Flow pattern and wave propagation induced by local energy deposition at droplet surface

Interaction between metallic droplets and picosecond laser pre-pulse can shape the droplet into a target more favorable for the main pulse to efficiently generate extreme ultraviolet (EUV) light for nanolithography. After the radiation of the pre-pulse, flow pattern and wave propagation in the droplet are responsible for the deformation and fragmentation of the droplet at a late time. In this study, we numerically investigate the acoustic response and dynamic behaviors of a droplet subjected to a localized heat pulse in the vicinity of the droplet surface, which models the energy deposition of a picosecond (ps) laser pre-pulse. A second-order conservative sharp interface method is adopted to simulate corresponding compressible inviscid two-phase flows. Based on the numerical results, we find that a wave structure of compression-expansion-compression waves propagates in the spherical droplet, and that the asymmetry of the heat source around the droplet surface accounts for the occurrence of the secondary compression wave. Then, we assess the occurrence and propagation of the wave structures, and correlate the wave amplitude with the intensity of the deposited energy. In particular, a theoretical model for the wave propagation is established under the small perturbation assumption, and indicates that the minimum pressure should be inversely proportional to its distance to the droplet center. This theoretical prediction is in good agreement with the numerical results with low intensity of heat source. With the increase of intensity of heat source, the numerical results gradually deviate from the theoretical prediction, because of the failure of the small perturbation assumption at high deposition energy and the effect of asymmetry in geometry on the wave propagation. This study provides an insight into the physical mechanisms of a droplet radiated by a ps laser pulse, which may be helpful in designing the desirable target for efficient laser-induced EUV light generation.