Fluorescence detection as a new diagnostics tool for electrostatic ion beam traps

In the development towards the Multi Ion Reflection Apparatus for Collinear Laser Spectroscopy (MIRACLS), an optical detection region for the observation of fluorescent light is added to an electrostatic ion beam trap (EIBT). In addition to its use for highly sensitive collinear laser spectroscopy, this fluorescence detection is introduced as a diagnostics tool for the study of the ion dynamics inside an EIBT. First measurements of collision-induced fluorescence in an EIBT demonstrate the technique’s diagnostics power by tracking the evolution of an ion bunch’s temporal width over its storage time inside the ion trap. Thereby, the time-focus point of the ion bunch can be determined and the influence of space-charge effects in the EIBT can be investigated. Good qualitative agreement is obtained between the measured trend of temporal widths and the simulations of the ions’ trajectories in the trap. Particularly, the observation of self-bunching on the ion-bunch structure for many simultaneously stored ions is reproduced.


Introduction
Collinear laser spectroscopy is a formidable tool for the exploration of the nuclear landscape in terms of ground state properties of short-lived radionuclides, such as nuclear spins, electromagnetic moments and charge radii [1,2]. In order to access these nuclear properties by laser spectroscopy, a beam of atoms or ions is (anti-)collinearly overlapped with a narrowband laser beam. Scanning the laser frequency around an optical transition of interest and counting the photons emitted by de-excitation from laser-excited atoms or ions reveals the hyperfine structure and the isotope shift can be determined. Fast beams at energies E of a few tens of kiloelectron volts allow one to approach the natural linewidth of an optical transition as the Doppler width δν D is minimized according to δν D ∝ δE/ √ E, where δE depicts the energy spread of the beam.
However, in order to access the most exotic nuclides produced with very low yields at radioactive ion beam facilities, methods with higher sensitivity have to be developed. To this end, the novel Multi Ion Reflection Apparatus for Collinear Laser Spectroscopy (MIRACLS) [3] is currently being built at ISOLDE/CERN [4]. It aims to combine the high spectral resolution of conventional collinear laser spectroscopy (based on the detection of the photons after resonant excitation) with high experimental sensitivity. This is achieved by trapping ion bunches in an electrostatic ion beam trap (EIBT) [5][6][7][8] in which the ions bounce back and forth between two electrostatic mirrors. In this way the laser-ion interaction time is increased by the number of reflections.
The EIBT used for the investigation described in this publication is very similar to multi-reflection time-of-flight (MR-ToF) mass spectrometers [9][10][11][12][13], applied for instance at ISOLDE for mass spectrometry of short-lived isotopes [14]. It is operated with ions of only ≈ 1.5 keV beam energy and serves to proof the principle of the future MIRACLS set-up for collinear laser spectroscopy designed for trapping 30-keV ions. To this end, an optical detection system is mounted in the middle of the field-free region of the EIBT in order to observe the fluorescent light.
Besides its use for collinear laser spectroscopy, fluorescence detection offers the opportunity to track the ion bunch for every passage through the optical detection region. In the following we show how this technique can be used to study the ion dynamics inside an EIBT. Specifically, collision-induced fluorescence, called residual gas afterglow in [15], has been used to examine space-charge effects and to determine the time-focus point of an ion bunch propagating inside the trap. Simulations of the evolution of the ion cloud's time structure inside the EIBT are presented and compared to experimental data obtained from fluorescence detection. These studies focus on the space-charge effect of "self-bunching", also known as "self-synchronization", in EIBTs [16][17][18][19]. Beyond its general relevance for EIBT operation with a large number of stored ions, it is crucial for the MIRACLS concept to investigate the potential influence of space-charge effects and self-bunching on collinear laser spectroscopy in an EIBT.

Experimental apparatus
The apparatus employed in this work is shown in Fig. 1. It is an EIBT setup originally described in [20] which has been modified for the purpose of collinear laser spectroscopy [3].
An electron-impact ion source, adapted from [21], delivers a continuous beam of singlycharged ions from stable magnesium isotopes. The Mg + ions are subsequently accumulated Schematics of the experimental setup. A beam of Mg + ions is injected into a helium buffer-gas filled Paul trap from which the ions are released in bunches and captured in an electrostatic ion beam trap (EIBT). The EIBT hosts an optical detection region in its field-free region to detect fluorescence light with a photomuliplier tube (PMT). See text for details and cooled in a helium buffer-gas filled Paul trap. They are extracted in well-defined bunches and accelerated to a transfer energy of E trans ≈ 2.305 keV. Thereafter, the ion bunch is guided by an electrostatic quadrupole bender onto the optical axis of the EIBT. A close-up view of this EIBT is shown in Fig. 2a, depicting a central drift tube surrounded by two electrostatic mirrors. The latter consist each of a set of ring electrodes to establish the mirror potential, for instance the one shown in Fig. 2b. Capturing the ion bunch into the EIBT is achieved by the in-trap lift technique [20,22] in which the electric potentials of the mirror electrodes are kept constant at all times. The central drift tube is switched from an initially positive bias voltage to ground potential when the ion bunch is located in the center of the tube (see Fig. 2b). Hence, the value of this "lift" potential, V lift , determines the ions' kinetic energy E inside the EIBT according to E = E trans − e · V lift . As long as their kinetic energy is too low to overcome the potential barrier imposed by the electrostatic mirrors, the ions are confined inside the EIBT. When the lift potential is switched back up, the ions leave the trap again. In this work, the Mg + ions are typically stored for a few milliseconds, while a single revolution accounts for only a few microseconds.
