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Implosion of a uniform current sheet in a low-beta plasma

Published online by Cambridge University Press:  13 March 2009

T. G. Forbes
T. G. Forbes
Affiliation:
Department of Applied Mathematics, The University, St Andrews, Scotland
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Abstract

Using ideal, one-dimensional MHD equations, numerical and analytic solutions are presented which describe the nonlinear behaviour of an imploding current sheet in a low-fl plasma. Initially the current density is uniformly distributed in asheet of finite thickness, and the Lorentz force tending to pinch the plasma together is unopposed by any fluid pressure force. As the implosion develops the current density in the sheet is concentrated into a thin layer at the centre of the sheet, and both the current density and the current in this layer become infinite in a finite time if β = 0. At the moment this occurs, fast-mode shocks are produced which propagate outward from the centre of the current sheet, and as the shocks move away an infinitely thin current sheet is left behind. Although the solutions are related to electric discharges, they are also closely related to a problem posed by Dungey concerning the evolution of a uniformly distributed current in the vicinity of an X-type magnetic neutral line. The implications of these solutions for Dungey's problemare discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 27 , Issue 3 , June 1982 , pp. 491 - 505
Copyright
Copyright © Cambridge University Press 1982

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References

REFERENCES

Boris, J. P. & Book, D. K. 1976 J. Camp. Phys. 20, 397.CrossRefGoogle Scholar
Brice, N. 1970 EOS Trans. AGU, 51, 811.Google Scholar
Cheng, A. F. 1979 J. Geophys. Res. 84, 2129.CrossRefGoogle Scholar
Chester, R. C. 1971 Techniques in Partial Differential Equations. McGraw-Hill.Google Scholar
Coppi, B. & Friedland, A. 1971 Astrophys. J. 169, 379.CrossRefGoogle Scholar
Courant, R. & Friedrichs, K. O. 1976 Supersonic Flow and Shock Waves. Springer.CrossRefGoogle Scholar
Dungey, J. W. 1953 Phil. Mag. 44, 725.CrossRefGoogle Scholar
Dungey, J. W. 1958a Cosmical Electrodynamics. Cambridge University Press.Google Scholar
Dungey, J. W. 1958b Electromagnetic Phenomena in Cosmical Physics (Ed. Lehnert, B.). Cambridge University Press.Google Scholar
Forbes, T. G. & Speiser, T. W. 1979 J. Plasma Phys. 21, 107.CrossRefGoogle Scholar
Heflinger, L. O. & Leonard, S. L. 1961 Phys. Fluids, 4, 406.CrossRefGoogle Scholar
Imshennik, V. S. & Syrovatskii, S. I. 1967 Soviet Phys. JETP, 25, 656.Google Scholar
Krall, N. A. & Trivelpiece, A. W. 1973 Principles of Plasma Physics. McGraw-Hill.CrossRefGoogle Scholar
Weber, W. J. 1978 Ph.D. Thesis, Rijksuniversiteit Utrecht.Google Scholar