Parametric Excitation of the Low-Frequency Oscillations in the Dusty Plasma of Planetary Rings

Abstract

The dusty plasma contains, along with electrons and ions, charged dust grains. If the macroscopic particles are sufficiently numerous they produce a noticeable effect on cooperative processes. As a rule, the charged grains are characterized by a broad spectrum of sizes, masses and charges. It reminds the situation in conventional plasma with many sorts of ions, but there are some important peculiarities. The spectrum of ion’s masses is always discrete, but the spectrum of dusty grains is practically continuos and it leads to the specific damping of longitudinal waves (analog of the Landau damping). On the contrary of ions the charge of dusty grains is not stable. It can be changed due to different factors. The change variations may lead to the parametric wave excitation. We shall consider the parametric instability developing in circular plasma flow of small cross-section as a result of periodic variations in the charge density of grains. The reason of such variations is the repeated transit of the particles through the light and shadow regions (e.g., Saturn’s rings are always partially shadowed by the planet, see Fig. 1). This causes changes in the intensity of the photoelectric effect, and hence in the charge of dust grains, the question whether the photoelectric current plays any important part in the general balance of currents responsible for electrical charging of the grains can be analyzed only experimentally. While in-situ measurements of the photoelectric current are not possible so far, the effect can be evaluated indirectly through other related phenomena that are detectable in observations.