On the validity of the guiding-center approximation in a magnetic dipole field

The problem of the charged-particle motion in an axisymmetric magnetic-dipole geometry is used to assess validity Hamiltonian guiding-center theory, which includes higher-order corrections associated with polarization induced by magnetic-field nonuniformity. When a magnetically confined orbit regular (i.e., its magnetic moment adiabatically invariant), approximation, conserves both energy and azimuthal canonical angular momentum, shown be faithful particle when effects are taken into account.