contents lists available at sciverse sciencedirect nuclear...

Nuclear Instruments and Methods in Physics Research A 674 (2012) 55–66

Contents lists available at SciVerse ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

n Corr

E-m1 N

journal homepage: www.elsevier.com/locate/nima

Characterization of a tagged g-ray beam line at the DAFNE Beam Test Facility

P.W. Cattaneo g,n, A. Argan a,s, F. Boffelli g, A. Bulgarelli e, B. Buonomo t, A.W. Chen c,d, F. D’Ammando u,L. Foggetta d,1, T. Froysland b,d, F. Fuschino e, M. Galli h, F. Gianotti e, A. Giuliani c, F. Longo s,M. Marisaldi e, G. Mazzitelli t, A. Pellizzoni q, M. Prest l, G. Pucella m, L. Quintieri t, A. Rappoldi g,M. Tavani a,b, M. Trifoglio e, A. Trois q, P. Valente i, E. Vallazza f, S. Vercellone r, A. Zambra c, G. Barbiellini s,P. Caraveo c, V. Cocco a, E. Costa a, G. De Paris a, E. Del Monte a, G. Di Cocco e, I. Donnarumma a,Y. Evangelista a, M. Feroci a, A. Ferrari d,p, M. Fiorini c, C. Labanti e, I. Lapshov a, F. Lazzarotto a, P. Lipari i,M. Mastropietro j, S. Mereghetti c, E. Morelli e, E. Moretti s, A. Morselli k, L. Pacciani a, F. Perotti c,G. Piano a,b,k, P. Picozza b,k, M. Pilia l, G. Porrovecchio a, M. Rapisarda m, A. Rubini a, S. Sabatini a,b,P. Soffitta a, E. Striani b,k, V. Vittorini a,b, D. Zanello i, S. Colafrancesco n, P. Giommi n, C. Pittori n,P. Santolamazza n, F. Verrecchia n, L. Salotti o

a INAF/IASF-Roma, I-00133 Roma, Italyb Dip. di Fisica, Univ. Tor Vergata, I-00133 Roma, Italyc INAF/IASF-Milano, I-20133 Milano, Italyd CIFS-Torino, I-10133 Torino, Italye INAF/IASF-Bologna, I-40129 Bologna, Italyf INFN Trieste, I-34127 Trieste, Italyg INFN-Pavia, I-27100 Pavia, Italyh ENEA-Bologna, I-40129 Bologna, Italyi INFN-Roma La Sapienza, I-00185 Roma, Italyj CNR-IMIP, Roma, Italyk INFN Roma Tor Vergata, I-00133 Roma, Italyl Dip. di Fisica, Univ. Dell’Insubria, I-22100 Como, Italym ENEA Frascati, I-00044 Frascati (Roma), Italyn ASI Science Data Center, I-00044 Frascati (Roma), Italyo Agenzia Spaziale Italiana, I-00198 Roma, Italyp Dip. Fisica, Universita di Torino, Torino, Italyq INAF-Osservatorio Astronomico di Cagliari, localita’ Poggio dei Pini, strada 54, I-09012 Capoterra, Italyr INAF-IASF Palermo, Via Ugo La Malfa 153, I-90146 Palermo, Italys Dip. Fisica Univ. di Trieste, I-34127 Trieste, Italyt INFN Lab. Naz. di Frascati, I-00044 Frascati (Roma), Italyu INAF-IRA Bologna, Via Gobetti 101, I-40129 Bologna, Italy

a r t i c l e i n f o

Article history:

Received 25 November 2011

Received in revised form

16 January 2012

Accepted 19 January 2012Available online 27 January 2012

Keywords:

Electron and positron beam

Photon beam

Position-sensitive detectors

Bremsstrahlung

02/$ - see front matter & 2012 Elsevier B.V. A

016/j.nima.2012.01.049

esponding author.

ail address: [email protected] (P.W. C

ow at LAL-CNRS, F-91898 Orsay, France.

a b s t r a c t

At the core of the AGILE scientific instrument, designed to operate on a satellite, there is the Gamma

Ray Imaging Detector (GRID) consisting of a Silicon Tracker (ST), a Cesium Iodide Mini-Calorimeter and

an Anti-Coincidence system of plastic scintillator bars. The ST needs an on-ground calibration with a

g-ray beam to validate the simulation used to calculate the energy response function and the effective

area versus the energy and the direction of the g rays. A tagged g-ray beam line was designed at the

Beam Test Facility (BTF) of the INFN Laboratori Nazionali of Frascati (LNF), based on an electron beam

generating g-rays through bremsstrahlung in a position-sensitive target. The g-ray energy is deduced

by difference with the post-bremsstrahlung electron energy [1,2]. The electron energy is measured by a

spectrometer consisting of a dipole magnet and an array of position sensitive silicon strip detectors, the

Photon Tagging System (PTS). The use of the combined BTF-PTS system as tagged photon beam requires

understanding the efficiency of g-ray tagging, the probability of fake tagging, the energy resolution and

ll rights reserved.

attaneo).

www.elsevier.com/locate/nima

www.elsevier.com/locate/nima

dx.doi.org/10.1016/j.nima.2012.01.049

mailto:[email protected]

dx.doi.org/10.1016/j.nima.2012.01.049

P.W. Cattaneo et al. / Nuclear Instruments and Methods in Physics Research A 674 (2012) 55–6656

the relation of the PTS hit position versus the g-ray energy. This paper describes this study comparing

data taken during the AGILE calibration occurred in 2005 with simulation.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

AGILE (Astro-rivelatore Gamma a Immagini LEggero) is a SmallScientific Mission of the Italian Space Agency (ASI), dedicated tohigh-energy astrophysics. It combines two co-aligned imagingdetectors operating respectively in the X and g-ray bands withlarge Field of Views (FoV). The Silicon Tracker (ST), at the core ofthe AGILE satellite, is designed to detect and image g-rays in the30 MeV–50 GeV energy range [3–6].