Similar to [23,24], an optical detection region for fluorescence detection adapted from [25] is situated above the trap's field-free region of the central drift tube (see Fig. 1). It consists of an optical lens system, which images photons emitted by ions onto a photomuliplier.

Collision-induced fluorescence and tracking of the ion bunch inside an EIBT
In principle, EIBTs demand excellent vacuum quality in order to prevent the ions from colliding with residual gas particles, which affects the ion trajectories in the trap and ultimately leads to ion losses. However, there is the possibility that the collision partners undergo Since these collisions are very rare under standard EIBT operation, the vacuum quality is purposely degraded for the following measurement. To this end, the helium flow into the Paul trap is adjusted such that the pressure in the EIBT section is increased as well. As a first application of the collision-induced fluorescence technique, the photon counts are recorded while ion bunches of stable magnesium isotopes are confined for 64 revolutions (Fig. 3). Each time an ion bunch passes the detector the number of recorded photons increases significantly above the background level.
Since a bunch passes the optical detection region twice per revolution in addition to the initial passage during capture, there are 129 pronounced peaks in Fig. 3. These are associated with 24 Mg + ions, the most abundant magnesium isotope (≈ 79%). Peaks corresponding to less abundant isotopes, 25 Mg + and 26 Mg + , can be resolved as well. This is shown in the inset of Fig. 3. The distances between peaks associated with different magnesium isotopes increase with each revolution, due to their mass difference and corresponding difference in revolution period T , e.g. T ≈ 6.79 μs for 24 Mg + compared to T ≈ 6.93 μs for 25 Mg + . In principle, this data allows the mass determination of the trapped ion species when considering the different revolution period of each isotope with respect to one magnesium isotope as a reference mass. This new fluorescence-based mass spectrometry will be Major signals are from fluorescence due to collisions of 24 Mg + ions with residual-gas molecules, smaller signals are from 25 Mg + and 26 Mg + (see inset). The configuration of the EIBT setup is the same as described in [20]. See text for details the topic of future work. Here, we focus our study of fluorescence detection on its capability as a diagnostics tool for the ion dynamics inside an EIBT.
In the beginning of the storage time in Fig. 3, the peak height of fluorescent light from 24 Mg + ion collisions rises with increasing revolution number. It reaches a maximum at around 17 revolutions. Then the peak height decreases again. This behavior can be explained by Fig. 4, which characterizes the width (a), amplitude (b) and area (c) for each fluorescence peak caused by 24 Mg + ions. Up to the 17th revolution (indicated by the blue vertical line) the peak width decreases, while the peak amplitude increases. Subsequently the behavior is reversed, with increasing width and decreasing amplitude. This is interpreted as a signature of a time focus of the ion bunch at revolution number 17. Such a time focus can for instance arise at the moment when higher energetic ions within the ion ensemble, which were initially at the temporal end of the ion bunch, overtake the slower, less energetic ions.
The almost continuously decreasing peak area shown in Fig. 4c reveals ion losses over time. These losses can arise from collisions of the ions with the residual gas. Such collisions may "kick out" ions due to the resulting transversal momentum or neutralize them by electron transfer reactions.
This first experiment illustrates that fluorescence detection in an EIBT allows one to track, in-situ and revolution by revolution, ion-bunch properties such as temporal width or relative ion number. This is complementary to the use of an image-charge detection via a pick-up electrode [16,18,19,26]. Similar investigations can also be performed by ejecting the ion bunch onto an ion detector after subsequent revolution periods and evaluating the signal properties [27]. However, the measurement based on fluorescence detection only requires a single experimental cycle to record the full information for all revolutions and is not limited by the saturation-effects of, e.g. micro-channel-plate detectors.

