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Containment forces in low energy states of plasmoids

Published online by Cambridge University Press:  13 March 2009

Daniel R. Wells
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida
Lawrence Carl Hawkins
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida

Abstract

The application of Hamilton's principle to the problem of the determination of the structure of low free energy state plasmoids is discussed. It is shown that Clebsch representations of the vector fields and representations involving side conditions on the functional result in the same sets of Euler–Lagrange equations. The relationship of these representations to the problem of containment forces in vortex structures (plasmoids) is considered. It is demonstrated that the lowest free energy state of an incompressible plasma is always Lorentz force and Magnus force free. For a compressible plasma obeying the adiabatic gas laws, the Magnus force is finite. Introduction of conservation of angular momentum as an additional side condition also results in finite containment forces.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1987

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References

REFERENCES

Arfken, G. 1966 Mathematical Methods for Physicists. Academic.Google Scholar
Clebsch, A. 1959 J. reine angew. Math. 56, 1.Google Scholar
Henyey, F. S. 1983 Phys. Fluids, 26, 40.CrossRefGoogle Scholar
Lamb, H. 1879 Hydrodynamics. Dover.Google Scholar
Lin, C. C. 1963 Liquid Helium, Proceedings of International School of Physics, Course XII. Academic.Google Scholar
Moffatt, H. K. 1969 J. Fluid Mech. 35, 117.CrossRefGoogle Scholar
Mokkison, P. J. 1981 AIP Conference Proceedings No. 88 (ed. M. Tabor).Google Scholar
Nolting, E. E., Jindra, P. E. & Wells, D. R. 1973 J. Plasma Phys. 9, 1.CrossRefGoogle Scholar
Rund, H., Wells, D. R. & Hawkins, L. C. 1978 J. Plasma Phys. 20, 329.CrossRefGoogle Scholar
Seliger, R. L. & Whitham, G. B. 1967 Proc. Roy. Soc. A 305, 1.Google Scholar
Taylor, J. B. 1974 Phys. Rev. Lett. 33, 1139.CrossRefGoogle Scholar
Wells, D. R. 1970 J. Plasma Phys. 4, 645.CrossRefGoogle Scholar
Wells, D. R. 1976 Pulsed High Beta Plasmas (ed. Evans, D. E.). Pergamon.Google Scholar
Wells, D. R. 1986 IEEE Trans. Plasma Sci. PS-14, 865.CrossRefGoogle Scholar
Wells, D. R. 1987 IEEE Trans. Plasma Sci. (To be published.)Google Scholar
Wells, D. R. & Norwood, J. 1969 J. Plasma Phys. 3, 21.CrossRefGoogle Scholar
Wells, D. R., Ziajka, P. & Tunstall, J. 1983 J. Plasma Phys. 31, 39.CrossRefGoogle Scholar
Wells, D. R., Ziajka, P. & Tunstall, J. 1986 Fusion Tech. 9, 83.CrossRefGoogle Scholar
Woltjer, L. 1958 Proc. Nat. Acad. Sci. USA, 44, 489.CrossRefGoogle Scholar