Evaporation of trapped anions studied with a 22-pole ion trap in tandem time-of-flight configuration

We have recently shown [J. Mikosch et al., Phys. Rev. Lett. 98, 223001 (2007)] that the storage time of a thermal ensemble of ions in a multipole radiofrequency (rf) ion trap is ultimately limited by ion evaporation. An analysis of the evaporation rate was used to determine an effective trap depth as a function of the rf amplitude. This revealed that already for moderate rf amplitudes and low average stability parameter $\eta$ the loss of ions is driven by nonadiabatic motion of the fastest ions in the rf field. Here we present the details of the experimental procedure together with our experimental apparatus, which combines a 22-pole rf ion trap with tandem time-of-flight mass spectrometry for ion selection and product analysis. We furthermore describe in detail the numerical and analytical models used in the interpretation of our results, which allows one to predict the most favorable trapping conditions in multipole rf ion traps. From a fit to our data we obtain a maximal value of the multipole stability parameter of ${\eta }_{\mathit{max}}=0.36\pm 0.02$ for adiabatic ion motion.

Figure 1

(Color online) Experimental setup consisting of a pulsed electron impact ion source, a temperature-variable 22-pole rf trap [2], and a mass-sensitive ion detection system based on time of flight. The trap is located in a copper case (partly omitted for clarity), such that buffer gas and reaction gases can be applied with a well-defined density and temperature.

Figure 2

(Color online) Typical time-of-flight mass spectrum recorded after extraction from the 22-pole ion trap when $\mathrm{O}{\mathrm{H}}^{-}$ anions were stored at $8\mathrm{K}$ in a mixture of hydrogen and helium buffer gas. With increasing storage time we observe clustering and deuteration of the hydroxyl anions. The graph shows a typical mass resolution of $m∕\Delta m=t∕\left(2\Delta t\right)\approx 40$ [31].

Figure 3

Measured ${\mathrm{Cl}}^{-}$ ion signal as a function of storage time in the trap for three different temperatures. No other ions have been observed in the time-of-flight spectra for any of the storage times. A dramatic increase in the lifetime from $9\mathrm{s}\text{to}10\min$ is observed for cooling the trap from $300\mathrm{K}\text{to}225\mathrm{K}$, whereas the lifetime is reduced to only $0.46\mathrm{s}$ when heating the trap to $370\mathrm{K}$. Lifetimes are obtained from exponential fits (solid lines).

Figure 4

(Color online) Measurements of the loss rate of ${\mathrm{Cl}}^{-}$ anions out of the trap as a function of the trap’s temperature at various rf amplitude $V_0$ between 7 and $150\mathrm{V}$. Exponential decays of the loss rate with decreasing temperature are observed. The blue lines represent fits following a Boltzmann or Arrhenius law $k\left(T\right)=\exp \left(A\right)\exp (-\frac{E_a}{k_{B}T})$ and yield activation energies $E_a$ for ion loss from the rf trap. Due to the absence of any chemical reactions, this energy is attributed to the effective trap depth induced by the confining rf field. For rf amplitudes in the interval $9–23\mathrm{V}$ we find a systematic deviation from the Boltzmann behavior for high temperatures and hence show fits for two temperature ranges (solid and dashed lines; see text for details).

Figure 5

(Color online) (a) Measurement of the effective trap depth as a function of the rf amplitude at a fixed frequency of $\omega ∕\left(2\pi \right)=4.7\mathrm{MHz}$. Each point originates from a Boltzmann fit [Eq. (4)] to a loss rate measurement as shown in Fig. 4. For rf amplitudes in the interval $9–23\mathrm{V}$ we show the fit results for two temperature ranges (upright and upside down triangles) as described in the text. We attribute the breakoff of the effective trap depth’s quadratic increase to the appearance of nonadiabatic ion motion in the trap. The solid line stems from a fit following the analytical model described in Sec. 4B. We obtain a maximum value of the multipole stability parameter of ${\eta }_{\mathit{max}}=0.36\pm 0.02$ for adiabatic ion motion. (b) Fit result for the prefactor $\exp \left(A\right)$ arising from the same measurement (see Fig. 4) as a function of the rf amplitude.

Figure 6

One-dimensional oscillating electric multipole field of order $n=11$ according to Eq. (5) as used in the numerical simulation. The solid line shows the potential at a given moment in time, whereas the dashed lines show the maximum and minimum amplitudes. Ions start at $r=0$ at random phase $\Phi$ with a velocity $v_{\mathit{\text{start}}}$ drawn from a two-dimensional Maxwellian distribution at temperature $T$. They are propagated in the time-dependent potential by numerically solving the equation of motion.

Figure 7

(Color online) Effective barrier height as a function of the rf amplitude obtained with the one-dimensional numerical model described in Sec. 4A. As in the corresponding experiment, each point originates from a Boltzmann fit [Eq. (4)]. The numerical model is well suited to interpret the general shape of the effective trap depth measurement shown in Fig. 5 by the introduction of nonadiabatic ion motion. The solid line stems from a fit following the analytical model described in Sec. 4B. We obtain a maximal value of the multipole stability parameter of ${\eta }_{\mathit{max}}=0.54\pm 0.03$ for adiabatic ion motion. Hence for the one-dimensional multipole field of the simulation adiabatic ion motion is possible up to a significantly higher value of the stability parameter as compared to the experiment.

Figure 8

Velocity of ions starting at zero radius with increasing velocity as they propagate in a one-dimensional multipole rf field of order $n=11$. For a low rf amplitude (upper panels) ions either return to the origin with the same velocity they started with or get lost in that they reach the rim of the rf field at $5\mathrm{mm}$ radius depending on their starting velocity. However, for high rf amplitudes (lower panels) ions can gain translational energy in the regions of high field, leading to subsequent loss at the next approach to the barrier. The figure demonstrates the introduction of regions of nonadiabatic ion motion into the trap for high rf amplitudes.

Figure 9

(Color online) (a) Schematic view of the electronic circuit diagram of the microchannel plate detectors employed for ion time-of-flight measurements. Ion packages are converted into bunches of electrons collected on an anode. This leads to the anode current $I\left(t\right)$ and the corresponding voltage drop $U\left(t\right)$ across a $50\text{−}\Omega$ resistor. (b) The upper panel shows a simulated $U\left(t\right)$ trace for a sequence of square pulses in $I\left(t\right)$ [44]. In the lower panel the reconstructed current signal is shown, which is obtained with the integral equation described in the Appendix.