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Hamiltonian theory of guiding centre motion revisited

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

The classical problem of the motion of a charged particle in a slowly varying electromagnetic field is reconsidered in the framework of ‘pseudo-canonical transformations’ in a Hamiltonian formalism. As compared with Littlejohn's important recent work, we develop a method which we believe to be more transparent. It consists, in essence, of exploiting directly the requirement that the Lie brackets of the guiding centre variables be independent of the (new) gyrophase. By using this method, we construct explicitly the complete set of functional relationships between the guiding centre variables and the particle variables, up to second order in the drift parameter є These expressions are valid for magnetic and electric fields of arbitrary geometry (within the drift approximation), which may be slowly varying in time.

Type
Research Article
Information
Journal of Plasma Physics , Volume 35 , Issue 3 , June 1986 , pp. 449 - 471
Copyright
Copyright © Cambridge University Press 1986

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