Coupled Oscillation‐Rotation Dynamics of Finite Dusty Plasma Clusters in a Gaussian Well: Role of the Confinement Radius

ABSTRACT The collective dynamics of strongly coupled dusty plasmas under external confinement remains insufficiently understood when the spatial scale of the potential is varied. Using two‐dimensional molecular dynamics simulations, we investigate the dynamical behavior of finite dust clusters trapped in a radially symmetric Gaussian potential well, focusing on the effect of the well radius . While the cluster exhibits stable periodic oscillations, we reveal a pronounced orbital rotation of its center of mass (CM)—an emergent phenomenon arising from the radially symmetric yet nonlinear confinement. As increases, the effective restoring force weakens, leading to a monotonic increase in both the oscillation amplitude and period. Notably, the CM orbital angular momentum is not conserved but evolves under a finite torque. We demonstrate that this torque originates from the coupling between the nonlinear potential landscape and the instantaneous asymmetric spatial distribution of the finite sized cluster, which breaks the effective radial symmetry of the net force. Through quantitative analyses of the oscillation amplitude, period, angular momentum evolution, and torque, we establish a direct regulatory mechanism linking the confinement scale to coupled oscillatory‐rotational dynamics. These findings provide new insights into nonequilibrium collective processes in confined strongly coupled systems and suggest pathways for controlling collective particle motion via potential‐well engineering.