## 1 Introduction  
Ejection refers to the emission of high-velocity spray particles from a substrate when a shock wave is reflected from a metal surface or a metal-gas interface. This complex dynamic phenomenon encompasses various fundamental scientific aspects, including shock-induced phase transformation, dynamic damage, multiphase flow, and particle aerodynamic deformation and fragmentation. The underlying mechanisms of ejection have been extensively studied globally due to their significance in shock compression science and engineering applications, such as pyrotechnics and inertial confinement fusion [1, 2]. Over the past decades, experimental [3, 4, 5, 6, 7], numerical [8, 9, 10, 11, 12], and theoretical [13, 14, 15, 16, 17] approaches have been employed to investigate ejection. [PERSON] et al. [3] studied ejection under high explosive loading and with a Ti64D impactor, respectively, and characterized the ejecta using piezoelectric pins and Asay foils. The results show that the total mass of the ejecta is linearly related to the shock pressure under supported shocks, whereas it increases sharply before and after unloading melting and then exhibits a relatively constant amount under unsupported shocks. [PERSON] et al. [5] developed a ps-pulsed laser-generatedX-ray source for the radiography of ejecta under laser shock loading. High-quality radiographs with good spatial and temporal resolution were obtained. In addition, the radiographs showed that low-density regions extend from the sides of the groove into the interior of the sample, forming subsurface damage due to localized tensions induced by rarefaction wave interactions. The advancement of computational technologies has further facilitated studies on ejection using molecular dynamics (MD) and hydrodynamic simulations, and the physical mechanisms of ejection have been further understood. [PERSON] et al. [11] conducted MD simulations to study the ejection process from shock-loaded tin surfaces in regimes where the metal first undergoes solid-solid phase transitions and then melts on release. The oblique interaction of the incident shock wave with the planar interface of the defect led to a sharp increase in temperature at the defect's bottom, causing spatially heterogeneous solid-liquid phase transitions and non-uniform fragmentation, which was different from the relatively uniform fragmentation process observed when the metal directly melts upon receiving the shock. [PERSON] et al. [12] used hydrodynamic simulations to investigate microjet formation from tin grooves under varying shock pressures. The results showed that relatively large variations in spall model parameters had minimal effect on quantities of interest (jet velocity and free-surface velocity). Three regimes were identified: a weakly driven regime where material strength limits material ejection, a moderately driven regime where solid-liquid phase change influences ejecta formation, and a strongly driven regime where behavior agrees with the steady-jet theory. Efforts have been made to model spike and bubble velocities and quantify ejecta mass based on experimental and numerical simulation results. Treating ejection as a limiting case of the Richtmyer-Meshkov (RM) instability at the metal-vacuum interface, [PERSON] et al. [13] proposed a model that replicated experimental spike and bubble velocities. Similarly, [PERSON] et al. [16] developed an analytical expression for the total mass of the ejecta, extending it to various initial perturbation shapes and achieving consistency with MD and hydrodynamic simulation data. In practical applications, the reflection of shock waves results in multiple shocks acting on disturbed surfaces. [PERSON] et al. [18] examined second ejections using an explosively driven two-shockwave apparatus, identifying additional mass ejection caused by the recompression of localized spallation. [PERSON] et al. [19] conducted combined numerical and experimental studies on second ejections from grooved tin surfaces subjected to laser-driven shock loading.