Correction Method for the Readout Saturation of the DAMPE Calorimeter
Chuan Yue, Peng-Xiong Ma, Margherita Di Santo, Li-Bo Wu, Francesca Alemanno, Paolo Bernardini, Dimitrios Kyratzis, Guan-Wen Yuan, Qiang Yuan, Yun-Long Zhang
CCorrection Method for the Readout Saturation of theDAMPE Calorimeter
Chuan Yue a, ∗ , Peng-Xiong Ma a,b, ∗ , Margherita Di Santo c,d , Li-Bo Wu e ,Francesca Alemanno f,g , Paolo Bernardini c,d , Dimitrios Kyratzis f,g , Guan-WenYuan a,b , Qiang Yuan a,b , Yun-Long Zhang e a Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory,Chinese Academy of Sciences, Nanjing 210008, China b School of Astronomy and Space Science, University of Science and Technology of China,Hefei 230026, China c Dipartimento di Matematica e Fisica E. De Giorgi, Universita del Salento, I-73100 Lecce,Italy d Istituto Nazionale di Fisica Nucleare (INFN)Sezione di Lecce, I-73100 Lecce, Italy e State Key Laboratory of Particle Detection and Electronics, University of Science andTechnology of China, Hefei 230026, China f Gran Sasso Science Institute (GSSI), Via Iacobucci 2, I-67100 L’Aquila, Italy g Istituto Nazionale di Fisica Nucleare (INFN) -Laboratori Nazionali del Gran Sasso,I-67100 Assergi, L’Aquila, Italy
Abstract
The DArk Matter Particle Explorer (DAMPE) is a space-borne high energycosmic-ray and γ -ray detector which operates smoothly since the launch on De-cember 17, 2015. The bismuth germanium oxide (BGO) calorimeter is one ofthe key sub-detectors of DAMPE used for energy measurement and electron-proton identification. For events with total energy deposit higher than decadesof TeV, the readouts of PMTs coupled on the BGO crystals would become sat-urated, which results in an underestimation of the energy measurement. Basedon detailed simulations, we develop a correction method for the saturation ef-fect according to the shower development topologies and energies measured byneighbouring BGO crystals. The verification with simulated and on-orbit eventsshows that this method can well reconstruct the energy deposit in the saturatedBGO crystal. Keywords:
DAMPE, BGO Calorimeter, Readout Saturation, Cosmic-rays ∗ Corresponding author
Email addresses: [email protected] (Chuan Yue), [email protected] (Peng-Xiong Ma)
Preprint submitted to Elsevier September 22, 2020 a r X i v : . [ phy s i c s . i n s - d e t ] S e p ACS:
1. Introduction
Measurements of the energy spectra of various cosmic ray (CR) nuclei are thekey to understanding the origin, propagation, and interaction of these energeticparticles [1–3]. Current measurements carried out by magnetic spectrometerexperiments reach very high precision up to TV rigidities [4]. At even higherenergies, direct measurements by calorimeter experiments show interesting hintsthat the spectra of CR nuclei may have complicated structures [5–7]. However,these results are still subject to relatively large uncertainties, due to eitherlimited statistics or large systematic uncertainties. Improved measurements areessential and necessary for addressing those important questions of CR physics.The DArk Matter Particle Explorer (DAMPE; [8, 9]) is an orbital mission forprecision measurements of CR nuclei, electron/positrons, and γ -ray, supportedby the strategic priority science and technology projects in space science of theChinese Academy of Science. It was launched into a sun-synchronous orbit atan altitude of 500 km on December 17, 2015, and has been working smoothly formore than 4 years since then. The scientific payload of DAMPE consists of foursub-detectors, including a Plastic Scintillator strip Detector (PSD; [10, 11]), aSilicon-Tungsten tracKer-converter (STK; [12, 13]), a BGO imaging calorimeter(BGO; [14, 15]), and a NeUtron Detector (NUD; [16]). These four sub-detectorswork cooperatively to enable good measurements of charge, track, energy andparticle-id of each incident particle [17–19]. Precise spectral measurements re-garding electrons plus positrons [20] and protons [21] in extended energy inter-vals, reveal interesting features and shed new light on the understandings of CRphysics, while improving the constraints on dark matter models [22–25]. The γ -ray identification technique [26] and analysis tool [27] have also been developed,with preliminary results [28].The BGO calorimeter is the main sub-detector for energy measurement,which is designed as a total-absorption electromagnetic calorimeter of about21.5 radiation length and 1.6 nuclear interaction length. It is composed of14 layers, each layer consists of 22 BGO crystals (25 × ×
600 mm ) placedorthogonally in two dimensions [14]. The fluorescence signal of each BGO crystalis read out by two PMTs mounted on both ends. This design provides twoindependent energy measurements. Apart from measuring the energy depositsof the cascade showers produced by incident particles, the calorimeter imagestheir shower developments, thereby serving as a hadron/lepton discriminator[20].At the very-high-energy end of DAMPE’s capability, saturations of the low-gain readouts appear , which affect the precise measurement of the particleenergy. For most of the saturated events, there are no more than one BGOcrystal in the same layer showing the saturation effect. In this work, we developa method to correct the saturated readout for those events, which is helpful inreconstructing the proper energy deposits of them. Applying such correctionswould enable us to significantly enlarge the measurable energy ranges of CRnuclei.