Space-charge effects in an EIBT
Space-charge effects are of particular importance in the application of an EIBT as a multireflection time-of-flight (MR-ToF) mass separator. Indeed, large numbers of stored ions are known to disturb the otherwise superb mass resolving power of an EIBT [20,28,29]. Hence, understanding space-charge effects and their impact on the ion cloud in EIBTs is essential, especially when the mass separation of large ion samples is aimed for. For instance, the elimination of undesired contaminants in the beam of radioactive isotopes via MR-ToF techniques becomes increasingly important when probing exotic rare isotopes. There, additional diagnostics tools such as fluorescence detection can help1 to study and ultimately extend the limits in MR-ToF operation imposed by space-charge effects.
EIBTs used for mass spectrometry can be operated in an isochronous mode, i.e. the voltages of the trap's mirror electrodes are chosen such that within a certain energy window the revolution period T remains independent of the exact ion energy, i.e. dT /dE = 0. Figure 5 depicts the simulated revolution period of a 24 Mg + ion bunch as a function of  Fig. 2b. For completeness, note that these potentials have been optimized for collinear laser spectroscopy and are not the same as those used in Section 3. As outlined above, different ion energies of the stored ions are facilitated by different lift potentials applied to the central drift tube. In Fig. 5, it can be seen that the revolution periods for lift potentials in the proximity of 860 V, corresponding to an ion energy of about 1445 eV, are very similar in a kinetic-energy range of about 10 eV. Hence, when considering ions at E ≈ 1445 eV with energy spreads of at most a few electron volts, their individual revolution period is largely the same and the temporal ion-bunch width is consequently kept constant over time.
Contrary, for lift potentials such as below 800 V, the revolution period is noticeably influenced by the ion energy, i.e. the trap is operated in a non-isochronous mode with dT /dE > 0. More energetic, faster ions exhibit a longer revolution period in the EIBT compared to slower, less energetic ones. Thus, even small energy differences comparable to the typical energy spread in realistic experimental conditions lead to different revolution periods. Hence, the ion-bunch width will quickly increase with time.
However, it has been shown [16][17][18][19] that for sufficiently large ion clouds, space-charge effects counteract this bunch dispersion. This phenomenon, known as "self-bunching" or "self-synchronization", can occur for combinations of mirror potentials and ion energies where dT /dE ≥ 0 [18] as it is the case for energies higher than E ≈ 1445 eV (see Fig. 5). In this case, the bunch width stays roughly constant even in otherwise non-isochronous settings.
In order to investigate the importance of self-bunching in the present setup, SIMION [30] simulations of ion trajectories inside the EIBT are carried out, which follow closely the procedure described in [31]. An ion bunch is thermalized in the Paul trap and then transferred into the EIBT. The storage in the EIBT over typically 300 revolutions is simulated separately at the highest computationally feasible geometrical resolution [31]. The mirror potentials, as shown in Fig. 2b, have previously been optimized for a lift voltage of V lift = 860 V, i.e. ion energies of 1445 eV, but are kept identical for all simulations. As the observable of interest, the temporal bunch width is evaluated in the middle of the EIBT's field-free region for every passage.
First, simulations of 1000 non-interacting 24 Mg + ions are carried out for different lift potentials and hence, different ion energies. The resulting temporal width of the ion bunch is shown in Fig. 6a. For ion energies of 1445 eV, the ion-bunch width (blue line in Fig. 6a) remains constant over the entire storage time. Thus, despite an energy spread of δE = 2.36 eV (FWHM), the EIBT operates in an isochronous mode as expected from Fig. 5. On the other hand, the bunch width increases linearly for ion energies above 1445 eV. Far away from the isochronous mode, as for V lift = 700 V (E ≈ 1605 eV), the ion ensemble will quickly de-bunch after a few tens of revolutions as discussed above.
In a second set of simulations, Coulomb interactions between ions as implemented in SIMION's charge repulsion method [32] are used to study the effect of space charge on the bunch width (see Fig. 6b). Already for 100 ions this is computationally expensive. To obtain results for larger ion clouds without increasing the computing time, a charge multiplication factor is applied to the Coulomb interaction between the ions [33]. When using a charge multiplication factor of 10 for example, each ion acts as a sub-bunch of 10 ions. This method may lack some degree of accuracy since the electric field does not reflect the ions' cloud charge density. However, we expect that it leads to a qualitative understanding of spacecharge effects at play in the EIBT in a time efficient way. The consistency of the method is benchmarked by comparing a simulated ion cloud of 250 interacting ions to an ensemble of 100 ions, interacting with a charge multiplication factor of 2.5. In this particular case, the results on the ion-bunch width agree within statistical uncertainties. Note that the Coulomb interaction between the ions is only considered while the ions are trapped inside the EIBT to clearly isolate the space-charge effects from those occurring in the Paul trap or during ion transfer. Thus, for one fixed lift potential the initial ion distribution inside the EIBT is identical and all differences in the ion cloud's temporal width are exclusively due to different multiplication factors in the Coulomb interaction. Figure 6b displays the results of simulations which include Coulomb interactions for a lift potential of V lift = 700 V (E ≈ 1605 eV). This configuration normally leads to a sizable dispersion and hence a rapid increase in the bunch width with revolution number. For 100 trapped ions, the difference in the bunch width for non-interacting and interacting ions is minimal and the slope of bunch width as a function of revolution number is quite similar. However, increasing the charge multiplication factor to resemble larger ion clouds has significant consequences: The increase in bunch width is considerably slower since Coulomb repulsion counteracts this de-bunching. This happens already for charge multiplication factors of 10 and 20, corresponding to 1000 and 2000 ions, respectively. For a charge multiplication factors of 40 and 100 the bunch width is practically constant as in the isochronous mode, indicating the effect of self-bunching.
