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Hamiltonian theory of guiding-centre motion in an electric field with strong gradient

Published online by Cambridge University Press:  01 February 1998

M. DIRICKX  and
B. WEYSSOW
M. DIRICKX
Affiliation:
Laboratoire de Physique des Plasmas–Laboratorium voor Plasmafysica, Association Euratom–Belgian State, Ecole Royale Militaire–Koninklijke Militaire School, 1000 Brussels, Belgium
B. WEYSSOW
Affiliation:
Association Euratom–Etat Belge, Université Libre de Bruxelles, Campus Plaine CP231, Boulevard du Triomphe, 1050 Bruxelles, Belgium
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Abstract

The guiding-centre equations of motion of a classical charged particle in a strong magnetic field and a strongly sheared electric field are derived. They can be used to analyse the dynamics of particles in electromagnetic fields whose spatial profiles are similar to those observed during the H mode in the DIII-D tokamak, for instance. The derivation of the equations of motion is performed up to second order in the drift parameter by applying a Hamiltonian pseudocanonical transformation that removes the gyrophase induced by the magnetic field. The main difference with the standard case of a slowly varying electric field relates to the variation of the new gyrophase and to the expression for the magnetic moment: mv2⊥/2B must be replaced by

formula here

The latter case is also reconsidered – mainly to reveal the consequences of the removal of a hidden divergence for small parallel velocities resulting from the usual averaging transformation.

Type
Research Article
Information
Journal of Plasma Physics , Volume 59 , Issue 2 , February 1998 , pp. 211 - 242
Copyright
© 1998 Cambridge University Press

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