Figure 5

Equilbrium positions (blue dots) calculated for (a), 10 (b), 15 (c), 20 (d) with and . (a)  is the maximum number of ions for a single ring. (b)  is the first instance where there is a second ring in the center of the configuration. (c) Similar to panel (a), is the maximum number of ions to have two rings. (d)  is the maximum number ions expected to operate within our trap. As previously noted, the additional ions when added to the equilibrium configuration occupy the outer rings instead of the center.