  A projectile impact onto a granular target produces an ejecta curtain with
the 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 the early stages of crater formation and is
terminated by the ejecta's expanding motion. In this study, we test this
prediction based on a hyper-velocity 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 ~ 10 microseconds 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.