The on-ground calibration of an astronomical instrument isimportant for the interpretation of its results. The goal isto reproduce in laboratory, under controlled condition, theresponse of the instrument in flight. This task requires a taggedphoton beam with position, direction and energy of each photonknown with a precision better than the instrument resolution.The realization of such a beam turns out to be a challengingendeavour. The Beam Test Facility (BTF) in the DAFNE collidercomplex at the INFN Laboratori Nazionali of Frascati (LNF) [7]was the elected site for realizing the tagged photon beamexploiting bremsstrahlung in a thin target and performing thecalibration. Preliminary results on the calibration of the AGILEST has been presented in Ref. [8] and will be subject of afuture paper.

This paper presents the experimental setup, a detailed MonteCarlo study of the system and the comparison with the experi-mental results collected during the calibration.

2. The experimental setup

The experimental setup is a complex system consisting of theBTF e� beam, the target to generate bremsstrahlung photons, thespectrometer magnet and the detector to measure the energy ofpost-bremsstrahlung electrons. The various subsystems aredescribed in the following with the convention that y is thecoordinate perpendicular to the BTF line plane, x the one trans-verse to the beam at the target in the BTF line plane and z is theone along the beam at the target, that is the direction of thebremsstrahlung photons.

Fig. 1. The initial section o

2.1. The electron beam

The e�s used for generating the photon beam are delivered bythe BTF. The BTF is fed by the DAFNE complex that provides e 7

under carefully controlled condition with predefined multiplicity.

2.1.1. The Beam Test Facility (BTF)

For the ST calibration we used the BTF in the DAFNE collidercomplex at LNF, which includes a LINAC at high eþ/e� currents,an accumulator of eþ/e� and two storage rings at 510 MeV. Theeþ/e� beam from the LINAC is directed into the accumulationring to be subsequently extracted and injected in the Main Ring.When the system injector does not transfer the beams to theaccumulator, the beam from LINAC can be extracted and trans-ported in the test beam area through a dedicated transfer line: theBTF line (Fig. 1). The BTF can provide a collimated beam of eþ/e�

in the energy range 20-750 MeV with a pulse rate of 50 Hz. Thepulse duration can vary from 1 to 10 ns and the average numberof e� per bunch Ne ranges from 1 to 1010 [7,9,10].

The BTF can be operated in two ways:

�

f the

LINAC mode: operating when DAFNE is off, with a tunableenergy between 50 MeV and 750 MeV and an efficiencyaround 0.9.
� DAFNE mode: operating when DAFNE is on, with a fixed
energy at 510 MeV and an efficiency around 0.6.

The extracted electrons are transported to the BTF hall, where thefinal section is located (Fig. 2); the experimental equipment undertest is positioned at the exit of the spectrometer magnetDHSTB02. All or part of the equipment can be mounted undervacuum continuing the beam line or, alternatively, the beam linecan be terminated with a thin window and the equipmentmounted in air.

In spite of some disadvantage from the point of view ofbackground, this last option was adopted with a 0.5 mm Bewindow because of the difficulties in implementing an extendedvacuum line incorporating all the required equipment.

BTF transfer line.

Fig. 2. The final section of the BTF transfer line including the last spectrometer

magnet DHSTB02.

impact of reducedmomentum electron

BTF e beam−

Si target

tagging detector

bending magnet

Bremsstrahlung photonelectrons

interactingnon

Fig. 3. A schematic view of the g-ray line: the target, the spectrometer magnet

and the PTS.

P.W. Cattaneo et al. / Nuclear Instruments and Methods in Physics Research A 674 (2012) 55–66 57

2.1.2. e� multiplicity per bunch

The calibration of the ST should be ideally performed in asingle-photon regime, avoiding simultaneous multi-photon pro-duction to reproduce the astrophysical conditions. Multi-photonevents should ideally identified and rejected otherwise they willbias the counting statistics.

On the other hand, bremsstrahlung is a continuous processand multi-photon generation (with photon energy Eg above agiven threshold) is possible also when a single e� crosses thetarget. The fraction of multi-photon events is approximatelyproportional to the single-photon emission probability. Thatimplies the need of a compromise between the photon beamintensity and the single-photon beam purity.

Considering that the target thickness was constrained by theavailability of the hardware, by the need to guarantee fulldetection efficiency of the beam electrons and by the need tomeasure electrons twice both in the x and y directions forstudying the beam size and divergence, the only free parameteris the e� multiplicity per bunch.

Another constraint is the limited time available for the calibra-tion campaign and the request of calibrating many different STgeometrical configurations. That puts a lower limit to the requiredphoton flux and therefore on the e� multiplicity per bunch.

