Elevating plasma physics: The role of higher-order nonlinearities in space dust shock waves with superthermal ions

This research explores the higher-order nonlinear and dissipative effects on dust acoustic shock waves in a complex plasma medium composed of inertial negative dust particles, Maxwellian electrons, and superthermal ions under the influence of polarization forces. Employing a perturbative approach, the research derives analytical descriptions of both first- and second-order potentials and electric fields, highlighting how these higher-order corrections significantly modify the shock wave structures. The analysis reveals that second-order potentials introduce negative contributions that reduce the overall wave amplitude, while the associated electric fields oppose the first-order fields, leading to self-regulating mechanisms that influence energy transport and wave stability. Numerical evaluations demonstrate how key plasma parameters, such as polarization strength, dust temperature, ion-to-electron density ratio, viscosity, and superthermality-affect phase velocity, nonlinearity, and shock profiles. The findings emphasize that including higher-order effects is crucial for accurately modeling shock dynamics in laboratory with direct relevance to astrophysical plasmas, notably the dynamics observed in planetary ring systems and cosmic dust environments, providing deeper insight into energy dissipation and wave evolution in complex dusty plasma systems.