  The Hamiltonian dynamics of a single particle in a rotating plasma column,
interacting with an magnetic multipole is perturbatively solved for up to
second order, using the method of Lie transformations. First, the exact
Hamiltonian is expressed in terms of canonical action-angle variables, and then
an approximate integrable Hamiltonian is introduced, using another set of
actions and angles.
  The perturbation introduces an effective ponderomotive potential, which to
leading order is positive. At the second order, the pseudopotential consists of
a sum of terms of the Miller form, and can have either sign. Additionally at
second order, the ponderomotive interaction introduces a modification to the
particle effective mass, when considering the motion along the column axis.
  It is found that particles can be axially confined by the ponderomotive
potentials, but acquire radial excursions which scale as the confining
potential. The radial excursions of the particle along its trajectory are
investigated, and a condition for the minimal rotation speed is derived, in
order for particles to remain radially confined.
  Last, we comment on the changes to the aforementioned solution to the
pseudopotintials and particle trajectory in the case of resonant motion, that
is, a motion which has the same periodicity as the perturbation.
