Instability analysis of Saturnian magnetospheric complex plasmas with heteropolar dust grains

ABSTRACT We investigate the instability features excited in complex plasmas in the Saturn’s middle magnetosphere (SMM) in the region between the orbits of Dione and Rhea. It comprises of bipolar dust grains (fluids), Maxwellian cold electrons and ions (primarily protons, $H^+$, and water-group ions, $W^+$), and suprathermal electrons. The term ‘bipolar’ signifies the dust population containing both positive and negatively charged dust grains. The charged dust dynamics incorporates the effects of the pressure gradient force, Lorentz force, and ion-neutral drag forces. Given the variability of the SMM, fluctuations in the dust grain potential are properly anticipated and incorporated in our model formalism. A standard cylindrical wave mode analysis leads to a generalized monic linear sextic dispersion relation. It is shown mainly that the explored instability propagates as a dust-acoustic wave (DAW) mode with a frequency of $10^{-2}$ s$^{-1}$ and phase velocity of $1-2$ cm s$^{-1}$ in realistic Saturnian plasma conditions. The multiparametric influences on the DAW growth rate and its non-trivial variation are extensively explored in light of the previously reported experimental (microgravity) and observational (Cassini) data.