In DAFNE mode with 5 e�/bunch the fraction of multi-photonevents having Eg420 MeV can be estimated to be � 10% by theformulae in Appendix. This uncertainty is greater than theaccuracy requirement on the effective area measurements. Onthe other hands, the DAFNE mode with 1 e�/bunch is consistentwith the accuracy requirements but the time necessary to collectenough statistics is incompatible with the time available for thecalibration. The ST cross-section for photons with Ego20 MeV isnot negligible and thus the fraction of interacting secondaryphotons will be larger than the numbers calculated in Appendix.Taking into account the above considerations, the best configura-tion for ST performance and calibration would be with 1 e�/bunch, but the flux requirement forced to select the configurationwith � 3 e�/bunch.

2.2. The bremsstrahlung target

Photons in the energy range relevant for the ST are producedby bremsstrahlung of electrons in a target; subsequently a

magnet bends away the electrons while the g-rays can traveltowards the AGILE instrument (see Fig. 3).

The bremsstrahlung target consists of two pairs of siliconsingle sided micro-strip detectors of area 8.75�8.75 cm2 and410 mm thick, each including 768 strips with 114 mm pitch. Onlyevery other strip is read, so that each target detector has 384readout channels with 228 mm readout pitch. Each pair measuresseparately the x and y coordinates transverse to the beam.A spatial resolution sr114=

ffiffiffiffiffiffi12p

mm� 33 mm is expected; thecluster size is often limited to one strip and therefore theresolution is limited by the strip pitch.

The target has two roles: to measure the coordinate and thedirection of the electrons and to cause the emission of brems-strahlung photons. The target detectors are positioned along thebeam direction between the last focusing magnet (QATB04 inFig. 2) and the spectrometer magnet (DHSTB02 in Fig. 2). The x

measuring ones are the first and the third, positioned respectivelyat 5.45 cm and 7.20 cm downstream the Be window, while the y

measuring ones are the second and the fourth, positioned respec-tively 6.45 cm and 8.20 cm downstream the Be window.

At the electron energy most used during calibration,Ee ¼ 463 MeV, the contribution to beam divergence due toCoulomb Multiple Scattering in each target detector is evaluatedunder the Gaussian approximation from Ref. [11] as � 2:0 mrad.

2.3. The photon tagging system (PTS)

The spectrometer magnet, visible in Figs. 2–4, generates adipolar field along the y direction over an angular range of 451. Inbetween the two magnet poles, there is a pipe made of stainlesssteel with rectangular section. It is composed of a straight section(‘photon pipe’) along which the bremsstrahlung g-rays travel tothe ST and a curved section (‘electron pipe’) defining the trajec-tory for e�s bent by the magnetic field.

The pipe is hollow with an air filled inner section with size5.50�3.50 cm2, its wall thickness is 0.35 cm. The magnetic fieldin the volume between the poles that includes the ‘’electron pipe’is assumed constant with strength B¼0.9 T when Ee ¼ 463:0 MeV,corresponding to a curvature radius R¼172.0 cm.

The equipment for the detection of the e�s that lost energy inthe target was developed and installed inside the spectrometermagnet by our team: the Photon Tagging System (PTS). It consistsof 12 micro-strip silicon detectors positioned on the internal wallsof the spectrometer magnet (see Figs. 2–4) grouped into two

Fig. 4. Geometry of the spectrometer magnet M drawn in GEANT3 including the

PTS detectors S displayed with an e� (entering from the right) irradiating a g-ray

in the target T and hitting the PTS at P. Photons are represented by dashed (blue)

lines and electrons by solid (red) lines. In this event the g-ray energy is � 75 MeV.

(For interpretation of the references to color in this figure legend, the reader is

referred to the web version of this article.)


modules of six detectors each, located into two hollow rectan-gular aluminum boxes few mm thick. In each module, thedetectors are located along a straight segment and thereforefollow only approximately the curved section of the ‘electronpipe’. The area of each detector is 11.86�2.00 cm2 with thickness410 mm and is subdivided in 1187 strips with 100 mm pitch. Onlyevery third strip is read resulting in 384 readout strips perdetector and 4608 in total.

Between each pair of consecutive detectors inside a module,there is a gap � 6 mm wide that is effectively a dead area.A larger gap � 2:0 cm wide is present between the two modulesthat contributes to the dead area as well. Electronic noise gives asmall contribution compared to the signals from e� amounting to� 2 keV that is of little relevance for the measurements. Depend-ing on the energy loss in the target, the electrons impinge ondifferent strips. The correlation in time between the signals of thee� in the target and in the PTS tags the photon; the position onthe PTS measures the photon energy.

The trigger for reading out the target and PTS data is given bythe delayed LINAC pre-trigger; it is read out independently fromthe ST data. This point has great relevance for the followinganalysis.

Fig. 5. Spectrum of the g-ray beam reaching the ST fit with a power law a=Eb.

3. The Monte Carlo simulation

A proper characterization of the BTF requires a careful com-parison of the data with a detailed Monte Carlo simulation. Thesimulation is realized using the GEANT3 package [12]. Thesimulation incorporates a description of the electron beamdelivered by the accelerator complex with beam parametersdetermined partly from design values and partly from measure-ments. The number of e� per bunch Ne can be fixed to an integervalue or can follow a Poisson distribution averaged at any realvalue Ne.

The material distribution of the bremsstrahlung target and ofthe spectrometer is simulated in detail. The target and the pipecan be simulated in air or in vacuum in various configurations.The default configuration is the one actually used during datataking with the target and the pipe in air.

The interactions of electrons and photons are driven by theGEANT3 routines with the possibilities of switching on and off therelevant physics processes like Coulomb Multiple Scattering,bremsstrahlung, Compton scattering, pair creation for all or only

for some of the materials. This option turned out to be very usefulin understanding the behaviour of the BTF/PTS system. Theenergy cuts for the e7 and photons are kept at the minimumallowed by the program (100 keV). A gauge of the quality of thesecuts is the average energy loss of a minimum ionizing particlescrossing a � 400 mm thick silicon layer comparable to a targetdetector or a ST layer thickness: it is � 100 keV. This level ofprecision is required to simulate spurious hits in the target and inthe ST that can affect the measurement.

The digitization simulation in the silicon micro-strip detectorsis based on a simplified model: the charge released in the volumebelow each strip is collected by the strip without accounting fordiffusion and charge trapping. Exploiting the capacitive coupling[13], the charges collected on all strips are fed into the readoutstrips with appropriate coefficients as described in Ref. [3]. Thenoise is simulated simply adding a Gaussian distributed charge oneach strip around a cluster; the width is determined by the dataand amount to � 2 keV.

The e� beam is generated inside the last straight section of theaccelerator � 5 cm upstream the target with a beam spot of ellipticalshape with a 2D Gaussian distribution, with angular divergencesperpendicular to the beam generated according two separateGaussian distributions and with a Gaussian distributed momentumspread. The momentum spread is provided by the DAFNE staff,while the other beam parameters are directly measured.

3.1. The simulated photon beam

The photon beam directed to the ST is simulated through theinteraction of the e� beam with the target. The photon generation isdue to the bremsstrahlung effect and follows Eq. (2) in Appendix. Thisformula shows an approximate 1=Eg dependency, that is a powerspectrum with index ��1. More precisely, a fit of Eq. (2) in theinterval 0.05–1.00 with a power spectrum returns an index ��1:2.

The simulated energy spectrum of the most energetic g raysreaching the ST (but not necessarily interacting with it) is shownin Fig. 5 with a power spectrum fit returning an index ��1:2 asexpected by the analytical formula. The number of e�s per bunchis set to Ne¼1 without Poisson fluctuation. The same result is

Fig. 6. Probabilities (in %) of multi-photon events versus Eg threshold for Ne¼1

(fixed, red dots) and N e ¼ 3:5 (Poisson distributed, green squares). (For interpreta-

tion of the references to color in this figure legend, the reader is referred to the

web version of this article.)


obtained when Ne ¼ 3:5 with Poisson fluctuation. This result isnot obvious because of the energy dependent interactions alongthe path that could change the spectrum, that turn out tobe small.

Another important element that characterizes the beam is thefraction of multi-photon events. Because in an astrophysicalenvironment there are no such events, they must be consideredbackground and must be minimized. If an event has two or morephotons with energy above the detection threshold in the ST(about few tens of MeV), they can interact simultaneously in theST. The reconstruction software, designed for the astrophysicalenvironment, is not fit to identify such events and will most likelyfail or return incorrect energy and direction. The percentagefraction of multi-photon events above a threshold is shown inFig. 6. Even for events with Ne ¼ 3:5, the fraction is not larger thana few % even for Eg as small as 10 MeV. Therefore their contribu-tion to errors in the measurement of the ST performances is atmost of comparable size.

A related but somehow different issue is the number of lowenergy photons, say Ego10 MeV, accompanying a photon in theST energy range (Eg430 MeV). This photons are not enoughenergetic to convert in a eþe� pair detectable in the ST, but theycan interact in coincidence with a photon of higher energygenerating spurious hits that can influence the proper reconstruc-tion of the event.

4. Results and discussion

The analysis of the target and the PTS data allows thevalidation of the Monte Carlo simulation required to correlatethe g-ray energy and the PTS hit position.

4.1. The bremsstrahlung target data

The analysis of the target data starts from looking for stripsabove a threshold, then neighbouring strips are grouped into

clusters. The cluster coordinate is obtained calculating its centroidby weighting each strip coordinate with the charge collected.

Ideally, each cluster should signal a hit of one e� in a targetdetector and the passage of each e� should be signaled by one hitin each target detector. In practice there is the possibility ofinefficiency in the detection of e� hits, noise hits, multipleclusters due to a single e� and single clusters on the same targetdetector associated to multiple e�s.

The efficiency of the hit searching algorithm is measured byselecting the events with one hit on three target detectors andzero on the fourth. This number is to be compared with the eventswith one hit on each target detector. With the available statistic,no event satisfies this requirement, so that the efficiency isbasically 100%.

The fraction of noise induced hits can be estimated by requir-ing one hit on one target detector and zero hit on the others. Alsoin this case, no event satisfies this requirement and therefore thefraction of noisy hits is basically 0%.

Particularly interesting samples are the 0-cluster events,where no cluster is detected in the target, and the 1-cluster ones,where one cluster per target detector is detected. For theconsiderations detailed above, the first sample can be safelyassociated to events with 0-e� events; even these events aretriggered because the target signal is not required by the triggerlogic. The 1-cluster sample mostly overlaps with 1-e� events andis used in the following for characterizing the beam. The maingoal of these measurements is inferring the beam properties to beused in the Monte Carlo generation.

4.1.1. Beam sizes

The beam sizes are measured only with 1-cluster sample. Thebeam profiles using the first x and y measured coordinates in thetarget are shown in the top row of Fig. 7 with the results ofGaussian fits superimposed. Using the second x and y measuredcoordinates in the target gives compatible beam sizes.

The beam sizes are sx � 1:5 mm and sy � 0:5 mm with asignificant non Gaussian tail in y. This numbers are representativebut subject to significant variations for different runs, due tochanges in the beam setting.

4.1.2. Beam divergences

Angular divergences are measured using the 1-cluster sample.The estimator is the difference between the cluster coordinates(xiðyiÞ,iAð1;2Þ) on the target divided by their distance dxðyÞ

sx ¼ ðx2�x1Þ=dx

sy ¼ ðy2�y1Þ=dy ð1Þ

In Fig. 7 (bottom row) the distributions of sx and sy are shown.The Gaussian fit returns sðsxÞ � 5:7 mrad and sðsyÞ � 4:2 mrad.

The beam divergences are, especially in y, smaller than thosepresented in Ref. [10]. That is due to an optimized setting of theaccelerator slits for this particular application.

The measured values for both the sizes and the divergences ofthe beam are fed into the Monte Carlo generator to reproduce theexperimental distributions as shown in Fig. 9.

4.1.3. e� multiplicity

The e� multiplicity of the BTF beam is one of the mostimportant parameters required for an appropriate simulation ofthe photon beam. As discussed in Section 2.1.2 the average of thePoisson distributed e� multiplicity is tuned by the acceleratorstaff. It is nevertheless important to monitor the e� multiplicityversus time to assess the reliability of the assumed multiplicityand its stability in time. The monitoring is possible by analyzingthe hit multiplicity on the target. The e� multiplicity is expected

/ ndf 2χ 861.3 / 84

Constant 8.6± 997.3

Mean 0.001± 4.202

Sigma 0.0007± 0.1484

X2 BC (cm) 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2

0

200

400

600

800

1000

/ ndf 2χ 861.3 / 84

Constant 8.6± 997.3

Mean 0.001± 4.202

Sigma 0.0007± 0.1484

BProfX2 / ndf 2χ 629.9 / 89

Constant 32.9± 3488

Mean 0.000± 4.488

Sigma 0.00027± 0.04423

Y2 BC (cm) 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4

0

500

1000

1500

2000

2500

3000

3500

4000 / ndf 2χ 629.9 / 89


Mean 0.000± 4.488

Sigma 0.00027± 0.04423

BProfY2

/ ndf 2χ 4524 / 88


Mean 0.04± 10.87

Sigma 0.043± 5.695

X Div BC (mrad) -80 -60 -40 -20 0 20 40 60 80 100

0

500

1000

1500

2000

2500

/ ndf 2χ 4524 / 88


Mean 0.04± 10.87

Sigma 0.043± 5.695

BDivX / ndf 2χ 3737 / 92


Mean 0.035± -5.233

Sigma 0.045± 4.212

Y Div BC (mrad) -100 -80 -60 -40 -20 0 20 40 60 80

0

500

1000

1500

2000

2500

3000

3500

4000

4500

/ ndf 2χ 3737 / 92


Mean 0.035± -5.233

Sigma 0.045± 4.212

BDivY

Fig. 7. Beam parameters at Ee¼463 MeV measured on data: x profile (top left), y profile (top right), x divergence (bottom left), y divergence (bottom right).


to follow a Poisson distribution with average m

PmðnÞ ¼mn

n!e�m

where m can be estimated from the fraction of 0-e� events givenby Pmð0Þ ¼ e�m, that is m¼�logðPmð0ÞÞ.

Another estimation is obtained from the ratio of 1-e� eventswith multi-e� events

f 12 ¼me�m

SnZ2mn

n!e�m

If f12 is measured, this relation can be inverted numerically toobtain m.

As previously mentioned the 0-e� events are readily identifiedas events with 0-cluster events, while the 1-e� sample largelyoverlaps with 1-cluster events.

In order to study e� multiplicity variation, events can begrouped in subsets of 1000 events with a sufficiently smallstatistical error. The estimated e� multiplicity is plotted versusthe event time for two calibration runs in Fig. 8.

These results show a broad agreement with the expected e�

multiplicity but also a quasi-periodic duty cycle of beam on-off.When beam is on, there are occasional spikes and sometimessmoother variations. The estimations from f12 is somehow lowerthan that from 0-e� events. That is expected if the chance that a

multi-e� event appears as a 1-cluster event is higher that thereverse. That is what is expected for a narrow beam with somechance of overlapping hits from different e�s.

4.1.4. Beam simulation and comparison with data

The data contained from the target are used to tune the MonteCarlo simulation of the beam. The relevant parameters are thecoordinates of the beam center, the widths of the beam spot, thebeam divergences, the e� multiplicity and the noise.

The measurements are performed on the target while theparameters of the beam in the Monte Carlo generator aregenerated upstream (see Section 4.1). These parameters maydiffer because of the spread of the uncollimated beam and ofthe multiple scattering along the path.

Nevertheless the simulation guarantees that the beam widthsat the origin of the Monte Carlo generator show no significantdifference with those measured on the target. Therefore themeasured widths sx and sy can be directly used for the genera-tion of the beam spot.

