Hyperfine Interact (2011) 199:21–27 DOI 10.1007/s10751-011-0297-5

Temperature measurement of 6 He+ ions confined in a transparent Paul trap X. Fléchard · G. Ban · D. Durand · E. Liénard · F. Mauger · A. Méry · O. Naviliat-Cuncic · D. Rodríguez · P. Velten

Published online: 19 April 2011 © Springer Science+Business Media B.V. 2011

Abstract The LPCTrap setup is a transparent Paul trap dedicated to the measurement of the β–ν correlation coefficient aβν in the β decay of trapped radioactive nuclides. In a first experiment, the system has been used to record ∼105 coincidences between the β particles and recoiling ions emitted from the decay of 6 He+ ions. The analysis of the collected data has already shown that the size of the 6 He+ ion cloud confined in the Paul trap is a critical parameter, potentially limiting the accuracy on the aβν measurement. We report here the precise determination of the trapped ion cloud temperature and size. This was performed by extracting the trapped ions toward a position sensitive micro channel plate detector at different phases of the RF driving field. We find a temperature Texp = 0.107(7) eV, consistent with the temperature values inferred using two other observables but 20% higher than the temperature Tsim = 0.09 eV predicted by realistic simulations of the ions interacting with the H2 buffer gas. Keywords Ion trapping and ion cooling techniques · β–ν correlations

1 Introduction Using the low energy radioactive beam line of SPIRAL at GANIL for ion production and a novel transparent Paul trap as a confinement device [1], the LPCTrap setup

X. Fléchard (B) · G. Ban · D. Durand · E. Liénard · F. Mauger · O. Naviliat-Cuncic · P. Velten LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3-ENSI, Caen, France e-mail: [email protected] A. Méry CIMAP, CEA/CNRS/ENSICAEN, Université de Caen, Caen, France D. Rodríguez Departamento de Física Atómica, Molecular y Nuclear, Universitad de Granada, 18071, Granada, Spain

22

X. Fléchard et al.

has been designed to measure, with an unprecedented precision, the β–ν angular correlation coefficient aβν in the 6 He+ beta decay. With the radioactive 6 He+ ions stored nearly at rest in a small volume, defined by the driving RF field of the transparent Paul Trap, the decay products can be detected in coincidence. The value of the correlation parameter aβν can then be inferred from the time of flight of the recoiling ion. In a first experiment, ∼105 decay coincidences between the beta particles and the recoiling 6 Li2+ ions have been measured, yielding a relative statistical uncertainty (aβν /aβν )stat of about 2% [2]. The complete analysis of the recorded data requires accounting for many effects like the background contribution, the response functions of the detectors, the influence of the RF field, and the temperature of the ions in the trap. A preliminary analysis has shown that the extracted value of the parameter aβν depends strongly on the ion cloud temperature. In order to limit the contribution of the systematic error at the 2% level, the cloud temperature must be determined with a precision smaller than 6.5%. Under these conditions, it is not anymore possible to only rely on the temperature value given by realistic simulations of the ion motion in a cooling buffer gas, and independent measurements have to be performed. Similar experiments dedicated to correlation measurements, but using magneto-optical traps, allow extracting the size of the ion cloud by imaging the fluorescence of the trapped atoms using a CCD camera [3, 4]. Such a direct measurement cannot be performed with trapped ions and alternative methods have to be used. These methods and the results will be detailed below after a brief description of the β–ν correlation experiment.

