Phase-Imaging Ion-Cyclotron-Resonance technique at the JYFLTRAP double Penning trap mass spectrometer

The Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique has been commissioned at the JYFLTRAP double Penning trap mass spectrometer. This technique is based on projecting the ion motion in the Penning trap onto a position-sensitive multichannel-plate ion detector. Mass measurements of stable 85 Rb +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ ^{+}$\end{document} and 87 Rb +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ ^{+}$\end{document} ions with well-known mass values show that relative uncertainties Δm/m≤7·10-10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \Delta m/m \leq 7\cdot 10^{-10}$\end{document} are possible to reach with the PI-ICR technique at JYFLTRAP. The significant improvement both in resolving power and in precision compared to the conventional Time-of-Flight Ion Cyclotron Resonance technique will enable measurements of close-lying isomeric states and of more exotic isotopes as well as ultra-high precision measurements required, e.g., for neutrino physics. In addition, a new phase-dependent cleaning method based on the differences in the accumulated cyclotron motion phases has been demonstrated with short-lived 127 In +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ ^{+}$\end{document} and 127m In +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ ^{+}$\end{document} ions.


Introduction
Accurate mass values of atoms are essential for various fields of physics [1,2]. For example, nuclear binding energies needed for understanding the evolution of nuclear structure far from stability and for nuclear astrophysics can be derived from atomic masses. Typically these nuclei are short-lived with low production rates requiring fast and accurate methods to determine their masses. In fundamental physics studies, e.g. to test the Standard Model of Particle Physics or for neutrino studies, where accurate mass differences (Q-values) are necessary, a rather highprecision (≤ 10 −9 ) for masses is required [3,4].
Penning-trap mass spectrometry is the most accurate and widely used method for high-precision atomic mass measurements at the moment. Conventionally, Penning trap mass spectrometry of short-lived ions has employed the Time-of-Flight Ion Cyclotron Resonance (ToF-ICR) [5,6] technique to determine ion cyclotron frequency in a strong uniform magnetic field B, where q and m are the charge and the mass of the ion, respectively. Additional three-fold gain in precision can be achieved using the Ramsey method of temporally separated oscillatory fields (Ramsey ToF-ICR) [7][8][9]. The ToF-ICR method can provide a relative mass accuracy of better a e-mail: dmitrii.nesterenko@jyu.fi than 10 −8 [3,10,11] when a production rate of 1-5 ions/s is detected. For ions with lower production rates (< 1 ion/s) or with short half-lives (< 100 ms) precision on the order of 10 −7 has been typically reached [12].
Recently, a novel approach to measure the ion cyclotron frequency (see eq. (1)) has been developed at SHIPTRAP double Penning trap mass spectrometer [13,14] at GSI. This Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique is based on projecting the ion motion in a Penning trap onto a position-sensitive ion detector. It has been shown to offer a 40-fold increase in the resolving power and a fivefold gain for the precision of the cyclotron frequency determination compared to the Ramsey ToF-ICR technique. The PI-ICR technique has been applied for the high-precision determination of mass differences of stable and long-lived nuclides at SHIPTRAP [15][16][17]. In this article, we report on the implementation of the PI-ICR technique at the JYFLTRAP double Penning trap mass spectrometer [18] at the IGISOL facility in the Accelerator Laboratory of the University of Jyväskylä. A measurement of the mass difference of stable 85 Rb and 87 Rb isotopes whose mass values are very well known with precisions of 5 and 6 eV/c 2 [19], respectively, was demonstrated.
A critical prerequisite for high-precision Penning trap mass measurements is that the studied ion sample consists only of ions of interest. Other ions (contaminants) can cause frequency shifts [20] due to their different mass (see eq. (1)), and in the worst case make a mass measurement impossible. A high resolving power is essential not only for mass measurements but also for state-selective decay spectroscopy (for details and examples, see the recent review [2]).
