Capture of an external anion beam into a linear Paul trap

Recently the very small group of atomic and molecular anions that may potentially be cooled using laser radiation has garnered increased attention [1, 2]. The successful demonstration of anion laser cooling would pave the way for creating ultracold ensembles of practically any negatively charged particle. A different negative-ion species sharing the same trapping volume with the laser-cooled anions could be sympathetically cooled, reaching temperatures well below that of the trap environment. One prominent application is the preparation of cold (<100 mK) antiprotons as a starting point for the production of cold antihydrogen via charge exchange with positronium [3]. Cold antihydrogen is a prerequisite for fundamental antimatter experiments using spectroscopy [4–6] or gravimetry [7–9].

Following theoretical predictions, several experimental groups have investigated the laser cooling candidate La⁻ using laser spectroscopy. Initial results suggested the existence of a dipole-allowed bound–bound transition between the 5d² 6s^{2 3}F₂^e ground and the 5d 6s² 6p ${}^{3}{{\rm{D}}}_{1}^{o}$ excited state in La⁻, which could be amenable to Doppler laser cooling [10]. More precise measurements, resolving the hyperfine structure of this transition for the anion of the only stable isotope ¹³⁹La, resulted in a laser cooling scheme feasible in the absence of magnetic fields [11, 12]. The required cooling radiation can be realized with a single laser and two electro-optical modulators that repump and cool all hyperfine levels of the ground state in a closed cycle.

With a view to realizing laser cooling in such conditions, we have been studying the trapping of anions from a continuous beam into a linear Paul trap. One of the challenges is the efficient loading of the trap. We have previously demonstrated [13] that a beam of La⁻ ions at a few keV energy can be produced by combining a Cs sputter ion source [14] with a dipole magnet for mass selection. However, La⁻ has a low electron affinity (U_EA ≈ 0.5eV [15]) and a low work function, presenting a considerable challenge to anion production, similar to that of other lanthanides [16]. With a low yield and a high kinetic energy compared to the electron affinity, the study of a capture process into the trap is of crucial importance.

In this article, we describe a trap design, a configuration of trapping potentials, as well as a trapping method to capture anions into a linear Paul trap. Measurements were carried out with O⁻ (U_EA = 1.46 eV), which is commonly produced as a contaminant by the Cs sputter ion source from a variety of targets. Compared to other realizations of linear Paul traps, the main differences of this design are twofold: first, the shape of DC fast switching electrodes that allows axial optical access and can be operated at relatively low voltages. Secondly, the floating of the trap (including all electronics) to a high voltage to match the keV beam energy of negative ions from a Cs sputter source.

In the setup used for the experiments reported here, negative ions are produced and extracted from a Cs sputter source as a continuous beam of ≈2 keV energy. Anions exiting the source are mass-selected by a 90° dipole magnet (radius r = 0.5 m) and directed towards the trap region. The mass separator was set to the mass of O⁻, readily separating the ion of interest from neighboring contaminants. The linear Paul trap is mounted about 3 m downstream of the magnet after some ion-optical elements. As shown in figure 1 (top), the trap consists of parallel cylindrical stainless-steel rods with radius 7.4 mm whose outer surfaces are at a radial distance r₀ = 7.0 mm from the trap axis. A radiofrequency voltage V_RF is applied to the rods with frequency Ω_RF/(2π) = 1.93 MHz. Pairs of opposing rods have the same phase; neighboring rods are phase-shifted by π.

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Each rod is composed of a stack of five cylindrical electrodes to which different DC voltages may be applied to shape the trap in axial direction. Both ends of each electrode are shaped to accommodate a cylindrical ceramic insulator to align electrodes in a stack, leaving an axial space of 0.5 mm between them for electrical isolation. The electrodes have lengths 44.5 mm (upstream), three times 14.5 mm and 46.5 mm (downstream), respectively, but in the present experiments the electrode stacks were used as single rods by shorting all axial segments. Circular plates at each end of the electrode stack have central orifices of 15 mm diameter to allow axial access for particles. The downstream plate (diameter 150 mm, thickness 6 mm) is attached to a CF160 flange by threaded rods in order to finely adjust the trap position.

The mutual positions of the rod stacks are defined by two insulating supports that attach at the first and last electrodes. At the axial position of the supports, fast switching electrodes are placed, which are electrically insulated from the rods and can be used for axial confinement and to rapidly modify the axial potential. The design of these electrodes is inspired by [17], but with two lobes extruding towards the axis instead of four, as shown in figure 2. The simplified geometry is justified by improved optical access in axial direction. According to our calculations, and confirmed by ion transmission measurements, about 18% of the potential applied to the switching electrodes is present on the axis at the axial center point of the electrode (see figure 1 (bottom)).

