Experimental quantification of strongly coupled clusters in two-dimensional complex plasmas to understand cluster to continuum transitions

We investigate static and dynamic behaviors of experimentally realized strongly coupled two-dimensional finite clusters in a complex (dusty) plasma. Clusters, ranging in size from N (number of grains) = 1 to 50 are obtained using a highly precise control arm assembly BECAA (bidirectional electrode control arm assembly) [24R. Kumar et al., Rev. Sci. Instrum. 95, 053503 (2024)10.1063/5.0203259], without any gaps and maintaining constant plasma discharge conditions. Crystalline (static) behavior of these clusters is characterized by the pair correlation function, shell structures,- and configurations, which are found to be in good agreement with simulation and previous experiments. The dynamic behavior of a cluster is quantified through recorded trajectories of individual grains and identification of their respective shells over time. Quantities such as angular rotation, intershell transitions and different regimes of mean-squared displacement (MSD) are highlighted to provide insights into the transition from individual to collective or bulk behavior of clusters. These transitions are typically studied via simulations due to significant challenges in controlling the number of grains in a complex plasma, whereas simulations allow easy adjustment of grain number. We have overcome this hurdle using BECAA and produced clusters with N=1-50 systematically and investigated their structures and dynamic properties to understand the individual-to-continuum transition.