Penning trap setups for short-lived ions typically rely on the sideband cooling technique to remove contaminants [21]. A mass resolving power m/Δm of about 10 5 can be reached with this technique, which is often sufficient for separating isobars. With a buffer-gas free cleaning SIMCO (SImultaneous Magnetron and resonant COnversion) method [22] a resolving power up to 7 · 10 5 can be reached. Also multi-reflection time-of-flight (MR-ToF) separators are available with a mass resolving power of few ×10 5 [23]. Many nuclei have long-living isomeric states that require even higher mass resolving power than these techniques are able to provide. In order to separate states with excitation energies of a few tens of keV, a mass resolving power m/Δm exceeding 10 7 is needed. This is challenging with the present cleaning methods.
The resolving power in the ToF-ICR technique is proportional to the excitation time in the trap and is ultimately limited by the half-life of the studied nuclei. For singly-charged ions of medium-heavy (A ≈ 100) radionuclides with half-lives of about 1 s or longer, a resolving power of about 10 6 (ν c ≈ 1 MHz in a 7-T magnetic field) is reached meaning that only states differing by several hundreds of keV can be separated. A method using an octupolar conversion of ion motion [24,25] can increase the resolving power by an order of magnitude compared to the ToF-ICR method with a conventional quadrupolar conversion. However, it does not improve the precision. Highly charged ions could increase both the precision and the resolving power but that would require an additional step of ion-charge breeding, which imposes strict restrictions on the vacuum in the trap and a number of other challenges [26].
Typically, states separated by ≈ 100 keV or more can be resolved with a Ramsey cleaning technique [27]. It enables contaminant-free mass measurements by separating and removing unwanted ions using an additional cleaning step lasting ≈ 100 ms before the ToF-ICR measurement. Unfortunately, the number of ions the Ramsey cleaning technique can handle has been found to be quite small. If there are a lot of contaminant ions present, the number of ions entering the trap has to be limited, and thus the overall transmission is reduced.
In this article, we present a new fast cleaning method (see sect. 2.3) which can offer a much higher resolving power compared to previous techniques. This phasedependent cleaning technique is demonstrated by using the separation of the ground and isomeric states of 127 In as an example in sect. 3.4.

Ion motion in a Penning trap
An ion is confined in a Penning trap by the superposition of a strong homogeneous magnetic field B = B z e z and a quadrupolar electrostatic potential. In cylindrical coordinates (z, ρ), the potential has the form where z and ρ = x 2 + y 2 are the axial and radial distance from the trap center, respectively, U 0 is the trap potential (the potential difference between the ring and the endcap electrodes [18]) and d is the characteristic dimension of the trap defined by the trap geometry. For ideal hyperbolic traps d = 2z 2 0 + r 2 0 /2, where 2z 0 is the distance between endcap electrodes and r 0 is the inner radius of the ring electrode [28]. In reality, z 0 and r 0 differ (especially for a cylindrical trap geometry [29]) from the ideal case.
The trajectory of an ion in the trap is a superposition of three independent harmonic eigenmotions: axial motion at frequency ν z along the magnetic field lines and two radial motions perpendicular to the magnetic field lines. Of the radial motions, the magnetron motion with a frequency ν − is almost mass-independent whereas the cyclotron motion's frequency, although reduced to the modified cyclotron frequency ν + , remains mass-dependent. In an ideal Penning trap, the sum of the two radial motion frequencies is the ion cyclotron frequency ν c Even with small misalignments of the magnetic and electric fields and ellipticity of the trapping potential, eq. (3) is precise enough for mass measurements with current Penning trap techniques for short-lived ions [30]. The hierarchy of the frequencies is ν c ≈ ν + ν z ν − [28]. The modified cyclotron frequency, the magnetron frequency and the axial frequency for 133 Cs + ions at the JYFLTRAP (see sect. 3.1) are ν + ≈ 807 kHz, ν − ≈ 1.7 kHz and ν z ≈ 52 kHz.
The operation of a Penning trap is based on the manipulation of the ion eigenmotions through the application of radiofrequency (RF) fields in different configurations. A dipolar excitation at an eigenfrequency of the ion (ν + , ν − , ν z ) can be used to excite the corresponding ion motion. An RF quadrupolar field at the cyclotron frequency ν c can convert one radial motion to the other [6]. The ring electrodes of JYFLTRAP are eight-fold segmented [18], and thus, dipolar, quadrupolar and even octupolar RF fields can be applied.

