A kinetic model for dust acoustic waves applied to planetary rings

We have derived a kinetic model for the propagation of low‐frequency waves in a dusty plasma containing dust particles and drifting plasma particles. The model includes Landau damping or growth and damping from charge variation on the dust particles, and is applied to dust‐acoustic waves in planetary rings. Analytic expressions for the dispersion function are used to examine the stability of this wave mode. The dispersion properties are also found numerically for dense dust clouds or large drift velocities, where the analytical expressions are not applicable. We show how the stability condition depends on the density of dust particles and the wavelength, for plasma and dust parameters which may apply to Saturn's F ring, G ring, and E ring, and to Jupiter's ring.