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For the present measurements, these lobular electrodes were used as end caps. The axial confinement was therefore achieved by the three voltage levels front, center and rear, applied to the first lobular electrode, the rods and the second lobular electrode, respectively. In actual trapping trials, the rear barrier was kept at a higher (absolute) potential than the front barrier. Due to the box-like axial potential, the outward radial force due to the axial confinement of the trapped particles by the end caps was present only at the very ends of the trap, where ions are reflected. By applying a suitable DC voltage ±U_DC to neighboring rods, it was possible to use the linear trap as a quadrupole mass filter. The motion of ions confined in the trap is then governed by the two Mathieu stability parameters a and q, which are defined as $a\,=8{{eU}}_{{\rm{DC}}}/({\rm{m}}{{\rm{\Omega }}}_{{\rm{RF}}}^{2}{r}_{0}^{2})$ and $q=2{{eV}}_{{\rm{RF}}}/({\rm{m}}{{\rm{\Omega }}}_{{\rm{RF}}}^{2}{r}_{0}^{2})$ [18].

The number of ions present in the trap and the distribution of their radial positions are measured destructively with a micro-channel plate detector (MCP) coupled to a phosphor screen and a camera (Allied Vision Mako). The MCP is located 5 mm downstream of the exit support plate. Anions were typically released onto the detector by switching the rear potential to the voltage of the rods. In figure 3 a typical camera acquisition is shown for a rod bias voltage of −1011 V. The detected particle number (which depends on the MCP voltages as well as the beam energy) was calibrated by an anion beam transmitted through the trap and pulsed to short intervals in order not to saturate the MCP. The calibration function was found to have a relative uncertainty of about 10%.

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In order to decelerate anions as they enter the trapping region, all trap power supplies are mounted on a high-voltage platform, which is brought to a common floating potential. In this way, most of the kinetic energy of incoming anions is reduced while entering the trap. Furthermore, the common floating reference allows varying the potential energy of already trapped anions with respect to ground without affecting the particles stored in the trap. The kinetic energy of ejected particles impinging on the MCP is the difference between the rod potential and the potential of the MCP's front face. The latter was constantly kept at 220 V above the reference ground to facilitate anion collection.

Anions traveling towards the MCP traverse a small axial distance without radial confinement before impinging on the detector. In this volume the cloud may be affected by inhomogeneous electric fields. In order to determine the influence of such focusing or defocusing effects on our detected images, we performed a Monte Carlo simulation taking into account the full geometry of the apparatus. The outcome of the simulation (in terms of a scaling factor between the detected image and the confined ion cloud) is compared with the experimental result in figure 4. For this purpose, we measured the Gaussian width of the anion cloud prepared under similar conditions but released at different rod voltages. The data show a marked reduction of the ion cloud width with increasing floating potential.

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The simulation correctly captures the general trend of the experimental data to better than 5%. Besides reproducing the trend, the simulation also allowed identifying the absolute mapping relation to reconstruct the effective anion cloud dimension inside the trap from the acquired images to ≈15% accuracy.

For anion capture, the 2 keV ion beam was first carefully aligned and passed straight through the trap on axis. The ion beam can be turned on and off by switching the voltage of an ion-optical element located between the mass-separating magnet and the trap. In a given trial, the time interval during which ions enter the trapping region is the anion loading time. With both the trap and the ion beam maintained in a steady state, the trap then gradually fills as the loading time progresses.

Anions become trapped by elastic or inelastic (e⁻detachment or charge exchange) collisions with anions in the reflected beam or with residual gas in the trap region. Anions enter the trap essentially in the axial direction. Scattering with other particles randomizes the ions' momenta, thus transferring axial to radial momentum. If the axial kinetic energy is reduced, ions can no longer overcome the static axial barrier on the entrance side and are confined. The radial confinement must, however, be strong enough to prevent anions from escaping in the radial direction. Hence this capture mechanism can be efficient only if ions are strongly decelerated and have a low overall kinetic energy prior to entering the trap. In addition, a significant deceleration reduces the likelihood of losing anions by collisional detachment. Therefore, the trap was prepared by setting the floating potential close (within a few V) to the beam acceleration potential.

First we mapped out and compared the stability regions in the Mathieu parameter space both in transmission and in trapping mode. Figure 5 shows the measurement obtained when using the trap as a quadrupole ion guide, recording the current transmitted through the trap in the absence of an axial trapping potential. Figure 6 shows the data acquired with trapping. In the trapping measurement the front and rear potentials were set to −35 V and −50 V, respectively, and anions were loaded for 20 s. The measured data show that optimal conditions for loading are achieved in a narrow range inside the stability region of the quadrupole guide, with maximum efficiency for q = 0.42(6) and a = 0.00(2). In this configuration the radial trap depth of the RF pseudopotential for O⁻ is about 13 eV at the radial distance r = r₀.