Principle of the Phase-Imaging Ion-Cyclotron-Resonance technique
A detailed description of the PI-ICR technique is given in ref. [14]. There are two ways to determine ν c of eq. (3); either by measuring both magnetron and modified cyclotron frequencies independently (see sect. 2.2.1) or quasi-simultaneously (see sect. 2.2.2).
In the following, we denote the values related to the magnetron and cyclotron motion by the indexes "−" and "+", respectively. With the word "radial", we will mean either a "magnetron motion" or a "cyclotron motion"; in this case the indexes are omitted.

Radial motion frequency measurement
The principle of the measurement is illustrated in fig. 1. After buffer-gas cooling [21] in the preparation trap, the ions are injected into the center of the measurement trap (see sect. 3.1) and have a spatial distribution with FWHM = 2Δr (position 1 in fig. 1). Then the ions are excited with a dipolar pulse at the radial frequency ν, and they reach a certain radius of motion (position 2 in fig. 1). After free revolution for a duration t the ion motion accumulates a phase ϕ + 2πn = 2πνt, where n is the full number of revolutions (position 3 in fig. 1). Here the positions 1, 2 and 3 are the trap center, the reference phase and the final phase, respectively.
In reality, ions gain initial magnetron motion due to misalignments between the magnetic field and the trap axis and also some axial motion after the injection into the measurement trap. Fortunately both of these are coherent and thus amplitudes of these motions can be reduced via dipolar RF pulses with the matched amplitudes and phases at the corresponding motion frequencies.
For simplicity, the electric potential center of the traps is set as the origin, (0, 0) in the following. The phase angle ϕ is deduced from the coordinates of the reference phase (x i , y i ) and the final phase (x f , y f ). The radial frequency ν and its uncertainty δν can be calculated as where ϕ = arccos(s) for 0 ≤ ϕ ≤ π and ϕ = 2π − arccos(s) for π ≤ ϕ ≤ 2π, and s ≡ cos(ϕ) = (x i x f + The direction of the radial motion and, correspondingly, the correct value for the angle can be determined from the projection image. A quick measurement of the radial frequency with a modest precision (with a shorter phase accumulation time than for the main measurement) allows to get the integer number of revolutions n in eq. (4). It is enough to perform such measurements once per several days, since the typical daily fluctuations of the magnetron and modified cyclotron frequencies do not exceed 100 mHz at JYFLTRAP. The ion radial motion is projected onto a positionsensitive ion detector (microchannel plate detector with a delay line anode) placed on the axis of the trap outside the magnet (see fig. 3) to determine the accumulated phase and deduce the radial frequency. The ideal projection magnifies the image on the detector relative to the ion motion in the trap and preserves the angle ϕ.
In order to determine the angle ϕ and the corresponding radial frequency, coordinates for the trap center, the reference phase and the final phase on the detector have to be measured.
After the injection of the ions into the measurement trap and reducing of the residual magnetron and axial motions, the ions are extracted from the trap and projected onto the detector to determine the coordinates of the trap center. The stability of the trap center position depends on the stability of electric potentials both on the trap electrodes and those in the drift section after the magnet. Usually, it is enough to measure the center once a day. To find the position of the reference phase, the ions are extracted from the trap right after applying the dipolar RF pulse at radial frequency ν. Extraction of the ions after a fixed time t later than for the reference phase allows the projection of the final phase to be measured (see fig. 1).
The projection of the cyclotron motion phase requires an additional step. Since the width of the time-of-flight distribution of ions between the trap and the detector is comparable with the period of the cyclotron motion (both about 1 μs for 133 Cs + , as example), a direct projection would lead to a smearing of the ion spot on the detector (see fig. 5(b)). Therefore, before extracting the ions, the fast cyclotron motion has to be converted to the slow magnetron motion by applying a short radial quadrupolar pulse at the cyclotron frequency ν c of the ions. The conversion preserves the modulus of the angle between the reference and the final phase of the corresponding motions and flips the sign of the angle [14,31]. Thus, the ion cyclotron motion and the movement of the image on the detector have opposite angular directions (in case of JYFLTRAP the image of the magnetron motion rotates clockwise and the image of the cyclotron motion rotates counterclockwise on the detector looking downstream in the beamline).

