On the canonical Hamiltonian structure of the drift equations of motion for a charged particle in a magnetic field

The equations which described the combined E x B, ∇B x B, and curvature drifts, the magnetic gradient force along magnetic field lines, the existence of the first adiabatic invariant, and the rapid cyclotron motions are shown to have a canonical Hamiltonian structure which relates directly to the local spatial coordinates. The use of Poisson brackets leads immediately to the drift kinetic equation, expressed in local spatial coordinates rather than magnetic field coordinates. When the magnetic field geometry is such as to give rise to mirroring, and the second and third adiabatic invariants exist, their physical identification follows at once from the canonical formulation. (author)