We show that planetary dust rings which are electrostatically supported, i.e., the ring thickness is determined by a balance between the component of gravity toward the central plane and the expanding electrostatic force on the dust, will oscillate if the ambient plasma conditions are changed. The oscillation frequency of tenuous clouds is found analytically to be √3 times the local Kepler frequency. This is confirmed by numerical results which also show that the oscillation frequency decreases for denser rings. While a tenuous ring has one oscillation frequency throughout, the different parts of a dense ring, e.g., the central density and ring edge position, oscillate with different frequencies. The oscillations become increasingly complex for denser rings.

We have concentrated on tenuous rings and looked for resonances between the oscillation frequency √3 &OHgr;&kgr; and other naturally occurring frequencies in a ring systems. We have investigated the consequences if magnetospheric corotating plasma is not symmetric in azimuth. This can lead to resonances with the vertical dust profile oscillations of orbiting dust rings. We determine the major resonance distances around Jupiter and Saturn and striking coincidences with features in both ring systems which indicate that such resonance may have effects beyond that of simply increasing the thickness of a ring at a resonance distance. ¿American Geophysical Union 1991