Cyclotron frequency measurement
The cyclotron frequency ν c can be determined directly by applying two excitation patterns alternately ( fig. 2). The patterns are identical except for the starting time of the quadrupole excitation. First, like in radial motion frequency measurement, the cooled and centered ions are transferred from the first trap to the center of the measurement trap (step 1), where the coherent component of their magnetron and axial motions are reduced via dipolar RF pulses at the corresponding motion frequencies (steps 2a and 2b). Then, the cyclotron motion of the ions is excited via a dipolar RF pulse at the frequency ν + and the ions acquire a certain radius of motion (step 3). In step 4 of pattern 1 a quadrupolar RF pulse at the cyclotron frequency ν c is applied immediately after the ν + -pulse to convert the cyclotron motion to the magnetron motion. After the conversion, ions rotate freely and the magnetron motion accumulates total magnetron phase where ϕ − ∈ [0, 2π) is the final phase and n − the integer number of revolutions after time t. Subsequently, the ions are ejected from the trap and their position is projected onto the position-sensitive ion detector (step 5). Pattern 2 differs from pattern 1 only in step 4. The quadrupolar conversion pulse at the cyclotron frequency ν c in pattern 2 is applied after the time t from the ν + -pulse, allowing ion motion to accumulate total cyclotron motion phase in the same way as for magnetron motion phase. After conversion, the ions are projected onto the detector giving the image of the cyclotron motion phase. As noted earlier, the conversion preserves the modulus of the angle between the reference and the final phase and flips the sign of the angle [14,31]. Thus, the polar angles of the spot position on the detector are α − = α 0 − ϕ − and α + = α 0 + ϕ + for the accumulated magnetron and cyclotron motion phases, respectively, where α 0 is the polar angle of the initial phase. Hence, the angle between the positions of two phase images is α c = α + − α − and the cyclotron frequency ν c is In order to eliminate the error of the conversion of radial motions, the phase accumulation time must be a multiple of a half the period of the cyclotron motion, i.e., 2πν c t = πn [14,31]. The durations of the excitation pulses can be chosen as short as the period of the corresponding RF excitation frequency. The main reason for short duration is to save measurement time but short pulse also ensures equally strong excitation in large frequency band. In practice they are limited by the available maximum amplitudes of the function generators (10 V in case of JYFLTRAP). A typical RF pulse duration at JYFLTRAP is 1 ms, which covers a 1 kHz band around the applied excitation frequency.

Phase-dependent cleaning method
The resolving power of the ToF-ICR method is defined by Fourier transformation of the excitation time profile and limited by the excitation time t exc or the observation time of the cyclotron motion [32]. The line width of the Fouriertransformation in the frequency domain Δν c (FWHM) is inversely proportional to the excitation time t exc . The resolving power obtained with the ToF-ICR method and a single quadrupolar excitation (conversion) pulse [33,34] is Since the magnetron frequency depends only very weakly on the mass of the ion, the resolving power of the PI-ICR method is defined by the ability to resolve the phase difference of cyclotron motions between two ion species after accumulating for a time t (see fig. 1) For a typical in-trap radius spread Δr + = 80 μm and excitation radius r + = 1 mm, the PI-ICR method provides around 40 times better resolving power than the ToF-ICR method. The following phase-dependent cleaning method is suitable for preparing isomerically pure beams for posttrap decay spectroscopy. After the mass-selective buffergas cooling [21] procedure in the preparation trap that provides a resolution of a few tens of Hz for Δν c (corresponds to ∼ 10 5 in mass resolving power for singly charged A = 100 ions in a 7 T field), ions are injected to the center of the measurement trap. A short dipolar RF pulse (about 1 ms) at the modified cyclotron frequency ν + will excite any remaining ions to a certain radius r + since the FWHM of the excitation with 1 ms duration is about 1 kHz. The ion motion accumulates the phase difference Δϕ for a time t, which is chosen to be long enough to resolve the ions of interest and the contaminants. Then, a short quadrupolar RF pulse at the cyclotron frequency ν c is applied just before the extraction of ions to convert the cyclotron motion to magnetron motion. Ions leave the trap and are projected onto the position-sensitive ion detector. The image of the ion motion projection allows the ions of interest and contaminant ions to be distinguished. By positioning movable and adjustable slits in front of the detector according to the position of the ions of interest on the detector the contaminants can be removed. Then, after removing the detector from the ion's way, a cleaned beam of the ions of interest can be transported to the experiment setups further downstream.
