Ion crystals in Paul traps

The dynamics of small ion crystals in a Paul trap has been studied by numerical solutions of deterministic equations of motion that include the time dependence of the trapping potential. For small trap voltage, the crystal shell structure agrees with earlier calculations based on a harmonic pseudopotential. Chaotic motion is also possible and, as in the 2-ion case, increasing the trap voltage gives rise to a transition from transient to stationary chaos that is consistent with boundary crisis theory. With increasing ion number, the critical trap voltage decreases, in accord with experiments on aluminum microspheres, but the lifetime scaling of the chaotic transients is independent of the number of ions