Global Dynamics of Charged Dust Particles in Planetary Magnetospheres

We study the global stability of charged dust grains orbiting an axisymmetric planet. The corotating magnetic field and induced electric field are described in an inertial frame using the magnetic stream function and a two-dimensional effective potential Uᵉ, parametrized by the conserved angular momentum p_φ. Stable equilibria form the centers of complex potential wells, so that a particle which loses local stability can still be trapped globally. Applying the results to Saturn, we find that nonequatorial ``halo'' orbits are dominated by positively charged grains.