The beam divergences measured with the target are compar-able with the angular multiple scattering contribution from eachof them (see Section 2.2). Therefore this contribution must besubtracted from the measured one to obtain the values to be usedin generation sðsxÞ � 3:6 mrad and sðsyÞ � 2:7 mrad with sx,y

defined in Eq. (1). The momentum spread is provided by theDAFNE staff as sðpÞ ¼ 5:0 MeV=c.

42 43 44 45 46 47 48 49 50

BTF

Bea

m m

ultip

licity

0

1

2

3

4

5

6

BZero

42 43 44 45 46 47 48 49 50

BTF

Bea

m m

ultip

licity

0

0.5

1

1.5

2

2.5

3

3.5

4

BMultT

11 12 13 14 15 16 17 18 19

BTF

Bea

m m

ultip

licity

0

1

2

3

4

5

6

BZero

Event Time (μs)Event Time (μs)11 12 13 14 15 16 17 18 19

×109 ×109

×109 ×109

Event Time (μs)Event Time (μs)

BTF

Bea

m m

ultip

licity

0

0.5

1

1.5

2

2.5

3

3.5

4

BMultT

Fig. 8. Estimation of e� multiplicity with the 0-e� (left) and 1-e� (right) samples in the runs 2328 (top), 2566 (bottom).


4.2. The PTS data

The PTS data are those tagging the production of a g-raydirected to the ST and providing an estimation of its energy.Ideally the emission of a bremsstrahlung g-ray from the targetwould result in an electron hitting the PTS delivering one clusterof neighbouring strips above a predefined threshold. In this casethe g-ray energy would be univocally correlated with the PTS hitposition.

The relation between g-ray energy and PTS hit position,estimated by the cluster centroid, is highly non-linear and mustbe calibrated. The calibration can be performed either with thehelp of analytical calculation or relying on Monte Carlo simula-tions. The former approach cannot easily account for the otherinteractions of the electron in addition to the bremsstrahlung inthe target. Therefore the g-ray energy, Eg, is estimated with thePTS energy estimator, EPTS, calibrated with the Monte Carlosimulations detailed in Section 4.2.1.

Another important point is the treatment of events withmultiple PTS clusters. Ideally these are multi-photon events andshould be discarded from the calibration sample. Yet, most of themulti-cluster events are genuine single-photon events whereadditional clusters are generated by secondary interactions.Furthermore for Eg � 100 MeV, the e� trajectories intercept PTSdetectors on both modules, resulting in high probabilities ofmulti-cluster events even for single-photon events. Therefore alsomulti-cluster events are retained.

The spectrum of EPTS is shown in Fig. 10. It displays ananomalous feature at high energy, close to the kinematic limit,where the increase with the energy looks incompatible with theexpected behaviour of the bremsstrahlung spectrum in Eq. (2).

Two possible explanations are compatible with this excessbackground: a production of non-bremsstrahlung related lowenergy electrons entering into the spectrometer or a photonbackground in phase with the BTF cycle (the rate of cosmic rayinduced hits being too low).

The source of the low energy electrons could be d-raysproduced in the interaction of the beam electrons with thetarget. They should be proportional to the number of electronsin the bunch and follow an approximate 1=E2

d spectrum, where Edis the energy of the d electron. This spectrum would fake a1=ðEe�EgÞ

2 spectrum that would qualitatively matches the highenergy tail of Fig. 10. On the other hand, Monte Carlo simulationsand analytical calculations show that this source is largelyinsufficient to account for the excess of PTS hits correspondingto high EPTS.

Furthermore the two sources can be discriminated by lookingat 0-e� events, where no PTS hits from beam related d rays areexpected. Fig. 10 shows a significant fraction of 0-e� events withPTS hits strongly peaked at high EPTS, that means at low stripnumbers.

Hence only the latter background source is compatible with allexperimental data. The existence of a low energy photon back-ground was also confirmed by the accelerator staff.

Fig. 9. Beam parameters at Ee¼463 MeV measured on a Monte Carlo sample: x profile (top left), y profile (top right), x divergence (bottom left), y divergence (bottom

right).

EPTS(MeV)102

dN/d

E PTS

102

103

104

105

106

EPTS Spectrum

Fig. 10. PTS energy spectrum: all events (red squares), only 0-e� events (blue

triangles), normalized difference (green dots). (For interpretation of the references

to color in this figure legend, the reader is referred to the web version of this

article.)


The spectrum of bremsstrahlung g-rays can be recovered bysubtracting the background spectrum appropriately rescaled withthe 0-e� rate but the background events cannot be tagged andremoved on a event by event basis.

4.2.1. PTS simulation and comparison with data

In order to provide an interpretation of the PTS data and usethem to characterize the PTS/BTF system, a detailed Monte Carlostudy is required. The Monte Carlo data contains together withthe PTS measurements also the true value at the generation levelof the particles (Monte Carlo truth), that can be compared toextract the PTS performances.

A crucial element is the calibration curve relating the PTScluster position and the electron (g-ray) energy already used inprevious sections. The calibration is obtained looking at MonteCarlo events generated with 1e� per bunch by plotting thefirst strip (lowest number) of the first PTS cluster versus Eg, theenergy of the most energetic g-ray as shown in Fig. 11(a). Thisplot is obtained requiring one PTS cluster, Eg410 MeV andadditional energy from g-ray other than the most energetic oneo10 MeV.