2 The β–ν correlation measurement 2.1 Experimental setup The LPCTrap setup has already been described in detail [1, 2] and only the main features will be given here. The 6 He+ ion beam produced at GANIL by the SPIRAL ion source is delivered to the LPCTrap at 10 keV through the LIRAT low energy beam-line. The incident ions are first decelerated, cooled, and bunched, using a RFQ buncher filled with H2 buffer gas [5] to reduce the beam emittance and time structure. The ion bunches are then extracted from the RFQ at a repetition rate of 10 Hz using a pulsed cavity, and are injected in the transparent Paul Trap. During the first 50 ms of the trapping cycle, the trapped ions are further cooled down by elastic collisions with H2 buffer gas at low pressure. The Paul trap, shown in Fig. 1 in the middle of the trapping chamber, is made of six stainless steel rings. This geometry allows the application of suitable voltages for an efficient injection and for the extraction of the ions towards a micro-channel plate position sensitive detector (MCPPSD) dedicated to the ion cloud monitoring. For the correlation measurement, a telescope for the β particles and a second MCPPSD are located 10 cm away from the trap in a back to back geometry. The β telescope comprises a 60 × 60 mm2 and 300 μm thick doubled sided strip silicon detector for position readout, followed by a plastic scintillator to measure the energy of the β particles. This detector provides the trigger of an event and generates a start signal for the recoil ion time of flight (TOF) from the trap center to the MCPPSD. For each coincidence event, the following parameters are recorded:

Temperature measurement of 6 He+ ions confined in a transparent Paul trap

23

R6 R4 R2

R5 R3 R1

Paul Trap details MCPPSD

MCPPSD Fig. 1 Sectional layout of the storage and detection system (see text). An enlarged view of the Paul trap is shown on the right. The rings are labelled R1 to R6

the positions of both particles, the recoil ion TOF, and the β particle energy. The combination of these observables allows reconstructing the rest mass of the antineutrino, which provides a useful mean to identify the sources of background and to control instrumental effects. 2.2 Data analysis The data analysis is based on a comparison between the experimental TOF spectrum and those obtained for two sets of Monte Carlo (MC) simulations performed with pure axial (aβν = −1/3) and pure tensor (aβν = +1/3) couplings. The experimental data are in a first step corrected for the background contributions: accidental coincidence events called “accidentals”, decay events from 6 He atoms filling the detection chamber volume (“out-trap events”), and decay events with β scattering on the trap and detector structures (“scattered events”). These contributions are also generated with MC simulations using the Standard Model value aβν = −1/3. The accidental and out-trap contributions are normalized to the experimental data using the TOF spectrum while the scattered events contribution is normalized using GEANT4 scattering yields. After this background correction, aβν can be deduced from an adjustment of the experimental TOF spectrum with a linear combination of the two sets of simulated decay events obtained for a pure axial and a pure tensor couplings (Fig. 2, left). With the available recorded events, the fit shown in Fig. 2 yields a statistical relative uncertainty of 2.1% [6]. The final step of the data analysis is the determination of the systematic uncertainties. These can be due to many sources like the detectors position and response

24

X. Fléchard et al. 3000

-0.28 -0.30

2000

aβν

Counts

-0.32 -0.34

1000 -0.36 -0.38 0

500

600

700

800

900

TOF (ns)

1000

0.08

0.10

0.12

0.14

0.16

Temperature (eV)

Fig. 2 Left: Corrected experimental TOF spectrum (dark line) and simulated TOF spectra for pure tensor and pure axial couplings (resp. dashed and solid gray lines). Right: aβν fit result versus cloud temperature (black dots) adjusted with a second order polynomial curve

functions, the background correction, the trap RF field effect on the ion trajectories, the shake-off ionization of the recoil ion, and the temperature of the trapped ion cloud in the MC simulations [6]. We found evidences for a strong correlation between the cloud temperature and the aβν value deduced from our fitting procedure (Fig. 2, right). As a consequence, the cloud temperature has to be known with a relative precision better than 6.5% to limit the relative systematic uncertainty below 2%.

