Investigating Shock Waves in Complex Plasmas via Molecular Dynamics Simulations

Abstract

Complex (dusty) plasmas serve as exceptional macroscopic analogues for studying the nonlinear dynamics of strongly coupled fluids and warm dense matter. While computational modelling provides deep insights into these systems, numerical simulations often idealise boundary conditions, omitting complex phenomena observed in physical experiments. This thesis bridges the gap between theoretical gas dynamics and physical laboratory environments by developing a high-fidelity molecular dynamics simulation pipeline specifically designed to replicate continuously driven compressional shock waves in two-dimensional strongly coupled dusty plasmas.

Employing rigorous thermostatting and drag models to accurately replicate the thermodynamic and kinetic dissipation inherent in the neutral gas background, the simulation perturbed a stable hexagonal microparticle lattice ($\Gamma = 1712$) using a constant-velocity exciter force. The primary objective was not a generalised study of all theoretical shock formations, but rather a targeted replication of specific experimental benchmarks to validate the computational framework against physical reality. The simulated shock fronts exhibited steady, monotonic steepening, with peak areal number densities reaching up to six times the undisturbed bulk density. Crucially, the simulations successfully reproduced the linear empirical relationship between the shock propagation speed and the exciter speed, expressed mathematically as $M_{s} = 1 + b M_{exciter}$. These simulated shock Mach numbers, reaching up to $M \approx 5.86$, demonstrated excellent quantitative alignment with corresponding continuous-drive experimental measurements of $M \approx 6.2$.

Beyond validating known experimental hydrodynamic relations, this computational framework revealed critical localised phenomena previously unobserved or idealised away in standard numerical models. Most notably, the simulations consistently captured \textbf{buckling} — the out-of-plane vertical displacement of microparticles ahead of the advancing exciter to minimise intense Coulomb repulsion. Observed across almost all simulation runs, this buckling highlights the physical limits of strict two-dimensional confinement under high-amplitude perturbation. Furthermore, the model captured anomalous precursor microparticles accelerating significantly ahead of the primary shock front, pointing toward complex, non-fluid energy channelling. By faithfully reproducing experimental shock kinematics and capturing complex, localised structural breakdowns such as buckling, this thesis establishes a robust, experimentally grounded computational analogue. The results underscore the need to incorporate physical dissipation and realistic confinement limits in numerical models, thereby providing a comprehensive tool for future investigations into the multidimensional energy transfer mechanisms of strongly coupled macroscopic fluids.