Prediction of the Formation of Dust Voids (Holes) in Nonextensive Dusty Plasmas With Adiabatic Charge Variation

Abstract

We present a self-consistent theoretical model for a dusty plasma comprising Maxwellian electrons, nonextensive (Tsallis) ions, and dust grains that follow a vortex-like trapped distribution, with the dust charge varying adiabatically. The model couples Poisson's equation, a modified dust density that accounts for trapped particles, and an adiabatic charge relation derived from orbital-motion-limited currents. Using parameters from 10 realistic plasma environments (e.g., cometary comae, Saturn's spokes, DC discharges), we demonstrate that the ratio of dust plasma frequency to charging frequency satisfies ${\omega }_{\mathrm{pd}}/{\nu }_{\mathrm{ch}}\ll 1$, justifying the adiabatic approximation. Numerical solutions reveal two qualitatively distinct regimes. In the supra-nonextensive regime (), the electrostatic potential forms a broad, large-amplitude hump (up to $\psi \sim 0.05$), accompanied by a deep dust density depletion-a well-defined dust void. In contrast, the sub-nonextensive regime ($q>1$) yields much narrower and smaller-amplitude structures ($\psi \sim 0.005$), with a shallower void. The dust charge becomes more negative at the void center, and this effect is significantly stronger for . The vortex-like dust distribution, characterized by a hole in velocity space (), is essential for producing a local minimum in dust density. Our results provide a theoretical framework for interpreting void formation in non-equilibrium dusty plasmas and suggest that ion nonextensivity can enhance void depth and width.