3 Determination of the temperature 3.1 Ion cloud simulations To perform accurate MC simulations of the β decay considering pure tensor and pure axial couplings, a realistic modelling of the ion motion in the Paul trap RF field is required. For this purpose, simulations of the ion motion in the RF field are performed using the SIMION8 software package. The Paul trap electrodes and the surrounding elements are included with their precise geometry. The collisions between the trapped ions and the H2 buffer gas molecules are also described at the microscopic level using interaction potentials as realistic as possible. The latter were validated with experimental mobility data and diffusivities in a previous work dedicated to the development of the RFQ buncher [7]. After thermalization of the ions in the Paul trap, the three dimensional distributions in space and velocity as a function of the RF phase are extracted from the simulation of the ion motion. Averaging over a full RF period, a mean temperature Tsim = 0.09 eV has been found. The characteristics of the simulated ion cloud can then be directly injected as an input in the β decay MC simulations. To mimic a cloud temperature slightly different than the one predicted by the SIMION simulations, we simply multiply the reduced mean square (RMS) of the cloud space and velocity distributions by an arbitrary scaling factor Tcoef . The cloud temperature has a quadratic dependency on the scaling factor Tcoef which is used along the following sections as a temperature parameter.

Temperature measurement of 6 He+ ions confined in a transparent Paul trap

200

VR3

200

0

2.45

2.50

100

0

2.55

2.60

TOF (μs)

300

Counts

Voltage (V)

400

VR1-R2

300

25

200 100 0 -20

-10

ϕ1 ϕ2ϕ3

-100 0

1

0

10

20

10

20

Y (mm)

300 200

2

Time (μs)

3

4

100 0 -20

-10

0

X (mm)

Fig. 3 Left: Time sequence and applied voltages for the ion cloud extraction. The three RF phases chosen for the measurement are shown by dotted lines. Right: TOF and positions spectra recorded by the ion cloud monitor (gray lines) and simulated for two different cloud temperatures (dotted black lines for Tcoef = 1.1 and solid black lines for Tcoef = 1.3), for the RF extraction phase φ2

3.2 Direct measurement The ion cloud temperature measurement is performed using an off-line source providing a 10 keV 6 Li+ ion beam. About 103 ions per bunch are first trapped and cooled down during 75 ms. Then, at a chosen RF phase, the trap RF voltage applied to the rings R1 and R2 are switched off while an extraction voltage of 300 V is simultaneously applied to the ring R3 (Fig. 3, left). The extracted ions are collected by the ion cloud monitor MCPPSD (see Fig. 1) for TOF and position recording. Several possible issues had first to be taken into consideration. We checked that the 75 ms cooling time was long enough to reach the thermal equilibrium, and that no effect due to space charge could affect the measurement in the present density regime. To suppress any deformation in the TOF or position spectra due to the detector dead time, two attenuation grids were also placed in front of the detector, reducing by a factor 500 the number of detected ions. This extraction scheme has been applied for three different RF phases φ1−3 , providing for each phase the three spectra shown in the Fig. 3 (right panel). From all the spectra, a cloud temperature measurement is obtained by comparing the experimental data with a set of simulations. In the simulations, we use the ion cloud characteristics obtained by the method described in Section 3.1, and adjust the temperature by varying the Tcoef parameter. Then, the extraction of the ion cloud is simulated with SIMION8 using the precise geometry of the setup and the applied voltages previously recorded with an oscilloscope probe. Typical positions and TOF spectra obtained with the simulations are shown in the Fig. 3. The RMS of these spectra is the most sensitive observable to the cloud temperature, and depends linearly of the Tcoef values used in the simulations. The adjustments of the simulated RMS to the experimental ones provide the Tcoef values displayed in Fig. 4.

26

X. Fléchard et al.

Fig. 4 Tcoef values obtained for the experimental TOF, X position, and Y position spectra recorded at RF extraction phases φ1 , φ2 , and φ3 . The weighted mean value < Tcoef >= 1.092 (37) is given by the horizontal line

1.4

Tcoef

1.2

1.0

0.8 TOF1 TOF2 TOF3

X1

X2

X3

Y1

Y2

Y3

measurement

Exp. data simulation (Tcoef =0.9)

8000

simulation (Tcoef =1.3)

Exp. data simulation (Tcoef =0.9)

2000

simulation (Tcoef =1.3)

1500

counts

counts

10000

6000 4000

500

2000 0

1000

-1

0

0 460

1

480

0.54 Simulation Experiment 0.52

520

χ2

50

Polynomial fit

40

0.50

30 2

0.48 0.46

20

0.44

10

0.42 0.8

500

TOF (ns)

