Particle canonical variables and guiding center Hamiltonian up to second order in the Larmor radius

A generating function, expressed as a power series in the particle Larmor r adius, is used to relate an arbitrary set of magnetic field line coordinate s to particle canonical variables. A systematic procedure is described for successively choosing the generating function at each order in the Larmor r adius so that the transformed particle Hamiltonian is independent of the La rmor phase angle. The particle guiding center Hamiltonian up to second orde r in the Larmor radius is thereby derived. The analysis includes finite ele ctric fields in which the particle "electric drifts'' can be of the order o f the particle velocity. The transformations which relate an arbitrary set of toroidal magnetic flux coordinates to particle canonical variables are a lso discussed. (C) 2000 American Institute of Physics. [S1070-664X(00)00401 -8].