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We discuss the basic principles of self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in disk geometry. The analysis is based on the cyclic symmetry and periodicity of the Coulomb interaction between particles located on several rings. As a result, a system of equations is derived, which allows us readily to determine with high accuracy the equilibrium configurations of a few hundred charged particles. For n≳200, we predict the formation of a hexagonal core and valence circular rings for the centered configurations.
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Cerkaski et al. (2015) studied this question.
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