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Lagrangian methods in plasma dynamics. Part 2. Construction of Lagrangians for plasmas

Published online by Cambridge University Press:  13 March 2009

J. P. Dougherty
J. P. Dougherty
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Most of this paper is concerned with the construction of suitable Lagrangian functions for the dynamics of a cold plasma, in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch type of representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behaviour of the canonical stress tensor is considered. The applicability of many of the general results of part 1 is ensured by establishing the existence of the Lagrangian function.

Type
Research Article
Information
Journal of Plasma Physics , Volume 11 , Issue 2 , April 1974 , pp. 331 - 346
Copyright
Copyright © Cambridge University Press 1974

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References

REFERENCES

Boyd, T. J. M. & Turner, J. G. 1972 J. Phys. A 5, 881.Google Scholar
Boyd, T. J. M. & Turner, J. G. 1973 J. Phys. A 6, 272.Google Scholar
Bretherton, F. P. 1968 Proc. Roy. Soc. A 302, 555.Google Scholar
Bretherton, F. P. 1970 J. Fluid Mech. 44, 19.CrossRefGoogle Scholar
Bretherton, F. P. & Garrett, C. J. R. 1968 Proc. Roy. Soc. A 302, 529.Google Scholar
Buneman, O. 1952 Proc. Roy. Soc. 215, 346.Google Scholar
Buneman, O. 1958 Phys. Rev. 112, 1504.CrossRefGoogle Scholar
Buneman, O. 1961 Radiation and Waves in Pla.slnas (ed. Mitchner, M.), p. 54. Stanford University Press.Google Scholar
Buneman, O. 1968 Relativietic Plasmas (ed. Buneman, O. and W. B. Pardo), p. 41. Benjamin.Google Scholar
Butcher, P. N. 1953 Phil. Mag. (7) 44, 971.CrossRefGoogle Scholar
Dewar, R. 1970 Phys. Fluids, 13, 2710.CrossRefGoogle Scholar
Dewar, R. 1972 J. Plasma Phys. 7, 269.CrossRefGoogle Scholar
Dirac, P. A. M. 1951 Proc. Roy. Soc. 209, 291.Google Scholar
Dirac, P. A. M. 1952 Proc. Roy. Soc. 212, 330.Google Scholar
Dougherty, J. P. 1970 J. Plasma Phys. 4, 761.CrossRefGoogle Scholar
Dysthe, K. B. 1974 J. Plaslma Phys. 11, 63.CrossRefGoogle Scholar
Eokart, C. 1960 Phys. Fluids, 3, 421.CrossRefGoogle Scholar
Galloway, J. J. & Kim, H. 1971 J. Plasma Phys. 6, 53.CrossRefGoogle Scholar
Landu, L. D. & Lifshitz, E. M. 1962 The Classical Theory of Fields (2nd edn.). PergamonGoogle Scholar
Lin, C. C. 1963 Proc. Int. School Phys. Course XXI, Liquid Helium. Academic.Google Scholar
Low, F. B. 1958 Proc. Roy. Soc. 248, 282.Google Scholar
Pars, L. A. 1962 An Introduction to the Calculus of Variations. Heinemann.Google Scholar
Seliger, R. L. & Whitham, G. B. 1968 Proc. Roy. Soc. A 305, 1.Google Scholar
Sturrock, P. A. 1958 Ann. Phys. (N.Y.) 4, 306.CrossRefGoogle Scholar
Whitham, G. B. 1965 J. Fluid Mech. 22, 273.CrossRefGoogle Scholar