Continuum theory for two-dimensional complex plasma clusters

Abstract

We develop a theoretical approach to obtain a new differential equation together with a new boundary condition for the density profile of two-dimensional clusters and apply it to the complex plasma case. In addition, we use the local-density approximation for the interaction energy and consider finite size effects. In this case, our differential equation and the previously used reduce to the same. By using the new boundary condition, a scale invariance appears and the obtained scale function can be used in many systems beyond complex plasmas. The obtained equations are confronted with molecular dynamics simulations. We find that the dependence of the system's size and the density profile with the number of particles, N , agrees very well with the results obtained from simulations. The theory has a surprisingly good accuracy for small systems (8 < N < 500). Moreover, we find by simulations that, for a given external potential, the final configuration from an experiment or simulation can provide us, at most, with two possible values for each interaction parameter, the charge and the screening length.