Scaling of energy and length for a two-dimensional classical system of charged particles under parabolic confinement

A two-dimensional classical system of charged particles under parabolic confinement is an important theoretical model that helps researchers understand fundamental interactions, explore new materials and devices, and study collective phenomena in low-dimensional systems. Its significance extends across multiple disciplines ranging from solid-state physics to plasma research. In this work we show how a particular scaling of energy and length in dimensionless form enables one to simplify considerably the determination of the global minimum energy of the system. This process allows for the identification of key parameters that govern the behavior of the system without being influenced by its scale. Results for small finite systems of particles are reported in order to illustrate the approach.