 Phys. Fluids, 4, 988.CrossRefGoogle Scholar
Morawetz, C. S. 1962 Phys. Fluids, 5, 1447.CrossRefGoogle Scholar
Polovin, R. V. 1964 Nuclear Fusion, 4, 10.CrossRefGoogle Scholar
Saffman, P. G. 1961a J. Fluid Mech. 11, 16.CrossRefGoogle Scholar
Saffman, P. G. 1961b J. Fluid Mesh. 11, 552.CrossRefGoogle Scholar
Sagdeev, R. V., Kadomtsev, B. B., Rudakov, L. I. & Vedyonov, A. A. 1959 Proc. 2nd Int. Conf. on the Peaceful Uses of Atomic Energy, Geneva, 31, 151. United Nations.Google Scholar
Sagdeev, R. Z. 1960 Proc. 4th Int. Conf. Ionization Phenomena in Gases, Uppsala. North-Holland.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Tantuti, T. & Washimi, H. 1966 Phys. Rev. Lett. 17, 996.Google Scholar