  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.