Motivated by the results of these simulations, measurements of collision-induced fluorescence are performed similarly to those in Section 3 for different numbers of ions simultaneously stored in the EIBT. To this end, the loading time of the Paul trap is varied. However, we do not have a reliable estimate of the absolute ion number. For these measurements, nitrogen gas is directly leaked into the EIBT's vacuum chamber. The lift potential is set to 700 V, to have considerable ion bunch dispersion and a direct comparison to the respective simulation in Fig. 6b. Fluorescence signals at different revolution numbers (0, 40 and 80) of 24 Mg + ions are presented in Fig. 7 for two different Paul trap loading times, 50 μs and 800 μs, respectively. The latter leads to ion clouds with significantly larger ion   24 Mg + ions, although 25 Mg + and 26 Mg + ions can be seen in the tail to the right at revolution 0 numbers. At revolution 0, the normalized and background-subtracted peaks are close to identical for both loading times. At revolution 40, however, an ion bunch with less ions shows already clear signs of dispersion, getting even more significant at revolution number 80. On the other hand, the width of the fluorescence peaks corresponding to 800 μs of loading time remains almost constant over revolution number. For a more quantitative analysis, the temporal signal widths, obtained by fitting the peaks in Fig. 7 with a Lorentzian profile, are listed in Table 1, along with the widths for 25, 100 and 250 μs loading time. The width at revolution 0 is similar for all loading times, except for 800 μs. Most probably, the small difference arises from space-charge effects in the Paul trap. For short loading times, i.e. small ion numbers, the bunch width increases with higher revolution number as expected from the simulations (Fig. 6b). According to the data, spacecharge effects are insignificant for loading times of less than 50 μs. For longer loading times this dispersion is more and more reduced until the beam width becomes (almost) constant, i.e. independent of the revolution number. This is the case for 800 μs loading time.
This qualitative agreement of the experimental data with the simulations suggests that the underlying EIBT mechanism at play is indeed self-bunching due to space-charge effects. This analysis underlines the strength and versatility of the fluorescence-based detection.

Conclusion and outlook
First measurements using collision-induced fluorescence demonstrate that photo detection offers an excellent diagnostics tool for studies in an electrostatic ion beam trap (EIBT). Among others, it allows the characterization of ion losses as well as the determination of the ion-bunch width and of the ions' time-focus point. These are all crucial parameters in the study of space-charge effects such as self-bunching. The qualitative agreement between simulations of ion trajectories and the data from fluorescence detection shows that space charge has a sizable influence on the time structure of the ion bunch. Upcoming investigations will include quantitative evaluations of the ion number within an ion bunch as well as of various aspects of the photon detection efficiency during the ions' passage through the optical detection region.
However, collisions of ions with residual gas particles lead to undesired ion losses and even with purposely degraded vacuum quality the fluorescence efficiency remains low. Thus, laser-induced excitation will be explored to overcome these disadvantages.
The combined approach of fluorescence detection and simulation of ion trajectories will play an important role in the development and optimization of the Multi Ion Reflection Apparatus for Collinear Laser Spectroscopy (MIRACLS). Although MIRACLS is aiming for the study of a few stored ions of rare radionuclides, for which space-charge effects are expected to be negligible, an accurate understanding of the space-charge limits will be crucial. For instance, "contaminant" ions have to be taken into account as well as reference measurements with stable high-yield isotopes. In this regard, these future studies at MIRACLS are similar to the investigations when Paul traps were first introduced for more sensitive collinear laser spectroscopy [34,35] and space-charge limits for the technique had to be established.
Beyond MIRACLS, fluorescence detection offers additional opportunities to probe and understand the ion dynamics in EIBT devices when used as multi-reflection time-of-flight (MR-ToF) mass separators. Here, the so-called "peak coalescence" [20,36] instead of ion separation in time-of-flight can pose a major challenge. The extension of the present studies can help to advance the technology of MR-ToF mass separation for larger ion samples, which will be beneficial with respect to delivering contamination-free radioactive ion beams to experiments. In addition, fluorescence detection may also be applicable to MR-ToF mass spectrometry.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.