Low frequency dust wave modes in planetary rings

The effects of gravity are taken into consideration for low frequency wave modes in a planetary ring. The electrons and ions are considered to be magnetized and corotate with the planet, while the dust grains are unmagnetized. Under the action of gravity the dust particles oscillate normal to the ring plane and move around the planet on Keplerian orbits. Two wave modes of low frequency in such dusty plasma, propagating along the ring in the azimuthal direction, have been analyzed based on the susceptibilities derived from the kinetic theory. The first is a gravity-drift wave which is found as an instability in planetary rings. The instability exists in a limited space region around the synchronous orbit. Grains of small sizes are most likely to produce the instability, and the unstable wavelength increases with the distance from the synchronous orbit. This instability could be of some importance for the evolution of spokes in Saturn’s rings. The second is a dust-magnetosonic wave in the gravity-influenced dust plasma of the ring. This mode has different dispersion and polarization character than a magnetosonic wave in an electron–ion plasma. A two-steam instability in the ring which can generate a dust-magnetosonic wave has also been analyzed.