Linear theory is used to determine the stability of the self-gravitating , rapidly ( and nonuniformly ) rotating , two-dimensional , and collisional particulate disk against small-amplitude gravity perturbations .
A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations .
The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic .
It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturbances ( e.g .
those produced by a spontaneous perturbation and/or a companion system ) the disk is subdivided into numerous irregular ringlets , with size and spacing of the order of 4 \pi \rho \approx 2 \pi h , where \rho \approx c _ { r } / \kappa is the mean epicyclic radius , c _ { r } is the radial dispersion of random velocities of particles , \kappa is the local epicyclic frequency , and h \approx 2 \rho is the typical thickness of the system .
The present research is aimed above all at explaining the origin of various structures in highly flattened , rapidly rotating systems of mutually gravitating particles .
In particular , it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine \sim 2 \pi h \stackrel { < } { \sim } 100 m structure in the main rings A , B , and C of the Saturnian ring system .