If the accumulated phase difference Δϕ between the ions of interest and contaminants is about π, the cleaning method can be performed without the slits in front of the detector. One more dipolar RF excitation step at the magnetron frequency ν − before the extraction of ions is needed. The phase and the amplitude need to be matched so that the ions of interest will move to the trap center. Since the contamination ions are on the opposite phase, they will move even further out and finally acquire magnetron radius 2r + . If the radius of the contaminants is large enough, they will be lost during the transportation from the trap, while the centered ions of interest will survive.
A similar idea for the cleaning procedure, based on the mass-selective ion centering, was described in [35]. The authors in [35] suggested to use a pulsed static dipolar excitation to center the ions of interest, in contrast to the magnetron excitation pulse presented in this work.

The JYFLTRAP setup
The JYFLTRAP double Penning-trap setup is extensively used for high-resolution beam purification and precise mass measurements of stable and radioactive ions [18]. The JYFLTRAP setup receives on-line beams from the Ion Guide Isotope Separator On-Line (IGISOL) facility [36]. The radioactive ions, produced either by fission or fusion reactions, are stopped in helium gas, extracted by using electric fields and a helium gas jet via a sextupole ion guide [37] to high-vacuum, where the ions are accelerated to 30z keV energy (z is the charge state of the ions). Behind a 55 • dipole magnet (M/ΔM ≈ 500), ions with the selected mass-to-charge ratio A/q are injected into a gas-filled radio-frequency quadrupole (RFQ) [38], where they are cooled and bunched. For offline measurements a surface-ionization ion source or laser-ablation ion source can be mounted in front of the RFQ cooler.
The ion bunches from the RFQ are transferred to the cylindrical Penning traps placed inside a 7 T superconducting magnet (fig. 3). In the first, gas-filled (10 −4 -10 −5 mbar of helium), preparation trap the ions are cooled, centered and purified via a mass-selective buffer gas cooling technique [21]. The ions are transferred through a diaphragm 1.5 mm in diameter between the traps into the second measurement trap operating under ultrahigh vacuum (≤ 10 −7 mbar, estimated from vacuum system conductances), where the masses of ions can be measured or high-precision cleaning procedures applied. The RFQ is placed on a 30 kV high voltage platform, which defines the electric potential the ions leave the RFQ. The Penning traps are on a high voltage platform that is 54 V higher than the RFQ platform. This way it is enough to use only negative DC power supplies for trap electrodes. No pulsed drift tubes [39,40] to change ions' electric potential are used in the whole setup. The MCP detector is located outside the strong magnetic field at the ground potential and thus the extracted ions will hit the detector with 30z keV of energy. The magnetic field in the traps and in the region of the detector is about 7 T and 45 mT, respectively.
The extraction part of the JYFLTRAP was modified to better serve the PI-ICR technique (see fig. 3). The inner diameter of the last two extraction electrodes and the ground electrode was increased from 32 mm up to 52 mm. A position-sensitive MCP ion detector with a delay-line anode (DLD40) from RoentDek GmbH [41] is placed on a feedthrough at a distance of about 923 mm from the center of the second trap. The detector is fully movable in the plane perpendicular to the beam and can also be fully retracted from the beam enabling the beam delivery to experiments further downstream. An einzel lens for transporting the ion beam towards post-trap decay spectroscopy setups is placed on the same feedthrough.
The voltages applied to the electrodes in the measurement trap and the extraction electrodes used for PI-ICR technique are shown in table 1. The procedure of the optimization of voltages on the correction trap electrodes is described in sect. 3.2. The first trap has the same trap potential U 0 = 100 V as the second trap. Figure 4 shows trajectories of ions leaving the second trap with an initial magnetron radius r − = 1 mm simulated using the SIMION program [42]. Potentials on the drift and extraction electrodes were set to −500 V (all voltages except the ground electrode and detector are relative to the trap high voltage platform level). Ions follow the diverging magnetic field lines in the region of constant electric potential. Then, near the ground electrode they have an intermediate focus point due to the transition from high voltage to the ground potential, thereafter the ion beam (that now has 30z keV of energy) diverges again. The projection of ions linearly magnifies the image on the detector. The magnification of the image on the detector depends on the ratio of the magnetic field in the trap to the magnetic field in the detector region, the drift potential (potentials on the drift and extraction electrodes) and the distance of the detector from the ground electrode. In our case the magnification factor is about 10.2. Measured projections of ion radial motions are shown in fig. 5.

