Nonlinear drift waves and their role in Saturn’s B-ring: implications of rotation-induced dispersive dust drift waves and plasma parameter effects on spokes

Both linear and nonlinear dispersive dust drift waves are investigated in a magnetized, rotating plasma in the presence of Cairns and kappa-distributed ions by using the two fluid model. In the linear regime, dispersion relation is obtained. In the nonlinear regime, nonlinear partial differential equation (NLPDE) is solved to obtain the exact solitary solution by using the functional variable method. Parameters of Saturn’s B-ring are used for the graphical analysis. Graphical illustrations show that the solved NLPDE admits both compressive and rarefactive solitary solution depending on the velocity of the solitary structure. 3-D representation of compressive and rarefactive solitary structuresd appear as the spokes like structures (dark and bright, respectively) which are wider at the base and become narrower as the radial distance increases. This observation further supports the hypothesis that nonlinear drift waves may indeed correspond to the spokes observed in Saturn’s B-ring. It is noted that bright and dark spokes exhibit distinct behaviors in response to variations in the plasma parameters. By applying plasma parameters typical of those found in Saturn’s B-ring, it is demonstrated that the theoretically predicted spatiotemporal scale lengths align closely with the observations of the spokes made by various space missions and the Hubble Space Telescope (HST).