Global dynamics of dust grains in magnetic planets

We study the dynamics of a charged particle orbiting a rotating magnetic planet. The system is modelled by the Hamiltonian of the two-body problem perturbed by an axially-symmetric potential. The perturbation consists in a magnetic dipole field and a corotational electric field. After an averaging process we arrive at a one degree of freedom Hamiltonian system for which we obtain its relative equilibria and bifurcations. It is shown that the system exhibits a complex and rich dynamics. In particular, dramatic changes in the phase flow take place in the vicinity of a circular equatorial orbit, that in the case of Saturn is located inside the E-ring.