Quadrupole electrostatic potential optimizations with simulations and PI-ICR technique
Imperfections of the electrostatic field, i.e., deviation of the trapping potential from the quadratic form (eq. (2)), result in amplitude-dependent eigenfrequency shifts in a Penning trap. The purely quadratic potential of eq. (2) can be expanded by adding higher order multipole terms. With the addition of octupolar and dodecapolar terms, characterized by the coefficients C 4 and C 6 , respectively, the trapping potential is expressed as [43] V The geometry of the JYFLTRAP Penning trap electrodes was simulated in COMSOL [44]. The contribution of each electrode to the electric field distribution in the  radial plane along the z = 0 line was determined by setting 1 V on the electrode while keeping the others at zero. The superposition of such contributions multiplied by the voltage on each electrode forms the final trap potential. Firstly, the voltage between the endcap and the ring electrodes was fixed to 100 V. Then, the voltages on the trap electrodes Correction 1 and Correction 2 were tuned to minimize the coefficients C 4 and C 6 of eq. (10). The final values for the voltages on the correction electrodes are shown in table 1.
The harmonicity of the trap can be checked and finetuned further with the PI-ICR technique. If the trapping potential is purely quadratic and no higher order components are present, the eigenfrequencies of the ions do not depend on motional amplitudes. This can be observed by exciting the ions to different amplitudes and observing the extracted motional phase. If the frequency has no amplitude dependence, i.e., the motion is harmonic, the extracted ions should form a straight line on the detector. The longer the accumulation time, the higher the sensitivity to the imperfections of the electric field. The magnetron motion is the most convenient to use because the phase of the fast cyclotron motion will get smeared due to the collisions of ions with the molecules of residual gas in the measurement trap. The shift of the magnetron frequency in the presence of the octupolar and dodecapolar components in the trapping potential is [43] where r − , r + and z are the amplitude of magnetron motion, cyclotron motion and axial motion, respectively; C(C 4 , C 6 ) is a constant, which does not depend on r − .  Figure 6 shows the phase spots for different magnetron radii after a phase accumulation time of 1 s. A measurement with r 0 = 1.03 mm was taken as the reference. The fits for this dependence ( fig. 6(b)) with the polynomials a + br 2 − and a + br 2 − + dr 4 − showed that coefficients b and d are compatible with zero. The reduced χ 2 /n for the fit with the constant function is 1.3 and even smaller than for polynomials. The estimated upper limit for the octupolar coefficient is |C 4 | < 7 · 10 −4 .

Mass measurements of stable ions with the PI-ICR technique
The mass difference between the isotopes 87 Rb and 85 Rb was determined by measuring the cyclotron frequency ra- tio R = ν c ( 85 Rb + )/ν c ( 87 Rb + ) with the PI-ICR scheme described in sect. 2.2.2. The 85 Rb + and 87 Rb + ions were produced with the surface-ionization ion source located in front of the RFQ cooler. The continuous ion beam from the source was cooled and bunched with the RFQ and transferred into the preparation trap, where the ions were cooled, centered and mass-separated. The cyclotron frequency measurements were performed in the measurement trap with a 200 ms phase accumulation time and alternately for 85 Rb + and 87 Rb + by changing the isotope every 5 minutes. The length of the measurement cycle was about 485 ms for pattern 1 and 2, that were applied alternately. During a 5 min long measurement of the cyclotron frequency, about 600 ions were collected for both the magnetron and the cyclotron phase images. A two-dimensional scan of the start time of the dipolar excitation pulse at frequency ν + over a magnetron period (≈ 600 μs) and the start time of the extraction pulse over a cyclotron period (≈ 0.8 μs) was carried out (see pulse scheme in fig. 2) to eliminate the shifts due to possible residual magnetron motion left after the magnetron amplitude reducing dipolar excitation and residual cyclotron motion after the conversion pulse. To reduce the errors due to possible distortions of ion-motion projection onto the detector the positions of the two phase images were chosen in such a way that the angles |α c | ≤ 2.5 • during the measurements.
