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

Abstract

The problem of finding equilibrium configurations of one-component charged particles, induced by external electrostatic fields in planar systems, is a subject of active studies in fundamental as well in experimental investigations. In this paper the results of numerical analysis of the equilibrium configurations of charged particles (electrons), confined in a circular region by an infinite external potential at its boundary are presented. Equilibrium configurations with minimal energy are searched by means of the hybrid numerical algorithm. The algorithm is based on the interpolation formulas, that are obtained from the analysis of the equilibrium configurations for an arbitrary finite number of charged particles, provided by the variational principle, developed in the circular model. The solution of the nonlinear equations of the circular model yields the formation of the shell structure which is composed of the series of rings. Each ring contains a certain number of particles, which decreases as one moves from the boundary ring to the central one. The number of rings depends on the total number of electrons. The interpolation formulas provide the initial configurations for the molecular dynamics calculations. Our results demonstrate a significant efficiency of using the method of classical molecular dynamics (MD) when using the interpolation formulas in comparison with algorithms based on Monte Carlo methods and global optimization. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods.