Development of Electrostatic Ion Beam Trap

for Beta Decay Correlation

Measurements

Yuan Mei !

Lawrence Berkeley National Laboratory

ARUNA, 2014

Beta-Neutrino Correlation Measurements with EIBT

•A precision test of Standard Model •Sensitive to some Beyond Standard Model

Scalar (CS) and Tensor (CT) interactions. •<0.1% precision of “a” could probe SUSY

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When the period of oscillation of the ions in the trapwas measured, it appeared that, at V1 ! 4.75 kV, thevalue of T was minimum and that, for voltages below thisvalue, dT/dv # 0.

To understand the importance of dispersion functiondT/dv for a system of many interacting particles movingin the trap, we represent their motion in the trap as asphere of radius R0 with charge density !, together with a

Fig. 2. Signal observed with the pick-up electrode for an ini-tially 170-ns wide bunch of Ar$ at 4.2 keV for four time intervalsafter injection: (a) 0.2–0.22 ms, (b) 0.3–0.32, (c) 0.5–0.52, and(d) 1–1.02 ms.

Fig. 3. Diffusion constant "T as a function of the voltage on thelast electrode of the mirrors.

Fig. 4. Signal observed with the pick-up electrode for an ini-tially 170-ns wide bunch of Ar$ at 4.2 keV for four time intervalsafter injection: (a) 0.5–0.52, (b) 15–15.02, (c) 50–50.02, and (d)90–90.02 ms.

1030 J. Opt. Soc. Am. B/Vol. 20, No. 5 /May 2003 Zajfman et al.

pickup electrode

Electrostatic Ion Beam Trap

Developed by Zajfman at WI, for chemistry Rev. Sci. Instrum., Vol. 69, No. 1, January 1998

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agree very well. As the bunch width Wc is given in units oftime, this agreement demonstrates that the bunch widths inunits of length for both Ar! and Xe! are identical. Thedecay numbers (!c) "Fig. 9#b$% are in reasonable agreementfor the two species as well.

V. ONE-DIMENSIONALMODELS OF SYNCHRONIZATION

In this section we demonstrate that the source of the syn-chronization for ions trapped in an electrostatic potential isthe repulsive Coulomb force between them. To illustrate howrepulsion can counteract diffusion and to gain further insightinto the dynamics of diffusion and synchronization, we havenumerically studied two models: The first is based on themean field approximation, while the second is a multiparticlecalculation with interacting ions. In both cases, we assumethe system to be trapped in a one-dimensional flat-bottomedpotential. Clearly, a one-dimensional model is a rather crudeapproximation of the experimental situation. However, aswill be shown, important characteristics related to diffusionand synchronization can be understood with the insightgained through these models. A detailed analysis of the datawill be given in Sec. VI.

A. The model potential

A drawing of the model potential is shown in Fig. 12, and

the potential is explicitly given by

U#z $"! 0 if "z"&L'w# "z"#L $ if "z"$L ,

#15$

where 2L"200 mm is the length of the field-free region and'w is the slope of the potential walls. It is important to real-ize that in such a potential the period of oscillation is not amonotonic function of the particle kinetic energy: For an'w%2E/(qL), the oscillation period of fast particles islonger than for slow particles. This is because the fast par-ticles climb higher on the potential wall, and the extra timespent in this region is larger than the time difference betweenslow and fast particles in the field-free region. There is aslope 'w"2E/(qL) for which the period of oscillation T ofthe particles is independent of small variations of their ki-netic energies E. Under such a condition (dT/dE"0) thediffusion of a bunch of particles moving in this potential isstrongly reduced. A convenient parameter to characterize themotion of a single ion in this potential is the logarithmicderivative ' of the oscillation time T with respect to the ionenergy E:

'"1TdTdE . #16$

This parameter is directly related to the slope of the potentialwalls by

'"12E

1#L#q/E $#'w/2$1!L#q/E $#'w/2$

. #17$

While the slope of the potential wall is bounded by ($'w$0, ' takes values in the interval #1&'&2E&1. Allproperties of the single ion motion can be expressed through' . Here we are particularly interested in the oscillation time,which is given by

T#'$"!M2E

4L1#2E'

#18$

where M is the ion mass.

