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A manifestly gauge-invariant Hamiltonian theory of the oscillation-centre dynamics

Published online by Cambridge University Press:  13 March 2009

B. Weyssow  and
R. Balescu
B. Weyssow
Affiliation:
Association Euratom-Etat Belge, Faculté des sciences CP 231, Campus Plaine, 1050 Bruxelles, Belgium
R. Balescu
Affiliation:
Association Euratom-Etat Belge, Faculté des sciences CP 231, Campus Plaine, 1050 Bruxelles, Belgium
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Abstract

The theory of the slow reaction of charged particles in the presence of a high-frequency electromagnetic field (oscillation-centre motion) is developed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The flexibility introduced by the latter features allows us to construct a theory which is manifestly gauge-invariant and involves only physical concepts (electromagnetic fields and particle velocities instead of potentials and canonical momenta). A complete description of the oscillation-centre dynamics is derived. The known expressions of the ponderomotive force are derived as special cases of our theory.

Type
Research Article
Information
Journal of Plasma Physics , Volume 37 , Issue 3 , June 1987 , pp. 467 - 486
Copyright
Copyright © Cambridge University Press 1987

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References

REFERENCES

Balescu, R. & Kotera, T. 1967 Physica, 33, 558.CrossRefGoogle Scholar
Balescu, R., Kotera, T. & Piña, E. 1967 Physica, 33, 581.CrossRefGoogle Scholar
Balescu, R. & Poulain, M. 1974 Physica, 76, 421.CrossRefGoogle Scholar
Bialynicki-Birula, I. & Iwinski, Z. 1973 Rep. Math. Phys. 4, 139.CrossRefGoogle Scholar
Cary, J. R. & Kaufman, A. N. 1981 Phys. Fluids, 24, 1238.CrossRefGoogle Scholar
Currie, D. G., Jordan, T. F. & Sudarshan, E. C. G. 1963 Rev. Mod. Phys. 35, 350.CrossRefGoogle Scholar
Davidson, R. C. 1972 Methods in nonlinear plasma theory. Academic.Google Scholar
Dewar, R. L. 1972 J. Plasma Phys. 7, 267.CrossRefGoogle Scholar
Dirac, P. A. M. 1949 Rev. Mod. Phys. 21, 392.CrossRefGoogle Scholar
Goldstein, H. 1980 Classical mechanics. Addison-Wesley.Google Scholar
Grebogi, C., Kaufman, A. N. & Littlejohn, R. 1979 Phys. Rev. Lett. 43, 1668.CrossRefGoogle Scholar
Kruskal, M. D. 1962 J. Math. Phys. 3, 806.CrossRefGoogle Scholar
Kentwell, G. W. 1985 a Plasma Phys. Contr. Fusion, 27, 855.CrossRefGoogle Scholar
Kentwell, G. W. 1985 b J. Plasma Phys. 34, 289.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
Littlejohn, R. G. 1979 J. Math. Phys. 20, 2445.CrossRefGoogle Scholar
Littlejohn, R. G. 1981 Phys. Fluids, 24, 1730.CrossRefGoogle Scholar
Littlejohn, R. G. 1983 J. Plasma Phys. 29, 111.CrossRefGoogle Scholar
Nayfeh, A. 1973 Perturbation methods. Wiley.Google Scholar
Statham, G. & Ter Haar, D. 1983 Plasma Phys. 25, 681.CrossRefGoogle Scholar
Sudarshan, E. C. G. & Mukunda, N. 1974 Classical dynamics. Wiley.Google Scholar
Washimi, H. & Karpman, V. I. 1976 Soviet Phys. JETP, 44, 528.Google Scholar
Weyssow, B. & Balescu, R. 1986 J. Plasma Phys. 35, 449.CrossRefGoogle Scholar