On the Equilibrium Configurations of Charged Ions in Planar Systems with Circular Symmetry

— The problem of finding equilibrium configurations of similarly charged particles (ions) induced by external electrostatic fields in planar systems is of great interest for fundamental and applied research. In this paper, the results of numerical analysis of equilibrium configurations of negatively charged particles (electrons) confined in a circular region by an infinite external potential at its boundary are presented. A hybrid numerical algorithm is developed to seek stable configurations with minimal energies. The algorithm is based on interpolation formulas derived using the analysis of equilibrium configurations obtained by means of the variational principle of the minimum energy for an arbitrary finite number of particles in a circular model. The solution of nonlinear equations of the given model make it possible to predict structure formation in the form of rings (shells) filled with electrons, the number of which decreases when passing from the external ring to the internal one. The number of rings depends on the total number of charged particles. The obtained interpolation formulas of the distribution of the total number of electrons over the rings are used as initial configurations for the molecular-dynamics method. Our results demonstrate the significant efficiency of the application of the classical molecular dynamics (MD) method when using interpolation formulas in comparison with algorithms based on Monte Carlo methods and global optimization. For an arbitrarily chosen number of particles in the considered system, the proposed method makes it possible to enhance the speed at which the stable configuration with the minimum energy is reached by several orders in comparison with the classical-molecular-dynamics method.