Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T00:39:17.828Z Has data issue: false hasContentIssue false
  • English
  • Français

Structural determination of electric field conditions in ionizing shock waves

Published online by Cambridge University Press:  13 March 2009

B. P. Leonard
B. P. Leonard
Affiliation:
Division of Pure and Applied Scieuces, Richmond College, City University of New York, Staten Island, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

Ionizing shock waves may involve a non-zero transverse electric field in the non-conducting upstream region. The possibility of this field means that two extra parameters are involved in ionizing shock transitions, in addition to the usual three MHD shock parameters. The present paper investigates the question of existence or absence of structurally determined relationships between the five parameters. The results show that ionizing shock waves can be categorized into three types, depending on the nature of their downstream singular points in a three-dimensional phase space. Thus, if shock Mach number, Alfven number, and upstream magnetic field angle are given, type 2 shooks are characterized by a unique transverse electric field in both magnitude and orientation, type 3 shocks allow one degree of freedom to the electric field but specify a relationship between the magnitude and orientation, and in type 4 shocks both electric field parameters are free to range between certain limits. These structural conditions correspond exactly to previously investigated evolutionarity conditions based on wave perturbations, the interpretation of which has been incomplete due to a lack of knowledge of the possibility of skew shocks. In light of the author's subsequent work on skew shocks and the new general three-dimensional results, a complete map of the behaviour of ionizing shock waves is now possible, and the present article attempts to construct its essential features. Earlier works are reviewed and clarified in reference to this general framework.

Type
Research Article
Information
Journal of Plasma Physics , Volume 10 , Issue 1 , August 1973 , pp. 13 - 51
Copyright
Copyright © Cambridge University Press 1973

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

Chu, C. K. 1964 Phys. Fluids, 7, 1349.CrossRefGoogle Scholar
Chu, C. K. & Gross, R. A. 1969 Advances in Plasma Physics, vol. 2 (ed. Simon, A. and Thompson, W. B.). Wiley.Google Scholar
Chu, C. K. & Taussig, R. T. 1967 Phys. Fluids, 10, 249.CrossRefGoogle Scholar
Cowley, M. D. 1967 J. Plasma Phys. 1, 37.CrossRefGoogle Scholar
Germain, P. 1960 Rev. Mod. Phys. 32, 951.CrossRefGoogle Scholar
Gross, R. A. 1965 Rev. Mod. Phys. 37, 724.CrossRefGoogle Scholar
Hoffert, M. I. 1968 Phys. Fluids, 11, 77.CrossRefGoogle Scholar
Hoffert, M. I. 1970 J. Plasma Phys. 4, 477.CrossRefGoogle Scholar
Kantrowitz, A. R. & Petschek, H. E. 1957 Magnetohydrodynamics (ed. Lands-hoff, R. M.), p. 3. Stanford University Press.Google Scholar
Kulikovskii, A. G. & Lyubimov, G. A. 1959 Dokl. Akad. Nauk SSSR, 129, 52.Google Scholar
Kunkel, W. B. & Gross, R. A. 1962 Plasma Hydromagnetics (ed. Bershader, D.), p. 58.Google Scholar
Leonard, B. P. 1966 Phys. Fluids, 9, 917.CrossRefGoogle Scholar
Leonard, B. P. 1969 Phys. Fluids, 12, 1816.CrossRefGoogle Scholar
Leonard, B. P. 1970 a Phys. Fluids, 13, 833.CrossRefGoogle Scholar
Leonard, B. P. 1970 b Phys. Fluids, 13, 3063.CrossRefGoogle Scholar
Leonard, B. P. 1972 a J. Plasma Phys. 7, 133.CrossRefGoogle Scholar
Leonard, B. P. 1972 b J. Plasma Phys. 7, 157.CrossRefGoogle Scholar
Leonard, B. P. 1972 c J. Plasma Phys. 7, 177.CrossRefGoogle Scholar
Marshall, W. 1955 Proc. Roy. Soc. A 233, 367.Google Scholar
Molander, R. C. & Berger, S. A. 1969 Phys. Fluids, 12, 2531.CrossRefGoogle Scholar
Stebbins, C. F. & Vlases, G. C. 1968 J. Plasma Phys. 2, 633.CrossRefGoogle Scholar
Taussig, R. T. 1965 Phys. Fluids, 8, 1616.CrossRefGoogle Scholar
Taussig, R. T. 1966 Phys. Fluids, 9, 421.CrossRefGoogle Scholar
Taussig, R. T. 1967 Phys. Fluids, 10, 1145.CrossRefGoogle Scholar
Todd, L. 1964 J. Fluid Mech. 18, 321.CrossRefGoogle Scholar
Todd, L. 1965 J. Fluid Mech. 21, 193.CrossRefGoogle Scholar
Todd, L. 1966 J. Fluid Mech. 24, 597.CrossRefGoogle Scholar