2D dust clusters in theory and experiments

The theory [1] is applied for more detail analysis of existing experiments of 2D dust clusters with parabolic confinement. It is shown that the equilibrium condition and the frequency of one of the modes of the cluster determines all dimensionless parameters of the cluster allowing to predict the value of other modes and compare them with existing experimental data. This comparison depends on the shielding model. the calculations starting with N = 4 cluster breathing mode predict for Debye shielding model without attraction the frequency of the antisymmetric mode in disagreement with the observed value [2] about 6 standard deviations, while the same calculations for the non-linear screening [3] model gives disagreement about 1 standard deviation. Including the attraction provides an agrement with observations only for non-linear screening model showing the sensitivity of cluster structure to dust attraction. The value of the obtained attractions coefficient is in reasonable agreement with the theoretically expected value. It is shown theoretically that in absence of external parabolic confinement a weak shadow attraction can provide an existence of equilibria for 2D clusters. The equilibrium radius is rapidly decreasing with an increase of the attraction coefficient and with number of grains N in a cluster. The energies of one shell clusters with different N and the energies of N - 1 grain clusters with additional grain in the center of the shell are calculated as functions of attraction coefficient. It is demonstrated that a dissociation of cluster in several smaller clusters needs less energy than a removal of one grain from the cluster. The calculations were performed for Yukawa screening and for non-linear screening and demonstrate the sensitivity of cluster structures to the screening. Frequencies of all modes are calculated up to N = 7 for one shell structure. Stable and unstable modes as well as universal magic numbers are found.