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

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 (mv²_⊥/2B) [1 + (e/2mΩ²) ∇_⊥·E]. 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.