Single-particle motion in nonaxisymmetric static electric and magnetic fields

The technique of iteration of canonical transformations for a Hamiltonian system is applied to study the motion of a single particle of small Larmor radius in static, nonaxisymmetric electric and magnetic fields. For use in applications in kinetic theory, it is asked when is μ(r,v), where μ is the magnetic moment adiabatic invariant, single valued in r, with v held fixed? Even when μ(r,v) is a good adiabatic invariant, it may fail this additional condition, so that f[1/2v2+Φ(r), μ(r,v)] is not an acceptable particle distribution function, where Φ(r) is a single-valued electrostatic potential. It is shown that in a toroidal domain the condition is satisfied only for axisymmetric fields, or for magnetic fields near a zero shear field with nested flux surfaces that fill a toroidal domain. The appropriate transformations to guiding center coordinates and Hamiltonians are given for these cases.