Gravito-electrodynamics of charged dust in planetary magnetospheres

The dynamics of small electrically charged dust grains within the rigidly corotating regions of planetary magnetospheres such as those of Jupiter and Saturn is considered. Depending on whether one is inside or outside the synchronous orbit, it is possible to have different populations of both positively and negatively charged particles moving in equilibrium circular orbits either in the prograd or retrograd sense. Not all these are stable, however, to small perturbations, such as would be produced by the gravitational tug of a neighboring satellite. The stable perturbed grains will perform a motion that can be described as an elliptical gyration about a guiding center which is in uniform circular motion. For different values of the specific charge, the ratio of the semiaxes of this ''epicyclic'' ellipse lies between 1/2 and 1, while the gyration frequency ω of the grain about the guiding center lies between the Kepler frequency Ω/sub K/ and ω0 In the environments of Jupiter and Saturn, where the grains are expected to be negatively charged both in the sunlit side and in the shadow and which move in the prograde sense, their guiding centers must have speeds intermediate to the Kepler speed and the corotation speed. Such particles with a unique specific charge could have a 1:1 magneto-gravitational resonance with a neighboring satellite. A dispersion relation between ω and the wavelength lambda of the perturbed orbits in the frame of the perturbed satellite has been derived. This result has been used to discuss the appearance and disappearance of the waves in the F ring of Saturn elsewhere. We merely point out here that, while the existence of a single well-defined wavelength implies a dust size distribution sharply peaked at a diameter of about 1 μ, the present theory also anticipates this situation