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  1. Abstract Nonlinear frequency response analysis is a widely used method for determining system dynamics in the presence of nonlinearities. In dusty plasmas, the plasma–grain interaction (e.g. grain charging fluctuations) can be characterized by a single-particle non-linear response analysis, while grain–grain non-linear interactions can be determined by a multi-particle non-linear response analysis. Here a machine learning-based method to determine the equation of motion in the non-linear response analysis for dust particles in plasmas is presented. Searching the parameter space in a Bayesian manner allows an efficient optimization of the parameters needed to match simulated non-linear response curves to experimentally measured non-linear response curves.
  2. Abstract

    In this paper, we report the first experimental observation of internal resonance in a dusty plasma, which shows the intrinsic nonlinearities of dust interactions in plasmas. When driving a system of vertically aligned dust particle pairs in the vertical direction, the horizontal motion is found to be excited during onset of internal resonance when the higher-frequency horizontal sloshing mode is nonlinearly coupled to the vertical breathing mode through the 1:2 commensurable relation. A theoretical model of the nonlinear interaction of dust particles in plasma is also provided and the results of the theoretical model are shown to match experimental observations.