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

References in corpus (2)

• Two-Dimensional Matter: Order, Curvature and Defects
• Topological defects in the crystalline state of one-component plasmas of non-uniform density