Thomson rings in a disk

Abstract

We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach 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 a high accuracy the equilibrium configurations of a few hundreds charged particles. For $n\gtrsim 200$ we predict the formation of a hexagonal core and valence circular rings for the centered configurations.

13 pages, 3 figures, 1 table. Published version with a new figure and extended discussion

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Cited by in corpus (8)

• Self-organization of charged particles in circular geometry
• Conformal Vortex Crystals
• Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid
• Comment to "Thomson rings in a disk"
• Reply to "Comment on 'Thomson rings in a disk' "
• Static and Dynamic Properties of Two Dimensional Coulomb Clusters
• Significance of the nature of disorder on the universal features of the spatio-temporal correlations of two-dimensional Coulomb-clusters
• Intrinsic statistical regularity of topological charges revealed in dynamical disk model