Two-dimensional and three-dimensional Coulomb clusters in parabolic traps

We consider the shell structure of Coulomb clusters in an axially symmetric parabolic trap exhibiting a confining potential U_c(ρ,z)=(mω^2/2)(ρ^2+αz^2) . Assuming an anisotropic parameter α = 4 (corresponding to experiments employing a cusp magnetic trap under microgravity conditions), we have calculated cluster configurations for particle numbers N = 3 to 30. We have shown that clusters with N ≤ 12 initially remain flat, transitioning to three-dimensional configurations as N increases. For N = 8, we have calculated the configurations of minimal potential energy for all values of α and found the points of configuration transitions. For N = 13 and 23, we discuss the influence of both the shielding and anisotropic parameter on potential energy, cluster size, and shell structure.