## Abstract

A method for investigating the small-amplitude nonlinear oscillations of low and moderately high optical depth regions of Saturn's main rings is developed through the using of the Boltzmann kinetic equation with a Krook model integral of interparticle collisions and the Poisson equation. A mathematical formalism in the approximation of weak turbulence (a quasi-linearization of the Boltzmann equation) is developed. Conditions under which the quasilinear approximation can be used to describe wave-particle interactions are calculated with reference to the excitation of Jeans-type gravity disturbances (those produced by a spontaneous perturbation and/or a companion system). It is shown that the spontaneous, almost aperiodically growing Jeans-unstable spiral gravity oscillations developing in the disk's plane must influence the distribution of mutually gravitating particles in such a way as to hinder the oscillations excitation, i.e., to increase the spread of random velocities. As a result, finally in the disk there can be established a quasi-stationary distribution so that the Jeans-unstable density waves are completely vanishing. Thus, in the nonlinear regime, the particles can continue developing gravity-unstable density condensations only if some effective mechanism of "cooling" exists. We suggest that in Saturn's rings the cooling mechanism leading to the long-term density waves activity is actually operating: inelastic (dissipative) collisions reduce the magnitude of the relative velocity of particles.

Original language | English |
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Pages (from-to) | 375-383 |

Number of pages | 9 |

Journal | Astronomy and Astrophysics |

Volume | 400 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2003 |

## Keywords

- Planets and satellites: individual: Saturn
- Planets: rings

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science