2. BGO Readout Saturation
To fulfil the requirement of a wide energy coverage, from 5 GeV to 10 TeVfor e ± /γ and up to 100 TeV for nuclei, the scintillation light signal of each BGOcrystal is read out from three different sensitive dynodes 2, 5, and 8 (Dy2, Dy5,and Dy8) of the PMTs, which corresponds to low-gain, medium-gain, and high-gain channels, respectively [29]. The response ratios of adjacent dynodes, i.e.Dy8/Dy5 and Dy5/Dy2, are carefully calibrated using high-energy shower eventscollected on orbit, which show good linear correlations and maintain stabilityover time [30]. Non-linearity effect from the conversion of the ionization energyto the light yield [31] has not been found for electrons up to a few TeV energies.However, for each PMT dynode, an upper limit of the ADC readout has been For protons and helium nuclei, the saturation may happen for deposited energies higherthan ∼
20 TeV. ∼ Deposited Energy [GeV] -1
10 1 10 N u m be r o f E v en t s High-Gain Channel Medium-Gain ChannelLow-Gain Channel
Figure 1: A typical energy deposit spectrum reconstructed from the S1 end of one BGOcrystal. The blue, green and red histograms correspond to the high-gain (Dy8), medium-gain(Dy5), and low-gain (Dy2) ranges, respectively. The vertical black line represents the upperlimit of the measurement.
Fig.1 shows a typical energy deposit spectrum reconstructed from the S1end of one BGO crystal after the attenuation correction. A smooth transitionbetween adjacent gain ranges can be clearly seen. The vertical black dashed linerepresents the upper measurement limit of the Dy2 readout channel, which is4
10 TeV. As different PMTs have different gains [15], the upper measurementlimit of the S1 end varies from ∼ ∼
15 TeV. This upper limit is highenough for the measurement of e ± /γ to energies of ∼
10 TeV. However, forCR nuclei which are expected to be measures above energies of 100 TeV, thedeposited energy in the calorimeter would exceed several tens of TeV, with themaximum energy in one single BGO bar exceeding several TeV. Therefore thesaturation may appear for those very-high-energy events. Fig.2 shows a heliumevent with saturation. The deposited energy is 49.4 TeV before correction. Theactual deposited energy of this event should be much larger.
X [mm] Y [mm] Z [ mm ] Z [ mm ] Figure 2: An illustration of a helium event with BGO readout saturation. The pre-correctiontotal energy deposit is 49.4 TeV. The two empty BGO crystals on the shower axis are satu-rated, while the other empty crystals on the edge of shower are the ones without any depositedenergy (or, the energy deposit is smaller than the noise threshold).
3. Method for the saturation correction
The saturation effect of the BGO readout has been taken into account inMonte Carlo (MC) simulation tool of DAMPE via importing saturation thresh-olds in the digitization procedure [33]. In this analysis, we use the protonsand helium nuclei sample generated with the FTFP BERT hadronic interac-tion physics list in the Geant4 software [34]. Fig.3 shows the ratios of digitizedenergy deposits ( E digi ) to simulated energy deposits ( E simu ) for MC protons(left) and helium nuclei (right) with incident energies ≥
10 TeV. The scattered5oints below 1 represent events that suffered from the readout saturation effect.The fraction of saturated events becomes higher with the increase of particleenergies. Particularly, at 100 TeV of incident energy, the fraction of saturatedevents is ∼ ∼ Incident Energy (TeV)10 20 30 40 50 60 70 80 90 100 S i m u / E D i g i E MC Proton
Number of Events1 10 Incident Energy (TeV)20 40 60 80 100 120 140 160 180 200 S i m u / E D i g i E MC Helium
Number of Events1 10 Figure 3: The ratios of digitized energy deposit to simulated energy deposit versus the incidentenergy for MC protons ( left ) and helium nuclei ( right ). For the flight data, there would be one or more saturated BGO crystal(s)for a single event, leading to a large discrepancy for energy measurement. Sincewe have lost the energy information of the saturated crystal, we need to esti-mate its energy deposit based on the other un-saturated crystals and the showerdevelopment information. By combining the energy information of neighbour-ing BGO crystals, we propose a two-step correction method to reconstruct theenergy deposit(s) of the saturated crystal(s).
