Coulomb clusters in harmonic traps

The classical Coulomb cluster in a cylindrically symmetric harmonic trap is treated in the approximation of a homogeneous volume distribution of particles. Analytical solutions for the cluster size and potential energy are obtained, which are only valid for clusters with a large number of particles. The influence of a possible inhomogeneity is determined, and it is established that this factor weakly influences the potential energy. The expression for the potential energy is extended to smaller clusters by introducing a correction factor derived through approximation of the results of numerical calculations.