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The measured q parameter which provides the maximal trapping efficiency agrees with the theoretical value q_max ≈ 0.495 that leads to the highest density reachable in a Paul trap, as calculated in [19, 20]. These calculations, however, apply to an ideal hyperbolical Paul trap, where the RF drive is applied on the end caps and the ring electrodes. In a linear trap, where the RF is only applied to the rods for radial confinement, the combined stability region is symmetrical about a = 0 (neglecting the deconfining effect of the axial potential). This explains why the optimal a parameter for trapping is a = 0 in our system. These values of the a and q parameters should hold also for other anions with different mass, but requiring proportionally modified RF drives V_RF to obtain the same optimal q value.

In carrying out trapping trials we observed a contamination of the trapped sample by a different (nonisobaric) negative-ion species, which was likely produced by inelastic scattering during loading. We were able to identify the contaminant by operating the trap in a mass-selective configuration. From the optimal DC potential U_DC value for contaminant trapping we estimate its mass to be in the range from m = 28 to 39 u. We also selectively removed the O⁻ ions by laser photodetachment. For this purpose, the trapped sample was illuminated for 5 s with a 532 nm laser (photon energy 2.33 eV) at 1 W power and with a beam waist of w = 2.81(3) mm, where the latter is defined via the intensity relation $I\propto \exp \left(-{r}^{2}/{w}^{2}\right)$.

The DC potential on the rods was kept at U_DC = 0 V and the number of trapped ions was compared with laser on and off. The results are shown in figure 7. By selectively removing one anion species with the laser, we were able to isolate the contribution of O⁻. Thus, in measurements such as figure 6, the pure O⁻ signal was obtained by subtracting the acquisition with laser on from that with laser off. We find that the production of the contaminant is favored if the floating voltage is approximately 200 V lower than the beam energy. This suggests that such anions might be formed by collisions of the primary beam with trap surfaces.

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We then investigated the optimal conditions for anion loading in terms of the axial potentials. Confinement of anions was successful only for a narrow range of front, central and rear potentials compared to the 2 keV beam energy. A two-dimensional plot of the number of trapped ions as a function of front and central potentials is shown in figure 8. Predictably, the rod (central) potential, which determines the deceleration, is critical and must be adjusted to a value near the beam energy to optimally slow the anions before entering the trap. Incidentally a similar behavior was also observed in trapping anions into a Penning trap [21]. Figure 9 shows the number of trapped anions as a function of the rear potential, with the front potential held at −10 V. Generally, to favor trapping, the absolute value of the rear potential must be higher than that of the front potential in order to reflect anions and thus increase the probability of scattering events in the trap. We observe a sudden rise in the trapping efficiency with the rear potential just above the front end cap potential, with an optimal value of −45 V.

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In the optimal loading conditions, we further analysed the trapped ensemble to better understand its composition. For this purpose, we performed more selective photodetachment trials at different photon energies around the electron affinity of O⁻. When illuminating the sample with a 786 nm laser (photon energy 1.57 eV) at 130 mW for 10 s, we found that 89% of the trapped anions were photodetached. Conversely, with a 1064 nm laser (photon energy 1.17 eV) at 140 mW for the same interval, no particle loss at all was observed. The lack of photodetachment of the 11% fraction by the 786 nm laser excludes as contaminants all atomic and molecular anions near the mass of oxygen (from m = 14 u to m = 18 u) except for OH⁻, because they all have electron affinities of less than 1.57 eV (see, for instance, table 10 in [22]).

Since OH⁻ is bound by 1.83 eV, the 786 nm laser beam cannot photodetach this molecular anion. In order to determine if the ≈11% remaining anions are indeed OH⁻, we illuminated the sample with a more intense 532 nm laser at 1 W, which would be able to photodetach the excess electron in OH⁻. However, as in the trial with the 786 nm laser, we observed that only ≈90% of all ions were removed. No further increase in the fraction of photodetached anions that could have been attributed to the presence of OH⁻ was observed. Therefore, about 89 % of the trapped ions are O⁻. The remaining ≈11% trapped anions belong to an unidentified contaminant species with mass ≈32 u, whose trapping efficiency is enhanced for a higher RF drive as compared to O⁻.

