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Transverse MHD shock waves in a partly ionized plasma. Part 1. Structure equations and topology

Published online by Cambridge University Press:  13 March 2009

C. D. Mathers
C. D. Mathers
Affiliation:
School of Physics, University of Sydney, NSW 2006, Australia
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Abstract

The structure of transverse MHD shock waves in an initially partly ionized plasma is studied using a three-fluid model with collisional transport coefficients. This model includes the effects of non-equilibrium ionization and of ion velocity slip. A closed set of structure equations is obtained and it is shown that they have a saddle-point – saddle-point topology which prohibits direct integration. In distinction from previous MHD shock structure studies, it is not possible to reduce the number of variables in a realistic manner to allow direct integration, nor is it possible to use the method of matched asymptotic expansions. An iterative solution method is presented in this paper, based on a detailed analysis of the integral curve topology.

Type
Research Article
Information
Journal of Plasma Physics , Volume 24 , Issue 1 , August 1980 , pp. 103 - 120
Copyright
Copyright © Cambridge University Press 1980

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References

REFERENCES

Anderson, J. E. 1963 Magnetohydrodynamic Shock Waves. M.I.T. Press.CrossRefGoogle Scholar
Bickerton, R. J., Lenamon, L. & Murphy, R. V. W. 1971 J. Plasma Phys. 5, 177.CrossRefGoogle Scholar
Bighel, L., Cramer, N. F., Millar, D. D. & Niland, R. A. 1973 Phys. Lett. A 44, 449.CrossRefGoogle Scholar
Bighel, L., Collins, A. R. & Cross, R. C. 1974 Phys. Lett. A 47, 333.CrossRefGoogle Scholar
Bighel, L., Collins, A. R. & Cramer, N. F. 1977 J. Plasma Phys. 18, 77.CrossRefGoogle Scholar
Braginskii, S. I. 1965 Reviews of Plasma Physics, vol. 1 (ed. Leontovich, M. A.), p. 205. Consultants Bureau.Google Scholar
Chapman, S. & Cowling, T. G. 1939 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.Google Scholar
Chubb, D. L. 1968 Phys. Fluids, 11, 2363.CrossRefGoogle Scholar
Collins, A. R. & Mathers, C. D. 1978 Phys. Fluids, 21, 1939.CrossRefGoogle Scholar
Craig, A. D. & Paul, J. W. M. 1973 Plasma Phys. 9, 161.CrossRefGoogle Scholar
Cramer, N. F. 1975 J. Plasma Phys. 14, 333.CrossRefGoogle Scholar
Cross, R. C. & Mathers, C. D. 1979 J. Plasma Phys. 21, 151.CrossRefGoogle Scholar
Dixon, V. A. & Woods, L. C. 1976 Plasma Phys. 18, 627.CrossRefGoogle Scholar
Horwitz, J. & Banks, P. M. 1973 Planet. Space Sci. 21, 1975.CrossRefGoogle Scholar
Hughes, W. F. & Young, F. J. 1966 The Electromagnetodynamics of Fluids. Wiley.Google Scholar
Jaffrin, M. Y. & Probstein, R. F. 1964 Phys. Fluids, 7, 1658.CrossRefGoogle Scholar
Jaffrin, M. Y. 1965 Phys. Fluids, 8, 606.CrossRefGoogle Scholar
Leonard, B. P. 1969 Phys. Fluids, 12, 1816.CrossRefGoogle Scholar
Lu, C. S. & Huang, A. B. 1974 Phys. Fluids, 17, 1527.CrossRefGoogle Scholar
Marshall, W. 1955 Proc. Roy. Soc. A 223, 367.Google Scholar
Mathers, C. D. 1978 Phys. Lett. 69 A, 119.CrossRefGoogle Scholar
Mathers, C. D. 1980 J. Plasma Phys.Google Scholar
Mathers, C. D. & Cramer, N. F. 1978 Aust. J. Phys. 31, 171.CrossRefGoogle Scholar
Minorsky, N. 1962 Nonlinear Oscillations. Van Nostrand.Google Scholar
Paul, J. W. M., Goldenbaum, G. C., Iiyoshi, A., Holmes, L. S. & Hardcastle, R. A. 1967 Nature, 216, 363.CrossRefGoogle Scholar
Paul, J. W. M., Daughney, C. C., Holmes, L. S., Runisky, P. T., Craig, A. D., Murray, E. L., Summers, D. D. R. & Beaulieu, J. 1971 Proceedings of 4th International Conference on Plasma Physics and Controlled Nuclear Fusion, Vienna, vol. 3, p. 251. IAEA.Google Scholar
Schneider, S. H., Chu, C. K. & Leonard, B. P. 1971 Phys. Fluids, 14, 1103.CrossRefGoogle Scholar
Shanmugasundaram, V. & Murty, S. S. R. 1978 J. Plasma Phys. 20, 419.CrossRefGoogle Scholar
Sherman, F. S. & Talbot, L. 1960 Rarefied Gas Dynamics (ed. Devienne, F. M.), p. 161. Pergarnon.Google Scholar
Taussig, R. T. 1973 Phys. Fluids, 16, 384.CrossRefGoogle Scholar
Velikovich, A. L. & Liberman, M. A. 1976 Soviet Phys. JETP, 44, 727.Google Scholar
Wilkins, D. R. & Gyftopoulos, E. P. 1966 J. Appl. Phys. 37, 3533.CrossRefGoogle Scholar
Woods, L. C. 1969 a Culham Report CLM-R96, UKAEA.Google Scholar
Woods, L. C. 1969 b Plasma Phys. 11, 25.CrossRefGoogle Scholar
Woods, L. C. 1971 J. Plasma Phys. 6, 615.CrossRefGoogle Scholar
Woods, L. C. 1975 The Thermodynamics of Fluid Systems. Oxford University Press.Google Scholar
Zel'dovich, YA. B. & Raizer, Yu. P. 1967 Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, vol. 2. Academic.CrossRefGoogle Scholar
Ziering, S., Ex, F. & Koch, P. 1961 Phys. Fluids, 4, 975.CrossRefGoogle Scholar