Bernsteinâ€"Greeneâ€"Kruskal Ion Modes in Dusty Space Plasmas Application in Saturn’s Magnetosphere.

Frequent observations of ion beams moving out from Saturn’s plasma environment hints at the generation of ion Bernsteinâ€"Greeneâ€"Kruskal (BGK) modes. As the plasma environments of Saturn and its moon Enceladus are characterized by the ubiquitous presence of massive negatively charged dust particles, the existing BGK theory for electron-ion plasma models cannot address this scenario. This manuscript develops a theoretical model for studying ion BGK modes in dusty plasmas. The analysis reveals that the presence of dust in the plasma enhances the stability of BGK modes. As the dust density increases, the effect of other parameters on stability, such as the electron temperature, becomes negligible. The model is developed by assuming that electrons and ions follow a kappa distribution, featuring a long tail trend in the superthermal component, in agreement with observations. Different scenarios with either electrons or ions obeying a Maxwell or kappa distribution function have been considered. A thorough analysis of the trapped ion distribution function considering various combinations indicates that a plasma where electrons are in thermal equilibrium and ions follow kappa distribution is the least favorable system for the generation of BGK modes. [ABSTRACT FROM AUTHOR]