On the stability of Saturn's rings: A quasi-linear kinetic theory

Evgeny Griv, Michael Gedalin, Chi Yuan

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23 Scopus citations


A self-consistent system of the Boltzmann kinetic equation and the Poisson equation is used to study the dynamical evolution of Saturn's main A, B and C rings composed of discrete mutually gravitating particles. The simplified case of relatively rare collisions between identical particles, when the collision frequency is smaller than (compared with) the orbital frequency, is examined. Equations describing the quasi-linear stage of Jeans instability of small-amplitude gravity perturbations in Saturn's rings are derived and solved analytically. Conditions under which the quasi-linearization of the Boltzmann equation can be used to describe a wave-particle interaction are calculated with reference to the excitation of Jeans-type perturbations. The theory, as applied to Saturn's rings, predicts for several features, such as numerous irregular Jeans-unstable wakes, with size and spacing between them of the order of 2πh ≤ 100 m, where h is the typical thickness of the system. The interaction of particles with these almost aperiodically growing gravity perturbations increases both the radial spread of the disc and random velocities of particles in a very short time-scale of only two to three disc orbital revolutions. The latter leads to an eventual stabilization of the system, unless some effective cooling mechanism exists, reducing the magnitude of the relative velocity of particles. It is suggested that inelastic (dissipative) interparticle impacts provide such a cooling mechanism, leading to the recurrent density waves activity. We predict that the high-resolution images from the forthcoming (2004) Cassini spacecraft will reveal this fine-scale recurrent ∼ 100 m or even less spiral structure in low and moderately high optical depth regions (τ ≤ 1, where T is the normal optical depth) of Saturn's main rings.

Original languageEnglish
Pages (from-to)1102-1116
Number of pages15
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
StatePublished - 11 Jul 2003


  • InstabilitiesWavesPlanets: rings
  • Planets and satellites: individual: Saturn

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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