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

• Published in: Journal of plasma physics 1998-02, Vol.59 (2), p.211-242
• Main Authors: DIRICKX, M., WEYSSOW, B.
• Format: Article
• Language: English
• Subjects: Applied classical electromagnetism; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics
• ISSN: 0022-3778; 1469-7807
• DOI: 10.1017/S0022377897005977

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.