Universal, non-monotonic structure in the saturation curves of a linear Paul trap*

A common technique to measure ion-atom collision rates in a hybrid trap if the ions have no optical transitions (e.g. alkalis) is to monitor the fluorescence of the neutrals in the presence of a saturated linear Paul trap (LPT) [1]. We present numerical simulations, analytical calculations, and experimental results that show that the steady-state ion capacity of an LPT, $N_s$, exhibits nonlinear, nonmonotonic behavior as a function of ion loading rate, $\Lambda$ [2]. The steady state as a function of loading rate, $N_s(\Lambda)$, shows four distinct regions. In Region I, at the lowest $\Lambda$, $N_s(\Lambda)$ increases monotonically. Then, $N_s(\Lambda)$ reaches a plateau in Region II, before decreasing to a local minimum in Region III. Finally, in Region IV, $N_s(\Lambda)$ once again increases monotonically. This behavior appears universal to any Paul trap, regardless of geometry or species trapped. We examine this behavior experimentally as a function of the $q$ stability parameter of the Paul trap and simulate numerically the effect of the particular trap geometry on the onset of each of the four regions. \\ \noindent [1] Goodman, et al. PRA {\bf 91}, 012709 (2015) and Lee, et al. PRA {\bf 87}, 052701 (2013)\\ \noindent [2] Bl\"{u}mel, et al. PRA {\bf 92}, 063402 (2015)