A KINETIC-MODEL FOR DUST ACOUSTIC-WAVES APPLIED TO PLANETARY RINGS

We have derived a kinetic model for the propagation of low-frequency w aves in a dusty plasma containing dust particles and drifting plasma p articles. The model includes Landau damping or growth and damping from charge variation on the dust particles, and is applied to dust-acoust ic waves in planetary rings. Analytic expressions for the dispersion f unction are used to examine the stability of this wave mode. The dispe rsion properties are also found numerically for dense dust clouds or l arge drift velocities, where the analytical expressions are not applic able. We show how the stability condition depends on the density of du st 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 rin g.