On the stability of 2D modulated electrostatic wavepackets in non-Maxwellian dusty plasma-application in Saturn's magnetosphere

Motivated by observations of localized electrostatic wavepackets by the Voyager 1 and 2 and Cassini missions in Saturn's magnetosphere, we have investigated the evolution of modulated electrostatic wavepackets in a dusty plasma environment. The well-known dust-ion acoustic (DIA) mode was selected to explore the dynamics of multidimensional structures, by means of a Davey-Stewartson (DS) model, by taking into account the presence of a highly energetic (suprathermal, kappa-distributed) electron population in combination with heavy (immobile) dust in the background. The modulational (in)stability profile of DIA wavepackets for both negative as well as positive dust charge is investigated. A set of explicit criteria for modulational instability (MI) to occur is obtained. Wavepacket modulation properties in 3D dusty plasmas are shown to differ from e.g. Maxwellian plasmas in 1D. Stronger negative dust concentration results in a narrower instability window in the K (perturbation wavenumber) domain and to a suppressed growth rate. In the opposite manner, the instability growth rate increases for higher positive dust concentration and the instability window gets larger. In a nutshell, negative dust seems to suppress instability while positive dust appears to favour the amplitude modulation instability mechanism. Finally, stronger deviation from the Maxwell-Boltzmann equilibrium, i.e. smaller κe values, lead(s) to stronger instability growth in a wider wavenumber window-hence suprathermal electrons favour MI regardless of the dust charge sign (i.e. for either positive or negative dust). The wavepacket modulation properties in 2D dusty plasmas thus differ from e.g. Maxwellian plasmas in 1D, both quantitatively and qualitatively, as indicated by a generalized dispersion relation explicitly derived in this paper (for the amplitude perturbation). Our results can be compared against existing experimental data in space, especially in Saturn's magnetosphere.