FIG. 11. Asymptotic bunch width Wc 100 ms after injection for#a$ Ar! and #b$ Xe! with V1"4.7 kV. The injected bunch widthwas about 5 )s.

FIG. 12. The one-dimensional model potential used in the simu-lations. The slope of the potential wall is 'w .

H. B. PEDERSEN et al. PHYSICAL REVIEW A 65 042704

042704-8

Ion bunching

and 2 mm diameter were located at the entrance and exit ofthe trap, respectively; while no collimators were used in thepresent setup.In order for the ions to be trapped, the electrode electrical

potentials have to satisfy certain conditions !12", which willbe described in more detail in the following section. As vari-ous configurations of potentials are possible, we define aparticular configuration by the vector #V1 ,V2 ,V3 ,V4 ,Vz$,which represents the potentials of the electrodes as shown inFig. 1. The electrode connected to potential Vz in each mirroris called the Einzel electrode, as it plays a major role indefining the focusing properties of the ion trap !12,13". In thepresent work, only symmetric configurations, where identicalpotentials are applied on each set of electrodes, areconsidered.Once the bunch is stored, its evolution was monitored

using a microchannel-plate %MCP& detector, located'50 cm after the trap %see Fig. 1&, which measures the num-ber of neutral Ar0 atoms emerging through the exit mirror.These atoms are produced in charge-exchange collisionswith the residual gas inside the trap. A second detection de-vice is a cylindrical pickup electrode of length lp!7 mmwith an inner diameter of 18 mm and a thickness of 1 mm,located at the center of the trap. The total capacitance of thepickup electrode, connectors, and vacuum feedthrough isCp'10 pF. When charged particles pass through thepickup, an image charge Qp is induced on its surface. Thischarge is converted into a voltage VA by a charge-sensitiveamplifier. The amplifier was calibrated by injection of aknown charge through a test capacitor using a voltage stepwith fast rise time ((20 ns). The calibration showed a lin-ear relation, VA!Qp /Cf , with Cf!1.3 pF. The output ofthe charge-sensitive amplifier is recorded on a digital oscil-loscope, from which the number of injected ions can beevaluated. The pickup electrode was used to follow the timebehavior of the injected bunch in the trap and a fast('300 )s) debunching always occured with the present setof electrode potentials.For stable trapping conditions, the rate of Ar0 atoms ex-

iting the trap and hitting the MCP detector is proportional tothe number of ions trapped between the mirrors, so that thebeam decay can be studied for different potential configura-

tions of the electrodes. Many of these potential configura-tions lead to a stable condition for trapping; we have chosena single set of voltages on the first four electrodes of eachmirror, which create a nearly linear decrease of potential onthe axis inside the mirror, namely, V1!6.5 kV, V2!4.875 kV, V3!3.25 kV, and V4!1.625 kV, while thevoltage on the Einzel electrode was varied over a large rangeof values for which trapping could be achieved, i.e., 2.7"Vz"4.5 kV.

III. RESULTS

Figure 2 shows an example for the measured number ofAr0 atoms hitting the MCP for three different values of theEinzel electrode potential: Vz!3.25 kV %upper curve&, Vz!3.05 kV %middle curve&, and Vz!4.15 kV %lower curve&.About 107 Ar# ions in a bunch of 5 )s were injected intothe trap for each injection, and the data shown here are thesum over 100 injections. Similar decay curves were mea-

FIG. 1. Schematic view of theion trap %not to scale&. The bunchis injected through the left-handside of the trap %entrance elec-trodes& and the neutralized Ar at-oms are counted by the MCP de-tector located at the right side. Thedistance between the innermostelectrode is 227 mm. The pickupelectrode in the center is used tomeasure the intensity of the in-jected ion bunch.

FIG. 2. Rate of neutral Ar atoms exiting the trap as measured bythe MCP detector. The Einzel-electrode voltage was Vz!3.25 kVfor the upper curve, Vz!3.05 kV for the middle curve, and Vz!4.15 kV for the lower curve. The data shown here are summedover 100 injections.

PEDERSEN, STRASSER, HEBER, RAPPAPORT, AND ZAJFMAN PHYSICAL REVIEW A 65 042703

042703-2

Forced bunching Self-bunching

served in the mean field model described in the previoussection.In summary, the results of these simulations demonstrate

that the Coulomb repulsion between the ions is responsiblefor the synchronization effect observed in the model poten-tial given in Eq. !15". For synchronization to occur, a mini-mum density of ions is required, and the effect is greatlyfavored when #$0. On the other hand, enhanced diffusionis observed for #%0. Based on these simulation results, weturn now to a detailed analysis of the experimental data inorder to develop general criteria for synchronization and dif-fusion.

VI. BUNCH DYNAMICS: DIFFUSION VERSUSSYNCHRONIZATION

In order to gain insight into the diffusion and synchroni-zation as observed in the experiments, numerical trajectorycalculations were performed in the actual three-dimensionalpotential of the trap. We used the SIMION program &17',which can both solve the Laplace equation for a specificpotential configuration in space, and propagate ions !withoution-ion interaction" on the computed potential grid. The ki-nematical properties of the trajectories for an ensemble ofions are obtained using Monte Carlo type calculations wherethe initial coordinates and velocities of the ions are chosen atrandom from realistic values. Two examples of ion trajecto-ries can be seen in Fig. 17, where only half of the trap isshown !the value of V1 was set to 4.7 kV". Details aboutthese calculation can be found in Ref. &13'.

A. Diffusion

Using trajectory calculations, it is possible to quantify andinterpret the experimental diffusion patterns observed in Fig.4!a" for V1!4.9 kV. As pointed out in Sec. III, when exter-nal and internal perturbations are neglected, there are twocontributions to the time spread per oscillation, namely, theintrinsic time spread (Ti and the time spread (Tv associatedwith the initial energy spread.

The intrinsic time spread (Ti was obtained directly fromSIMION by filling the trap with a beam with a Gaussian pro-file of width )(x)")(y)"2 mm, where r"!x2#y2 is theradial coordinate, and a Gaussian distribution of the radialcomponent of velocity vr , of width )(vr /v t)"0.001, wherev t is the speed. Analysis of the oscillation times was thenperformed and the widths !corresponding to (Ti) were ob-tained for different values of V1.To evaluate (Tv , the derivative of the oscillation time

with respect to energy, i.e., dT/dE , must be calculated forthe populated trajectories. This value was also extracted fromSIMION calculations, and folded with a realistic value of en-ergy width (E0"1 eV, to obtain the time spread (Tv .The total time spread (Tp"!(Tv

2#(Ti2 was calculated,

and the results are shown in Fig. 18!a" as a function of V1.Comparison of these results with the experimental data !Fig.5", for values where synchronization was not observed, i.e.,V1!4.9 kV, shows that the calculation underestimates thetime spread by a factor of *4, although the overall shape isreproduced correctly. The value of (Tp is dominated by theintrinsic time spread (Ti , and the dependence of (Tp on V1as shown in Fig. 18!a" mainly reflects the variations of the

FIG. 17. Two examples of trajectories as calculated with SIMION.The heavy black lines show the location of the mirror electrodes.

FIG. 18. Calculated parameters of the diffusion as a function ofthe trap configuration (V1). !a" Total time spread per oscillation,(Tp . !b" Mean value of the derivative of oscillation time withrespect to energy, (dT/dE), at E"4200 eV.

H. B. PEDERSEN et al. PHYSICAL REVIEW A 65 042704

042704-12

Figures 15!c" and 15!d" show the value of Cn for #!2E"#0.3 !c" and #!2E"0.3 !d", both for interacting!dots" and for noninteracting !solid curve" ions. While fornoninteracting ions Cn$0 for all n, this is not true for inter-acting ions when #!2E"0.3. In this case, the correlator isalways negative, and it was found to be negative for all val-ues 0$#$0.9/2E . Thus, in this case, it is clearly the Cou-lomb interaction between the particles that is inducing themotion synchronization observed in the simulations.The dependence of Cn on the number of oscillations can

to a good approximation be represented by a linear function%see Figs. 15!c" and 15!d"&. Therefore the evolution of thebunch width can still be well represented by Eq. !10", sincehere the corresponding correlator equals Cn"(2n#1)'Tp

2 .Thus, to further quantify the effects of synchronization andenhanced diffusion following from the one-dimensionalmodel, we defined an effective time spread per oscillation'Te as determined from the linear slope of Cn . 'Te wasthen determined for several values of # .In Fig. 16 'Te is plotted versus #!2E . The solid curve

shows the behavior expected for noninteracting ions %Eq.!19"&, the open circles show the results of the simulation withnoninteracting ions, and the solid circles show the results forinteracting ions. Where synchronization was observed, thevalue of 'Te is zero. There is very good agreement betweenthe expected 'Te and that obtained from simulation withnoninteracting ions. The small deviation stems from the fi-nite number of ions used in the simulations, which causedthe value of 'E0 to differ slightly from run to run. For in-teracting ions, enhanced diffusion, due to the Coulomb re-pulsion between the ions, is observed whenever #% 0. At#"0 there is a sharp transition to ion motion synchroniza-tion, which persists until #"0.9/2E , after which the diffu-

sion is much like the diffusion of noninteracting ions. Thus,in the present case, synchronization is observed only for #$0. Although a complete parametrization as a function of Nwas not made !due to the relatively large computational timerequired for performing these calculations", samples demon-strated that synchronization could also be obtained but onlyfor specific values of N and 'z when #%0, much as ob-

FIG. 15. Evolution of N"30ions, each of mass M"40 amuand charge q"!e!, trapped in thepotential Eq. !15" for two differentvalues of # . The initial energies ofthe ions were randomly selectedfrom a uniform distribution ofmean (E)"4200 eV and width'E"0.6 eV. The solid curvesshow the results obtained withnoninteracting ions, while the dotsshow the results for interactingions %see Eq. !22"& with *"1 +m. !a" The width of the ionbunch for #!2E"#0.3. !b" Thewidth of the ion bunch for #!2E"0.3. !c" The correlator for#!2E"#0.3. !d" The correlatorfor #!2E"0.3.

FIG. 16. Effective time spread per oscillation as a function of#!2E as obtained from numerical simulations for the samebunches and initial conditions as in Fig. 15. The solid curve showsthe expected behavior for noninteracting ions, i.e., 'Te"'E0!#!T(#). The open circles show the simulation results ob-tained with noninteracting ions and the dots show the results forions interacting through the force Eq. !22" with *"1 +m. Thecases for which synchronization occurs, i.e., when 'Te"0, are pre-sented on the logarithmic scale by adding 10#4 ns to their values.

DIFFUSION AND SYNCHRONIZATION IN AN ION- . . . PHYSICAL REVIEW A 65 042704

042704-11 H.B. Pedersen et. al. PRA 65 042704

agree very well. As the bunch width Wc is given in units oftime, this agreement demonstrates that the bunch widths inunits of length for both Ar! and Xe! are identical. Thedecay numbers (!c) "Fig. 9#b$% are in reasonable agreementfor the two species as well.

V. ONE-DIMENSIONALMODELS OF SYNCHRONIZATION

In this section we demonstrate that the source of the syn-chronization for ions trapped in an electrostatic potential isthe repulsive Coulomb force between them. To illustrate howrepulsion can counteract diffusion and to gain further insightinto the dynamics of diffusion and synchronization, we havenumerically studied two models: The first is based on themean field approximation, while the second is a multiparticlecalculation with interacting ions. In both cases, we assumethe system to be trapped in a one-dimensional flat-bottomedpotential. Clearly, a one-dimensional model is a rather crudeapproximation of the experimental situation. However, aswill be shown, important characteristics related to diffusionand synchronization can be understood with the insightgained through these models. A detailed analysis of the datawill be given in Sec. VI.

A. The model potential

A drawing of the model potential is shown in Fig. 12, and

the potential is explicitly given by

U#z $"! 0 if "z"&L'w# "z"#L $ if "z"$L ,

#15$

where 2L"200 mm is the length of the field-free region and'w is the slope of the potential walls. It is important to real-ize that in such a potential the period of oscillation is not amonotonic function of the particle kinetic energy: For an'w%2E/(qL), the oscillation period of fast particles islonger than for slow particles. This is because the fast par-ticles climb higher on the potential wall, and the extra timespent in this region is larger than the time difference betweenslow and fast particles in the field-free region. There is aslope 'w"2E/(qL) for which the period of oscillation T ofthe particles is independent of small variations of their ki-netic energies E. Under such a condition (dT/dE"0) thediffusion of a bunch of particles moving in this potential isstrongly reduced. A convenient parameter to characterize themotion of a single ion in this potential is the logarithmicderivative ' of the oscillation time T with respect to the ionenergy E:

'"1TdTdE . #16$

This parameter is directly related to the slope of the potentialwalls by

'"12E

1#L#q/E $#'w/2$1!L#q/E $#'w/2$

. #17$

While the slope of the potential wall is bounded by ($'w$0, ' takes values in the interval #1&'&2E&1. Allproperties of the single ion motion can be expressed through' . Here we are particularly interested in the oscillation time,which is given by

T#'$"!M2E

4L1#2E'

#18$

where M is the ion mass.

FIG. 11. Asymptotic bunch width Wc 100 ms after injection for#a$ Ar! and #b$ Xe! with V1"4.7 kV. The injected bunch widthwas about 5 )s.

FIG. 12. The one-dimensional model potential used in the simu-lations. The slope of the potential wall is 'w .

H. B. PEDERSEN et al. PHYSICAL REVIEW A 65 042704

042704-8

Electric potential profile

bunch size phase transition

pickup electrode waveform

ion trajectory inside of mirror

Other applications in nuclear physics

Multireflection time-of-flight mass spectrometer at CERN’s radioactive-ion-beam facility measures mass differences between nuclear isobars such as calcium-53 and chromium-53. Here a bunched beam containing 3-keV 53Ca+ and 53Cr+ ions bounces repeatedly between electrostatic end mirrors. As the flight path lengthens, the slightly lighter 53Cr+ ions forge ahead. Ejected after several hundred round trips, the two species have formed well-separated bunches whose flight-time difference yields a precision measurement of their mass difference. (Adapted from ref. 1 .) Citation: Phys. Today 66, 9, 15 (2013); http://dx.doi.org/10.1063/PT.3.2104

IRIS ECRIon Source

CO Transfer LineCold Trap

RadioactiveCO

8m Transfer Line Spectrometer

6 GHz Waveguide

Analyzing Magnet

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1 Meter

CarbonTargetCave 0

20 MeV He Beam88-Inch Cyclotron

and2mmdiameterwerelocatedattheentranceandexitof

thetrap,respectively;whilenocollimatorswereusedinthe

presentsetup.

Inorderfortheionstobetrapped,theelectrodeelectrical

potentialshavetosatisfycertainconditions!12",whichwill

bedescribedinmoredetailinthefollowingsection.Asvari-

ousconfigurationsofpotentialsarepossible,wedefinea

particularconfigurationbythevector#V1,V2,V3,V4,Vz$,

whichrepresentsthepotentialsoftheelectrodesasshownin

Fig.1.TheelectrodeconnectedtopotentialVzineachmirror

iscalledtheEinzelelectrode,asitplaysamajorrolein

definingthefocusingpropertiesoftheiontrap!12,13".Inthe

presentwork,onlysymmetricconfigurations,whereidentical

potentialsareappliedoneachsetofelectrodes,are

considered.