Count-rate analysis [45] for the determined cyclotron frequencies was performed to study ion-ion interactions. The data were divided into five groups according to the detected ions in bunches. No dependence of the frequency ratio on the number of detected ions were observed and only the data with up to 5 ions/bunch were taken into account. For a single frequency ratio measurement, the cyclotron frequency of 85 Rb + was linearly interpolated to the measurement time of 87 Rb + between the two 85 Rb + measurements. The nonlinear drift of the magnetic field between two neighboring frequency measurements was negligible compared with the statistical errors. A typical distribution of 85 Rb + ions on the detector for a single cyclotron frequency measurement is shown in fig. 7.
During two measurement days 58 cyclotron frequency ratios R = ν c ( 85 Rb + )/ν c ( 87 Rb + ) were measured ( fig. 8). The weighted mean ratio R = 1.023523278677(654) stat results in a Q-value (m( 87 Rb + ) − m( 85 Rb + ))c 2 = 1860557.540(52) keV. The Birge ratio [46] was 0.91, which indicates that the statistical errors for the ratios R are slightly overestimated. The larger internal uncertainty was used for the weighted mean of the frequency ratios. The received cyclotron frequency ratio R is in a perfect agreement with the Atomic Mass Evaluation 2016 (AME2016) value R AM E = 1.023523278693(96) [19]. The difference (−2 ± 66) · 10 −11 for the frequency ratio or 1(52) eV for the Q-value is comparable with zero.
The cyclotron frequency ratios were also analyzed using a different approach. The frequencies in time t were simultaneously fitted with fifth-order polynomials where R day is the cyclotron frequency ratio and the coefficients a i are the same for both polynomials (see fig. 9). The weighted mean ratio for two days R = 1.023523278629(662) stat is similar to the frequency ratio received in the interpolation method and differs from it by (−5 ± 90) · 10 −11 . The main systematic uncertainties were estimated. The maximum of possible cyclotron frequency ratio shift Fig. 9. The cyclotron frequency ratios R day for each day were obtained by fitting fifth-order polynomials simultaneously to the 85 Rb + and 87 Rb + frequency points (see text for details). The reduced χ 2 /n was 0.81 and 0.77 for the first and the second day, respectively. There were 5 days between the 1st and the 2nd day of the measurements.   11. Image of ion distribution for the ground and first isomeric states of 127 In + on the position-sensitive ion detector. The big circle with a ∼ 20 mm radius depicts (roughly) the outer edge of the position sensitive ion detector. (a) The ions were extracted from the trap after first accumulating the phase of the cyclotron motion for 160 ms and conversion to magnetron motion. The amplitude of the 1 ms pulse for the ν +-excitation was A+ = 0.9 V and Ac = 3 V for the 2 ms long conversion pulse. (b) As (a) with additional dipolar excitation pulse at the magnetron frequency (amplitude A − = 0.85 V, applied for one magnetron period (∼ 600 μs)) before the extraction. 127 In + ions move to the center while 127m In + ions moves further out. (c) and (d) The same images as in (a) and (b), but with the higher amplitudes for ν +-and ν−-excitations (A+ = 1.2 V for 1 ms, A − = 1.13 V for one magnetron period). Since the two states do not exactly have 1π phase difference, the spots in (b) and (d) do not move exactly to the same direction.
due to electrostatic imperfections of the trapping potential, that lead to the cyclotron frequency shifts [43] Δν c = −C 4 3 2d 2 was estimated as |ΔR elec | ≤ 10 −10 , by using the upper limit for the coefficient C 4 (sect. 3.2). For the cyclotron frequency ratio of mass doublet the ratio shift |ΔR elec | would be significantly less, because the frequencies (and their shifts) are very similar in this case. The shift due to distortions of ion-motion projection onto the detector [14] |ΔR orb | was also below 10 −10 , since the angles α c were close to zero. There is an uncertainty related to the drift of the image of the trap center on the detector, since we determined its position only before and after several hours of measurements of the magnetron-motion and cyclotronmotion phases. With the typical drift velocity of the center's coordinate of the image on the detector, which does not exceed 25 μm/h at JYFLTRAP, the frequency ratio shift |ΔR cent | is less than 10 −10 . Comprehensive systematic studies are under way and results of these will be published in the near future.