The points are distributed along a band plus a small set ofoutliers, whose origin will be discussed later; in order to use onlythe points in the band, an additional graphical cut is appliedbefore the 2D histograms is plotted in form of profile histogram.The profile histogram is fitted with a 5-th order polynomial asshown in Fig. 11(b). The fit has been also tested on simulatedevents produced with Ne ¼ 3:5 with Poisson distribution, byallowing multiple PTS clusters or by requiring only one g-rayabove 100 keV; the fit results are insensitive to the cuts. Thisfunctional dependence defines EPTS as the PTS measured energy.The comparison between the data and Monte Carlo EPTS

Fig. 11. Eg versus PTS strip number: (a) two dimensional and (b) fitted with 5-th order polynomial.

Fig. 12. PTS energy spectra for data (green square) and Monte Carlo (red circle).

(For interpretation of the references to color in this figure legend, the reader is

referred to the web version of this article.)

Fig. 13. Eg versus EPTS scatter plot. The events far from the central band are

divided into classes. See text for more details.


distributions is shown in Fig. 12. The agreement is reasonableeven if some features appear systematically shifted.

4.2.2. PTS inefficiency, false positive and outliers

The fit in Fig. 11(b) is obtained using only events where thePTS energy measurement and the true g-ray energy are signifi-cantly correlated. There are events in which that is not the case,that can be divided in three broad classes: PTS inefficiency, Falsepositive and Outliers.

Inefficiency: the plot Eg versus EPTS for Monte Carlo events with1-e� per bunch is shown in Fig. 13. The PTS inefficiencies,displayed in the vertical line on the left, are events where anelectron emits a g-ray by bremsstrahlung but it does not reachthe PTS detectors. Such inefficiencies are understood consideringthe path of an electron inside the ‘electron pipe’: in absence of afocusing magnet and subject to multiple scattering due to thetarget (and to the air along the path) the electrons diverge fromthe ideal trajectory and may hit the wall of the pipe. That is


particularly easy along the y direction where the pipe inner half-height is only 1.75 cm. In this case the e� showers and the showerparticles (e7 s and photons) may hit or not the PTS detectors.

Another source of inefficiency originates when the e� hits the3.5 mm thick steel inner face of the guide, as expected, anddevelops a shower fully in the iron. A third cause is due to the e�

hitting the inner face as expected but the particles exiting fromthe outer face do not hit the PTS detectors that have an half-height of only 1.00 cm.

False positive: The main cause of false positives that is EPTS40and Eg � 0 is the first reason detailed before to explain

Fig. 14. PTS efficiency for events with 3e� per bunch following Poisson distribu-

tion versus Eg .

Fig. 15. Absolute (a) and relative (b) spread in EPTS distribution for eve

inefficiencies: an e� that has not emitted a bremsstrahlungg-ray showering in the electron pipe on the top (bottom) facewith some particles hitting the PTS detectors. The probability ofsuch events is proportional to the extent of the e� divergence andtherefore to the e� path length. Therefore it should increasealmost linearly with the strip number, that is inversely with EPTS.

False positive may also be the results of g-rays actuallyproduced by bremsstrahlung and absorbed along their path inair or by e� emitting bremsstrahlung g-rays in air along its pathin the electron pipe.

Outliers: outliers are generated by a combination of processessimilar to those described above. An e� emitting a g-ray and thenhitting the top (bottom) face of the pipe and delivering a PTSsignal generates an outlier. Outliers can be generated also whenthe bremsstrahlung g-ray interacts with air creating a eþe� pair,that in turn irradiates a lower energy g-ray such that EgoEPTS.

In presence of multiple e�s per bunch, a combination of a falsepositive and of an inefficiency generates a outlier.

Another relevant source is e�s that, after having emitted ag-ray, cross the inner face of the pipe showering withoutdelivering a PTS signal close to the crossing point. The showerphotons may nevertheless convert in the PTS detectors at higherstrip number, so that EPTSoEg.

4.3. PTS simulation results

Starting from the complex picture previously discussed thePTS can be characterized in different ways. The first step isunderstanding which is the best requirement on the number ofPTS clusters. The possibilities are 1 cluster, 2 clusters and Z1clusters. The first is expected to have low efficiency but also smallnumber of outliers and better energy resolution, the latter has theopposite features while the second is a compromise.

In Fig. 14 the PTS efficiencies for the three cases are shown.The option with Z1 clusters seems to be preferred not onlybecause it has higher efficiency but also because it is less sensitiveto the presence of secondary clusters generated by showeringparticles. In this plot a loose definition of efficiency is used that

nts with 3e� per bunch following Poisson distribution versus Eg .


requires only a PTS cluster regardless of the EPTS�Eg relation thatis also outliers are included.

The absolute and relative RMS spreads in the EPTS versus Egdistribution limited to the central band, that is excluding outliers,are shown in Fig. 15(a) and (b).

Another approach is looking at the fraction of events with a PTScluster associated to an energetic g-ray versus EPTS. That measuresthe probability of fake positive with the PTS as a photon tagger.A problem with this definition is that there is no infrared limit toEg. The lower limit is set by the GEANT threshold for g production.

Fig. 16. Probability of having Eg41ð8Þð15ÞMeV for events with 3e� per bunch

following Poisson distribution versus EPTS.

Fig. 17. Absolute (a) and relative (b) spread in Eg for events wit

A more robust definition is to set a threshold defined by the lowestEg for which the PTS has a reasonable efficiency, that isOð10 MeVÞ.

