Influence of Lorentzian Distributions in Formation of Structures in Magnetized Dusty Plasmas

This study investigates structure formation via gravitational instability in a magnetized collisional dusty plasma system composed of Lorentzian-distributed electrons and ions. The presence of these non-Maxwellian distributions significantly alters the plasma's fundamental characteristics, including the Debye length and quasi-neutrality condition. Employing a three-fluid model for electrons, ions, and dust, we analyze the net force on magnetized dust, which incorporates the dust polarization force (DPF), dust charge gradient (DCG) force, thermal pressure, and dust-neutral collisions. Modified expressions for the DPF and DCG, derived for Lorentzian distributions, are utilized to obtain the generalized dispersion relation, analyzed for both parallel and perpendicular propagating modes. Our findings reveal a significant influence of the Lorentzian particle distributions on the dust acoustic wave, critical Jeans length, and Jeans mass in parallel propagation. Furthermore, these non-Maxwellian distributions profoundly affect the critical parameters governing perpendicular propagation, where system stability is evaluated using the Routh-Hurwitz criterion. The potential applications of this work are significant for understanding the formation of gravitational wakes in the outer regions of Saturn's A and B rings. The estimated critical length is found to be approximately \({L}_{J}={10}^{8}\) meters, and the critical mass approximately \({L}_{J}={10}^{8}\) kg, showing a notable correlation with observational data from the Cassini spacecraft.