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Hamiltonian theory of the generalized oscillation-centre transformation

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, Boulevard du Triomphe, 1050 Bruxelles, Belgium
R. Balescu
Affiliation:
Association Euratom–Etat Belge, Faculté des Sciences, CP 231, Campus Plaine, Boulevard du Triomphe, 1050 Bruxelles, Belgium
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Abstract

The theory of the slow reaction of a charged particle in the combined presence of a strong quasi-static magnetic field and a high-frequency electromagnetic field (generalized oscillation-centre motion) is constructed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The theory combines the features studied in our previous works for the case in which only one of the previously mentioned fields is present. The new averaging transformation is based on the fact that the Larmor frequency of the quasi-static field is of the same order as the external frequency of the high-frequency field. Our theory is manifestly gauge-invariant and involves only physical quantities (particle velocity and electromagnetic fields). Explicit expressions for the drift velocity of the oscillation centre and for the ponderomotive force are derived.

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 1 , February 1988 , pp. 81 - 102
Copyright
Copyright © Cambridge University Press 1988

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Cary, J. R. & Kaufman, A. N. 1981 Phys. Fluids, 24, 1238.CrossRefGoogle Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Grebogi, C., Kaufman, A. N. & Littlejohn, R. G. 1979 Phys. Rev. Lett, 43, 1668.Google Scholar
Grebogi, C. & Littlejohn, R. G. 1984 Phys. Fluids, 27, 2003.Google Scholar
Gurevich, A. V. & Pitaevskii, L. P. 1964 Soviet Phys. JETP, 18, 855.Google Scholar
Kentwell, G. W. & Jones, D. A. 1987 Phys. Rep. 145, 319.Google Scholar
Kruskal, M. D. 1962 J. Math. Phys. 3, 806.CrossRefGoogle Scholar
Littlejohn, R. G. 1981 Phys. Fluids, 24, 1730.Google Scholar
Littlejohn, R. G. 1983 J. Plasma Phys., 29, 111.Google Scholar
Nayfeh, A. 1973 Perturbation Methods. Wiley.Google Scholar
Pitaevskii, L. P. 1961 Soviet Phys. JETP, 12, 1008.Google Scholar
Weyssow, B. & Balescu, R. 1986 J. Plasma Phys. 35, 449.CrossRefGoogle Scholar
Weyssow, B. & Balescu, R. 1987 J. Plasma Phys. 37, 467.CrossRefGoogle Scholar