Oncethebunchisstored,itsevolutionwasmonitored

usingamicrochannel-plate%MCP&detector,located

'50cmafterthetrap%seeFig.1&,whichmeasuresthenum-

berofneutralAr0atomsemergingthroughtheexitmirror.

Theseatomsareproducedincharge-exchangecollisions

withtheresidualgasinsidethetrap.Aseconddetectionde-

viceisacylindricalpickupelectrodeoflengthl p!7mm

withaninnerdiameterof18mmandathicknessof1mm,

locatedatthecenterofthetrap.Thetotalcapacitanceofthe

pickupelectrode,connectors,andvacuumfeedthroughis

Cp'10pF.Whenchargedparticlespassthroughthe

pickup,animagechargeQpisinducedonitssurface.This

chargeisconvertedintoavoltageVAbyacharge-sensitive

amplifier.Theamplifierwascalibratedbyinjectionofa

knownchargethroughatestcapacitorusingavoltagestep

withfastrisetime((20ns).Thecalibrationshowedalin-

earrelation,VA!Qp/Cf,withCf!1.3pF.Theoutputof

thecharge-sensitiveamplifierisrecordedonadigitaloscil-

loscope,fromwhichthenumberofinjectedionscanbe

evaluated.Thepickupelectrodewasusedtofollowthetime

behavioroftheinjectedbunchinthetrapandafast

('300)s)debunchingalwaysoccuredwiththepresentset

ofelectrodepotentials.

Forstabletrappingconditions,therateofAr0atomsex-

itingthetrapandhittingtheMCPdetectorisproportionalto

thenumberofionstrappedbetweenthemirrors,sothatthe

beamdecaycanbestudiedfordifferentpotentialconfigura-

tionsoftheelectrodes.Manyofthesepotentialconfigura-

tionsleadtoastableconditionfortrapping;wehavechosen

asinglesetofvoltagesonthefirstfourelectrodesofeach

mirror,whichcreateanearlylineardecreaseofpotentialon

theaxisinsidethemirror,namely,V1!6.5kV,V2

!4.875kV,V3!3.25kV,andV4!1.625kV,whilethe

voltageontheEinzelelectrodewasvariedoveralargerange

ofvaluesforwhichtrappingcouldbeachieved,i.e.,2.7

"Vz"4.5kV.

III.RESULTS

Figure2showsanexampleforthemeasurednumberof

Ar0atomshittingtheMCPforthreedifferentvaluesofthe

Einzelelectrodepotential:Vz!3.25kV%uppercurve&,Vz

!3.05kV%middlecurve&,andVz!4.15kV%lowercurve&.

About107Ar#ionsinabunchof5)swereinjectedinto

thetrapforeachinjection,andthedatashownherearethe

sumover100injections.Similardecaycurvesweremea-

FIG.1.Schematicviewofthe

iontrap%nottoscale&.Thebunch

isinjectedthroughtheleft-hand

sideofthetrap%entranceelec-

trodes&andtheneutralizedArat-

omsarecountedbytheMCPde-

tectorlocatedattherightside.The

distancebetweentheinnermost

electrodeis227mm.Thepickup

electrodeinthecenterisusedto

measuretheintensityofthein-

jectedionbunch.

FIG.2.RateofneutralAratomsexitingthetrapasmeasuredby

theMCPdetector.TheEinzel-electrodevoltagewasVz!3.25kV

fortheuppercurve,Vz!3.05kVforthemiddlecurve,andVz

!4.15kVforthelowercurve.Thedatashownherearesummed

over100injections.

PEDERSEN,STRASSER,HEBER,RAPPAPORT,ANDZAJFMAN

PHYSICALREVIEWA65042703

042703-2

Elec

trost

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Ion

Beam

Tra

p

Located on Cyclotron roof

!!!!!!

Compact ECR Ion Source!

provided by Dan Xie

Part of O-14 apparatus

Jason Burke, Ph.D. thesis, UC Berkeley 2004

Features

• Simultaneous and full event-by-event reconstruction of decay vertex, beta, and recoil nucleus momentum vectors

• Direct measurement of cos(θ), in addition to recoil time-of-flight

• Field-free region for beta decay and ion flight.

