The Jeans instability is a fundamental mechanism driving the gravitational collapse and subsequent structure formation in diverse self-gravitating astrophysical environments. We present comprehensive numerical fluid simulations of the Jeans instability in a three component dusty plasma system. The high-energetic nonthermal electrons and ions are considered to follow κ distribution in velocity space with inertial dust as cold fluid. A Gaussian-type of initial density perturbation is introduced in the equilibrium density to initiate the simulations. The effects of the self-gravity parameter $\left({\alpha }_G\right)$ and nonthermal spectral index $\left(\kappa \right)$ on the Jeans instability have been investigated by tracking the evolution of plasma parameters in the simulations. In the absence of gravity $({\alpha }_G=0)$, the system exhibits stable dust acoustic wave propagation with no Jeans instability growth, confirming pressure-dominated dynamics. Whereas, for ${\alpha }_G>0$, the density increases exponentially at center of plasma system manifesting localized collapse. The nonlinear growth rates estimated from our simulations increase with ${\alpha }_G$ and show good agreement with the linear theory, particularly for lower ${\alpha }_G$ values. Simulations further demonstrate that the nonlinear growth rate is weakly dependent on $\kappa$; however, lower $\kappa$ values significantly decrease the characteristic collapse time $\left({\tau }_c\right)$. These findings establish that nonthermal (non-Maxwellian) environments in protoplanetary disks and molecular clouds are more efficient at catalyzing rapid structure formation than previously predicted by traditional thermal (Maxwellian) models.

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• Astrophysical fluid dynamics
• Nonlinear dynamics in fluids
• Plasma instabilities