Equilibrium configurations of systems of trapped ions

We have computed the equilibrium conformations of clusters of up to 100 ions in a spherically symmetric harmonic trap by a simple optimization strategy called seeding in which ions are added or removed from previously discovered minima. In each case, we have found at least as good a minimum as was previously known and believe that we have located the global minimum. We have additionally located a number of local minima and some saddle points. A balancing condition between the Coulomb and trapping terms which all of the critical points of the potential energy surface must satisfy was used to estimate the errors in the computed energies.