The gravito-electrodynamics of charged dust in planetary magnetospheres

The orbital dynamics of small electrically charged dust grains within the corotating regions of planetary magnetospheres is considered. Equations are derived for the elliptical epicyclic motion of positively and negatively charged particles about the guiding center in an equilibrium circular orbit under the influence of small perturbations. Those orbits that are stable to the perturbations are found to have a ratio of the semiaxes of the epicycle between 1/2 and 1, depending on the specific charge, and a gyration frequency about the guiding center between the Kepler frequency and the grain gyrofrequency in a nonrotating frame. In the magnetospheres of Jupiter and Saturn, where the grains are expected to be negatively charged and move in a prograde sense, the guiding centers are predicted to have speeds intermediate to the Kepler speed and the corotation speed and thus may undergo a 1:1 magneto-gravitational resonance with a neighboring satellite. Results may be used in the interpretation of the waves in the F ring of Saturn in terms of the dust size distribution.