Online demonstration of phase-dependent cleaning method
The phase-dependent cleaning method (described in sect. 2.3) was tested with radioactive 127 In + ions produced in the fission reaction of U with a 30 MeV proton beam. The ions of the ground and the first isomeric state, 127 In + (T 1/2 = 1.09(1) s [47]) and 127m In + (T 1/2 = 3.67(4) s, E = 408.9(3) keV [47]), have a cyclotron frequency difference of about 3 Hz. This is a difference large enough that the states can also be isolated with the Ramsey cleaning method [27]. Here, the Ramsey cleaning method was used as an independent means to identify the states. The scan of dipolar excitation frequency (see fig. 10) shows separated peaks for 127 In + and 127m In + in the region of their modified cyclotron frequencies. One of the two states can be chosen by setting the appropriate frequency of the dipolar cleaning excitation. Thus, we can keep either the ground or the isomeric state using the Ramsey cleaning technique, or study both states when no Ramsey cleaning is applied. Firstly, both the ground and the first isomeric states of 127 In + were injected into the measurement trap. A 1 ms long dipolar excitation pulse at ν + frequency was applied and the ions were left for ≈ 160 ms to obtain a phase difference of about π. Finally, a 2 ms long quadrupolar conversion pulse at ν c frequency was applied to convert the cyclotron motion to magnetron motion. The two states are clearly separated on the position-sensitive ion detector (see fig. 11(a)). When using Ramsey cleaning to remove the ground state ions, only the right spot remains on the detector; and when the isomer is removed, the left spot remains. Thus, as it was expected from fig. 10, the spot with the higher number of detected ions corresponds to the more populated ground state.
After the two states were separated to have opposite motional phases, an additional dipolar excitation pulse at the magnetron frequency ν − was applied to move the ground state ions of 127 In + towards the trap center ( fig. 11(b)). Since the amplitude and the phase of the dipolar pulse was chosen so that the ground state ions are centered while the isomeric state ions, having opposite motional phase with respect to the dipolar field, move further away. When contaminants and the ion-of-interest have a phase difference of π, the contaminants can be driven to orbit with twice the radius. If the contaminants are driven to large enough orbit, they will be lost upon extraction. In the case shown in fig. 11(d), the ions of 127m In + are placed about 23 mm away from the center of the detector, a distance that is larger than the radius of the detector. When the detector is removed and the einzel lens with a 16 mm inner radius is put in its place, the contaminants will be lost.

Conclusion
The Phase-Imaging Ion-Cyclotron-Resonance technique has been successfully commissioned and implemented at JYFLTRAP. The performance was tested with the stable ions 133 Cs + , 85 Rb + and 87 Rb + using a surface ionization ion source. The voltages on the Penning trap electrodes were optimized to reduce higher order terms in the trapping potential and minimize related systematic errors. The accuracy of the PI-ICR technique was tested with 85 Rb + and 87 Rb + ions. The measured cyclotron frequency ratio is in an agreement with the AME2016 value [19]. Thus, even at such a high level of accuracy of around 6.4 · 10 −10 , we do not observe systematic shifts in the PI-ICR mass measurement, even for ions which are not from the same mass doublet.
A new phase-dependent cleaning method was demonstrated with short-lived 127 In + ions. The ground and first isomeric state of 127 In were separated by accumulating the phase difference of about π of cyclotron motion in the trap. An additional excitation pulse at the magnetron frequency (with proper phase and amplitude) centered the ions of one state while the ions of the other state gained even bigger radius. If this is chosen to be bigger than the inner radius of the einzel lens, the contaminants will be lost after the extraction from the trap. The installation of adjustable slits in front of the position sensitive ion detector will enable cleaning with the accumulated phase difference smaller than π. This increases the resolving power or, alternatively, decreases the time needed for the cleaning process.