Modeling Early Clustering of Impact-induced Ejecta Particles Based on Laboratory and Numerical Experiments

A projectile impact onto a granular target produces an ejecta curtain with heterogeneous material distribution. Understanding how the heterogeneous pattern forms is potentially important for understanding how crater rays form. Previous studies predicted that the pattern formation is induced by inelastic collisions of ejecta particles in early stages of crater formation and terminated by the ejecta's expanding motion. In this study, we test this prediction based on a hypervelocity impact experiment together with N-body simulations where the trajectories of inelastically colliding granular particles are calculated. Our laboratory experiment suggests that pattern formation is already completed on a timescale comparable to the geometrical expansion of the ejecta curtain, which is similar to 10 mu s in our experiment. Our simulations confirm the previous prediction that the heterogeneous pattern grows through initial inelastic collisions of particle clusters and subsequent geometric expansion with no further cluster collisions. Furthermore, to better understand the two-stage evolution of the mesh pattern, we construct a simple analytical model that assumes perfect coalescence of particle clusters upon collision. The model shows that the pattern formation is completed on the timescale of the system's expansion independently of the initial conditions. The model also reproduces the final size of the clusters observed in our simulations as a function of the initial conditions. It is known that particles in the target are ejected at lower speeds with increased distance to the impact point. The difference in the ejection speed of the particles may result in the evolution of the mesh pattern into rays.