χ

mν 2 RMS (MeV2/c4)

mν2(MeV2/c4)

0.9

1.0

1.1

1.2

1.3

1.4

0

0.9

Tcoef

1.0

1.1

1.2

1.3

Tcoef

Fig. 5 Upper panels: Experimental antineutrino mass and TOF spectra compared to simulations performed with two different cloud temperatures. Lower panels: Determination of the Tcoef parameter using the neutrino mass spectrum RMS (left) and a χ 2 test applied to the TOF spectrum between 480 and 520 ns (right)

3.3 Fast recoil ions and antineutrino mass reconstruction The ion cloud temperature can also be indirectly extracted from the β–ν correlation experiment data. From the recorded observables, the full momentum vectors of both

Temperature measurement of 6 He+ ions confined in a transparent Paul trap

27

the recoil ion and the β can be determined, providing a mean to reconstruct the antineutrino invariant mass: Mυ2 = Eυ2 − Pυ2 The width of the antineutrino invariant-mass spectrum (Fig. 5 left panel) depends strongly on systematic effects such as the response function of the β telescope and the size of the ion cloud [8]. Similarly, the leading edge of the recoil TOF spectrum (Fig. 5 right panel), corresponding to the fastest recoil ions, is sensitive to the ion cloud temperature, to the position of the recoil MCPPSD, and to the Paul trap RF voltages. Since both observables are weakly sensitive to the correlation coefficient aβν , the comparison of these experimental spectra with the MC simulations discussed in the Section 2.2 provides an additional way to determine the ion cloud temperature. For the simulations, the reasonable assumption of a pure axial coupling can be made, and the cloud temperature is adjusted by varying the Tcoef parameter. Concerning the neutrino mass spectrum, the RMS is the relevant parameter and the best adjustment is obtained for Tcoef = 1.04(7). A χ 2 test applied to the rising edge of the TOF spectrum leads to the value Tcoef = 1.17(5). Both results are compatible with the direct measurement presented in the Section 3.2.

4 Conclusion The temperature of the ion cloud trapped in the LPCTrap has been determined using three independent ways providing compatible results. We found an average weighted value Tcoef = 1.104(27) for the parameter characterizing the temperature. This corresponds to a cloud temperature of 0.110(5) eV, and to an associated relative systematic uncertainty on the β–ν correlation coefficient oaβν /aβν ptemp = 1.6%, which is lower than the statistical error. The temperature measurement gives a result 20% higher than predicted by the simulation. This could be explained by the presence of H2 O and N2 residual gas in the Paul trap chamber, or by the approximated interaction potentials between the ions and the H2 buffer gas molecules. Acknowledgements We are grateful to J. Bregeault, J.F. Cam, Ph. Desrues, B. Jacquot, Y. Merrer, J.C. Thomas, Ph. Vallerand, and Ch. Vandamme for their assistance during the different phases of the project. This work was supported in part by the Région Basse Normandie, by the NIPNET RTD network within the 6th FP (Contract No. HPRI-CT-2001-50034) and by the TRAPSPEC JRA within the I3-EURONS (Contract No. 506065).

References 1. 2. 3. 4. 5. 6. 7. 8.

Rodríguez, D., et al.: Nucl. Instrum. Methods. Phys. Res. A 565, 876 (2006) Fléchard, X., et al.: Phys. Rev. Lett. 101, 212504 (2008) Vetter, P.A., et al.: Phys. Rev. C 77, 035502 (2008) Gorelov, A., et al.: Phys. Rev. Lett. 94, 142501 (2005) Darius, G., et al.: Rev. Sci. Instrum. 75, 4804 (2004) Fléchard, X., et al.: J. Phys. G 38, 055101 (2011) Ban, G., et al.: Nucl. Instrum. Methods. Phys. Res. A 518, 712 (2004) Rodríguez, D., et al.: Eur. Phys. J. A 42, 397 (2009)