Evaporation of Buffer-Gas-Thermalized Anions out of a Multipole rf Ion Trap

We identify plain evaporation of ions as the fundamental loss mechanism out of a multipole ion trap. Using thermalized negative ${\mathrm{Cl}}^{-}$ ions we find that the evaporative loss rate is proportional to a Boltzmann factor. This thermodynamic description allows us to extract the effective depth of the ion trap. As a function of the rf amplitude we find two distinct regimes related to the stability of motion of the trapped ions. For low amplitudes the entire trap allows for stable motion and the trap depth increases with the rf field. For larger rf amplitudes rapid energy transfer from the field to the ion motion can occur at large trap radii, which leads to a reduction of the effective trapping volume. In this regime the trap depth decreases again with increasing rf amplitude. We give an analytical parametrization of the trap depth for various multipole traps that allows predictions of the most favorable trapping conditions.

Figure 1

Measured loss rate of ${\mathrm{Cl}}^{-}$ anions out of the 22pole trap (see schematic view) versus temperature at an rf amplitude of $V_0=33\mathrm{V}$. The solid line is a fit to Eq. (1). A similar result is obtained with a 1D numerical model (see inset) in the same temperature range at an rf amplitude of $V_0=10.5\mathrm{V}$.

Figure 2

Experimentally determined effective trap depth (a) and numerically obtained effective barrier height (b) as a function of the rf amplitude. Each point is derived from a fit similar to Fig. 1. Inserted lines stem from the analytical model for different parameters of the maximum adiabaticity parameter ${\eta }_{\max }$. The two inserted phase space trajectories represent ions with a starting velocity just below the threshold for direct escape. At low rf amplitudes the ion returns from the barrier with the initial velocity. Strong transfer of energy from the field to the ion motion is seen at high rf amplitudes.

Figure 3

Effective trap depths for multipoles of different order $n$ as derived from the analytical model assuming a maximum adiabaticity parameter ${\eta }_{\max }=0.4$ (calculation for ${\mathrm{Cl}}^{-}$ ions, $r_0=5\mathrm{mm}$, $\omega =2\pi \times 5\mathrm{MHz}$).