• One trap and one setting for most ion species

• Utilizing light ion beams from 88 Cyclotron for copious isotope production: 6He, 16N, 19Ne, 23Ne, 35Ar, etc. (>107 observed decays in the trap).

• Recoil nucleus boosted by ion bunch momentum (re-acceleration of recoil nucleus unnecessary)

TOF in field-free regionPlastic scintillator

Silicon pixel tracker

p̂�

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[keV]kE0 2 4 6 8 10 12

#

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5000

10000

15000

20000

25000

30000

Recoil Ion Energy

CM

Lab (5keV 6He)

s]µtof [0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

#

0

500

1000

1500

2000

2500

3000

3500

Time of Flight

[keV]kE0 2 4 6 8 10 12

#

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

Recoil Ion Energy

[keV]kE0 2 4 6 8 10 12

#

0

500

1000

1500

2000

2500

3000

Recoil Ion Energy

a=0

a=-1/3

+ Instrumental acceptanceReconstruct Ek from dt and

MCP positionMeasured TOF

MCP resolution 0.1mm

dT

dv!

4m

qF"

2L

v2 ! 0. (5)

When the period of oscillation of the ions in the trapwas measured, it appeared that, at V1 ! 4.75 kV, thevalue of T was minimum and that, for voltages below thisvalue, dT/dv # 0.

To understand the importance of dispersion functiondT/dv for a system of many interacting particles movingin the trap, we represent their motion in the trap as asphere of radius R0 with charge density !, together with a

Fig. 2. Signal observed with the pick-up electrode for an ini-tially 170-ns wide bunch of Ar$ at 4.2 keV for four time intervalsafter injection: (a) 0.2–0.22 ms, (b) 0.3–0.32, (c) 0.5–0.52, and(d) 1–1.02 ms.

Fig. 3. Diffusion constant "T as a function of the voltage on thelast electrode of the mirrors.

Fig. 4. Signal observed with the pick-up electrode for an ini-tially 170-ns wide bunch of Ar$ at 4.2 keV for four time intervalsafter injection: (a) 0.5–0.52, (b) 15–15.02, (c) 50–50.02, and (d)90–90.02 ms.

1030 J. Opt. Soc. Am. B/Vol. 20, No. 5 /May 2003 Zajfman et al.

pickup electrode

Direct cos(θ) reconstruction

Plastic scintillator

Silicon pixel tracker

p̂�

MCP �

t0, E�

�tD

a

u

g

h

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I

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⌫Ion bunch

Two-layer silicon trackerOne layer silicon + ion bunch located by pick-up electrode

MCP position resolution 0.1mm

STAR HFT silicon tracker thickness: 50µm position resolution: 20µm

Ion bunch longitudinal extent: ~5mm

p2⌫ = p2e + p2+ + 2pep+ cos ✓e+

p2+ = p2e + p2⌫ + 2pep⌫ cos ✓p

p2e +m2e +

pp2⌫ +m2

⌫ = Q+ (me +m⌫ +m+)� E+

Sufficient to measure: beta direction (no energy) recoil direction and energy

σ [m

m]

[°]

Eβ [MeV]

σ after 1cmScatter angle (σ)

0.5

1

1.5

2

2.5

3

0.5 1 1.5 2 2.5 3 3.5 2

4

6

8

10

12

14

16

18

Transverse beam profile measurement

• 80X80µm pixel size, 64x64 pixel array

• Standard 0.35µm CMOS process, no post-processing

• First version already working, with high noise

• Second version, <30 e- noise on each pixel, available late-2014

• In-chip signal processing, good for large scale array

q

C=200fF Out

ee

e

Status and future plan

• Progress so far:

• Most of the hardware already in place

• Tested STAR HFT sensors for beta tracking

• About to:

• Trap stable ions

• Before the end of 2014:

• Integrate MCP for ion detection

• Integrate beta detector into the trap

• Demonstrate the trapping of 19Ne ions and the detection of beta and recoil nucleus in coincidence

End