  We study the stability of charged dust grains orbiting a planet and subject
to gravity and the electromagnetic force. Our numerical models cover a broad
range of launch distances from the planetary surface to beyond synchronous
orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating
the spinning planetary magnetic field as an aligned dipole, we map regions of
radial and vertical instability where dust grains are driven to escape or crash
into the planet. We derive the boundaries between stable and unstable
trajectories analytically, and apply our models to Jupiter, Saturn and the
Earth, whose magnetic fields are reasonably well represented by aligned
dipoles.