In Fig. 16 the probability of having a g-ray above the giventhreshold versus EPTS is reported for events with Z1 PTS cluster.The complement of this plot gives the fraction of false positive.This fraction is understandably high for low EPTS where theprobability of a non-emitting e� hitting the PTS is high and forhigh EPTS where the false positives originate from background. Formost of the energy range the false positive fraction is r10% andweakly dependent on the Eg threshold.

The absolute and relative RMS spreads in the Eg versus EPTS

distribution limited to the central band, that is excluding outliers,are shown in Fig. 17(a) and (b). Outliers constitute at most a fewpercent of the events and their distribution cannot be easilyparameterized.

5. Conclusions

The BTF/PTS has been described in detail. It has been char-acterized by studying the data taken in LNF during the AGILEcalibration campaign. Analysis of the target data has allowed tocharacterize the e� beam precisely.

The parameters of the Monte Carlo generator have beenmostly determined from the data. Corrections to the data havebeen necessary to account for a background contamination notincluded in the simulation.

The relation between PTS coordinate and g-ray energy hasbeen calibrated with the Monte Carlo simulation and the EPTS

distributions from simulation and data are in good agreement.This calibration of the system allows to use it for calibrating

photon detectors, like the ST of AGILE, as presented in aforthcoming paper.

Important parameters of the system like point spread function,effective area and energy resolution versus the g energy has beenextracted through the Monte Carlo simulation validated with thissystem and used to extract relevant scientific results since theAGILE launch in 2007 [6].

h 3e� per bunch following Poisson distribution versus EPTS.


Appendix

The photon flux can be predicted analytically with someapproximated formulae from Quantum Electrodynamics to becompared with the Monte Carlo predictions.

The formula for the bremsstrahlung differential cross-sectionfor photon emission with energy Eg from an electron with energyEe is, with good approximation [11]

dsdy¼

A

X0NAy

4

3�

4

3yþy2

� �ð2Þ

where A is the atomic number of the material, X0 its radiationlength, NA the Avogadro number and y¼ Eg=Ee.

Eq. (2) can be integrated to predict the number of photonswith relative energy between ymin and ymax emitted by a radiatorof thickness d

Ngðymin,ymaxÞ ¼d

X0

4

3ln

ymax

ymin

� ��

4

3ðymax�yminÞþ

1

2ðymax�yminÞ

2

� �

ð3Þ

In our setup the radiator consists of four silicon layer 410 mmthick, a window of Be 0.5 mm thick and about 35.0 cm of Air.

The total thickness d expressed in radiation lengths is (withXAir

0 ¼ 30 500:0 cm, XBe0 ¼ 35:3 cm and XSi

0 ¼ 9:36 cm)

d

X0�

35:0 cm

XAir0

þ0:05 cm

XBe0

þ4� 0:041 cm

XSi0

� 2:0� 10�2

Ng follow the Poisson distribution. Also the number of elec-trons per bunch follows a Poisson distribution with average Ne,therefore the probability of emitting 1 or more photons is

PNeðNg ¼ 1Þ �NeNg�ðNeNgÞ

2ð4Þ

PNeðNg41Þ �

ðNeNgÞ2

2ð5Þ

References

[1] B. Buonomo, et al., A tagged photon source at the Frascati beam-test facility(BTF), in: Proceedings of DIPAC 2007, Venice, Italy, 2007, p. 63.

[2] S. Hasan, et al., A Photon Tag Calibration Beam for the AGILE Satellite. LNF-05/24, 2005. Presented at the 9th ICATPP Conference on Astroparticle, Particle,Space Physics, Detectors and Medical Physics Applications, Como, Italy,October 2005.

[3] G. Barbiellini, et al., Nuclear Instruments and Methods in Physics ResearchSection A 490 (2002) 146.

[4] M. Prest, et al., Nuclear Instruments and Methods in Physics Research A 501(2003) 280.

[5] M. Tavani, et al., Nuclear Instruments and Methods in Physics Research A 588(2008) 52.

[6] M. Tavani, et al., Astronomy and Astrophysics 502 (2009) 995.[7] G. Mazzitelli, A. Ghigo, F. Sannibale, P. Valente, G. Vignola, Nuclear Instru-

ments and Methods in Physics Research A 515 (3) (2003) 524.[8] P.W. Cattaneo, et al., Nuclear Instruments and Methods in Physics Research A

630 (1) (2011) 251. Proceedings of the 2nd Roma International Conference onAstroparticle Physics (RICAP 2009).

[9] B. Buonomo, G. Mazzitelli, P. Valente, Performance and upgrade of theDAFNE beam test facility, in: IEEE Nuclear Science Symposium ConferenceRecord, Rome, Italy, October 2004.

[10] G. Mazzitelli, B. Buonomo, L. Quintieri, P. Valente, The DAFNE beam testfacility: from 1 to 10 milliards of particles, in: Proceedings of EPAC 2006,Edinburgh, Scotland, 2006.

[11] W.M. Yao, et al., Journal of Physics G 33 (2006).[12] R. Brun, et al., GEANT3-Detector Description and Simulation Tool, CERN

Program Library Long Writeups W5013, 1993.[13] P.W. Cattaneo, Nuclear Instruments and Methods in Physics Research A 295

(1990) 207.

contents lists available at sciverse sciencedirect nuclear...

Documents