We then operated the trap in the optimal configuration and measured the number of trapped anions as a function of the loading time. The plot acquired with a primary anion current of 0.777(5) nA is shown in figure 10. According to an empirical model for the loading process, the number of stored anions as a function of time N(t) is given by

$$\begin{eqnarray}&&N(t)={N}_{0}\left(1-\exp \left(-{\left(\displaystyle \frac{t}{\tau }\right)}^{\beta }\right)\right).\end{eqnarray} \tag{ 1 }$$

This dependency resembles a bounded-growth law, but with a temporal behavior that deviates from a pure unitary exponent. The upper bound arises from the fact that the space charge of already trapped particles reduces both the axial and the radial trap depth and thus hampers the further trapping of ions. The stretched exponential function is equivalent to a superposition of ordinary exponentials with several different relaxation times. Indeed, we observe at least two distinct particle loss lifetimes during initial loading and closer to equilibrium. A fit of equation (1) to the data of figure 10 yields a number of trapped particles N₀ = 8.43(8) × 10⁴, approached with a time constant τ = 23.8(8) s and an exponent β = 0.76(2).

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Next, we investigated the dependency of the loading efficiency on the primary anion current. For this purpose, we measured the loading rate as a function of the incoming ion current, which was adjusted in the range from 0.06 to 0.74 nA by a defocusing einzel lens located a few hundred mm in front of the trap. The evolution of the trapped ensemble was then recorded for loading times from 1 to 64 s. For such short times the trapping rate can be approximated by the first-order Taylor expansion of equation (1): N(t) ≈ αt^β. All trials resulted in similar β parameters (≈0.71(2)), suggesting that in the first second one out of a million anions is trapped. Hence, a higher incoming current translates into a larger number of trapped anions. For very long loading times, the number of trapped particles is limited by their lifetime in the trap.

The lifetime of trapped anions is affected by the residual-gas pressure in the trap volume, which was 5 × 10⁻¹⁰ mbar during the present measurements. O⁻ anions are mostly lost by charge exchange reactions with residual-gas atoms or molecules. We found the lifetime of the more massive contaminant(s) to be much longer, such that in considering the exponential decay of O⁻ we assumed the asymptotic value to be constant. The number of remaining particles in the trap N(t) hence follows the a modified decay law:

$$\begin{eqnarray}&&N(t)={N}_{0}\left(f+(1-f)\exp \left(-\displaystyle \frac{t}{\tau }\right)\right),\end{eqnarray} \tag{ 2 }$$

where f is the (constant) fraction of contaminant ions and τ is the storage lifetime. We found the fraction of contaminant ions f to be approximately 10%, compatible with the measurement of figure 7.

A plot of the number of remaining anions as a function of the storage time is shown in figure 11. For these measurements, anions were loaded during 100 s and the number of remaining particles measured destructively after an initial waiting time of 3 s. The data were fitted with the decay law of equation (2); the results of the fit are given in table 1. Without laser illumination, the trapped anions have a storage lifetime of about one minute. We also measured the effect of the 532 nm laser on the anion lifetime for different laser powers ranging from 36 to 370 mW. The observed lifetime reduction is compatible with photodetachment losses. In fact, the storage time constants scale approximately with the inverse of the laser power for the three data points measured.

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In this work we presented a linear Paul trap using a novel end cap design for the trapping of anions from a continuous beam of several keV energy. The trap was tested using a O⁻ beam at 2 keV, and a loading technique involving only electrostatic potentials was developed and tested. We performed a series of photodetachment measurements at different wavelengths to ensure that the trapped ions contained only a small fraction of contaminant species.

Ions were trapped in a static configuration by making use of the strong deceleration obtained when floating the entire RF trap to a high voltage nearly matching the beam energy. The loading process takes advantage of the continuous nature of the beam and allows trapping several 10⁴ O⁻ in our setup within a few tens of seconds. Collisional detachment by inelastic collisions with residual gas is likely to take place, but a high fraction (≈90%) of the desired species was nevertheless obtained. Trapping was found to be efficient only in a narrow range of a and q parameters as compared to the stability region of the equivalent mass filter in transmission mode.

In the current setup the trapping of La⁻ would require an RF drive amplitude between 1.9 and 2 kV (peak-to-peak). Alternatively, a smaller trap with reduced r₀ would allow trapping at lower RF drives. For instance, the capture of La⁻ at V_RF ≈ 1 kV amplitude may be realized with a trap of size r₀ = 5.3 mm.

The transverse projection of the ion cloud on the MCP detector shows a typical Gaussian shape. This is compatible with a thermal distribution of ions in the harmonic pseudopotential of the RF trap. Thus, we may estimate the temperature of trapped ions by analysing the shape of the ions' image on the detector. This is a prerequisite to observing a cooling effect on trapped anions (such as La⁻) under the effect of laser radiation.

The authors thank J Crespo (MPIK) for the loan of a quadrupole mass filter which inspired our linear Paul trap design. We also thank the MPIK mechanical workshop for their excellent work in constructing the linear RF trap. This work was supported by the European Research Council (ERC) under Grant No. 259209 (UNIC).