Resonant excitation of density waves in Saturn's rings

Abstract

The dynamics of regions in the Saturnian ring system with rare collisions between particles, that is, Ω 2⪢ν c 2 , where Ω is the orbital angular frequency and ν c the collision frequency, is considered. According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring and the A ring. Kinetic theory with the Vlasov and Poisson equations is used to obtain the eigen-frequencies of oscillations propagating in the plane of the system. In the considered case of rare collisions the resulting kinetic equation for the perturbed distribution function can be solved by successive approximations, neglecting the effect of binary particle collisions in the zeroth-order approximation. An oscillating instability of the kinetic type is discussed. This instability of a particulate disk is similar to the magneto-drift instability first discovered by Krall and Rosenbluth ( Physics Fluids 6, 254–265, 1963) in a nonuniform magnetic plasma, and belongs to the class of microinstabilities of an inhomogeneous plasma. The cause of the oscillating instability in Saturn's rings is a resonant interaction of drifting particles with nonaxisymmetric Jeans-stable waves at the corotation. The waves that may be produced by the corotation-resonance interaction represent non-radial normal modes of the gravitationally stable disk modified by a particle drift. It is shown that density waves are effectively excited at this resonance: the growth rate of the mode of maximum instability is large, Im ω∗∼Ω. The resonant excitation of density waves investigated in the present paper may be proposed as the cause of the irregular, small-scale ∼ 100 m structure in regions of low optical depth in Saturn's rings. It is suggested that Cassini spacecraft high-resolution images of low optical depth regions will show this kind of structure.