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Dust kinetic temperature is a measure of the energy of the stochastic motion of a dust particle and is a result of the combination of the Brownian motion and the fluctuations in the dust charge and confining electric field. A method using the equilibrium value of the mean square displacement was recently introduced to obtain the dust kinetic temperature experimentally. As a follow up, this paper investigates the relationship between the dust kinetic energy derived from the mean square displacement technique and a technique using the probability distribution of the displacements obtained from random fluctuations of the dust particle. The experimental results indicate that the harmonic confinement potential acting on the dust particle can be obtained by combining the two methods, allowing the nonlinear effect of the confining force to be investigated. The thermal expansion in a 1-D vertical chain is discussed as a representative application as it is related to the nonlinear confinement force, or the asymmetric confinement potential. 

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.