The simulations indicate that the saturated crystal should be the one withthe maximum deposited energy in a certain BGO layer. As a prime estimation,we construct a correction variable η LR based on the energies in the left and right neighbouring bars (see Fig.4), defined as follows: η LR ,j = E Max ,j E Max ,j + E Left ,j + E Right ,j , (1)6 igure 4: Classifications of events that need corrections: (a) for the top layer ( j = 1); (b) formiddle layers ( j = 2 , ..., j = 14); (d) for saturated bar on theleft edge; (e) for saturated bar on the right edge. where E Max ,j is the maximum energy deposit in the j th layer, E Left ,j ( E Right ,j )is the energy deposit in its left (right) neighbouring crystal. When the saturatedbar is located on the edge of one layer (classes (d) and (e) in Fig.4), E Right ,j or E Left ,j are counted twice.From the simulation data, we obtain the η LR distribution of each layer re-spectively. In the left panel of Fig.5, the η LR , distribution of the 8th BGOlayer versus the layer energy for MC helium events is shown as an illustra-tion. The profile can be fitted with an empirical function: η LR ,j = p + p / log( E layer ,j / GeV)+ p · log( E layer ,j / GeV), where E layer ,j is the sum of energydeposits in all crystals of the j th layer. The parameters p , p and p of eachlayer are obtained respectively. Moreover, the parameters for different nuclei,e.g. protons and helium nuclei, are obtained individually based on correspond-ing MC simulations.Given the fact that the saturated crystal is the one with the maximum energy7eposit in its layer, the η LR ,j can be applied for saturation correction. Since theenergy information of the saturated crystal is totally lost, we firstly presume aninitial estimation of E Sat ,j = 5 . · ( E Left ,j + E Right ,j ) to calculate the E layer ,j .After that, we obtain η LR ,j as the relation function of E layer ,j . With η LR , j , theenergy deposit in the saturated crystal would be corrected as: E Sat ,j = η LR ,j − η LR ,j · ( E Left ,j + E Right ,j ) , (2)With the updated E Sat ,j , we re-calculate E layer ,j and η LR , j , and then applyEq.(2) once more to obtain a better estimation of E Sat ,j . For the case of morethan one saturated crystals in a single shower, but existing in different layers,the correction can be performed independently for each layer. The left-right correction is taken as the first step for the following up-down global correction. BGO Layer Energy Deposit [GeV] η L R / ndf χ ± ± -3.088 p2 0.0032 ± -0.2279 / ndf χ ± ± -3.088 p2 0.0032 ± -0.2279 Total Energy Deposit [GeV] η UD / ndf χ ± ± -9.134 q2 0.002215 ± -0.4065 / ndf χ ± ± -9.134 q2 0.002215 ± -0.4065 Figure 5: The profiles of η LR of the 8th BGO layer versus the layer energy ( left ) and η UD ofthe 8th BGO layer versus the total deposited energy ( right ) for MC helium events. The bluepoints and the error bars represent the fitted MPVs (most probable values) in each energybin and their uncertainties ( ± σ ) from the fit using a local gaussian function. After the left-right correction, we obtain a prime energy estimation of thesaturated crystal. However, to obtain a more precise energy deposit, we need tofurther take into account the longitudinal shower development. By consideringthe energy deposits of up and down layers, we construct another variable η UD ,8efined as η UD ,j = E Max ,j E Max ,j + E Left ,j + E Right ,j + E Up ,j + E Down ,j . (3)There are three types of definitions of E Up ,j and E Down ,j , corresponding toclasses (a), (b), and (c) in Fig.4). For case (a), E Up ,j is defined as the sum of themaximum bar energy and the energy deposits in its left and right neighbouringbars (Sum3 for short) of the second layer, while E Down ,j is defined as the Sum3of the third layer. For case (b), E Up ,j is defined as the Sum3 of the layer j −
1, and E Down ,j is defined as the Sum3 of the layer j + 1. For case (c), E Up ,j is the Sum3 of layer 12, and E Down ,j is the Sum3 of layer 13. As anillustration, the right panel of Fig.5 shows η UD , versus the total depositedenergy E dep for the MC helium events. We also use the empirical form, η UD ,j = q + q / log( E dep / GeV) + q · log( E dep / GeV), where E dep is the total energydeposit in the calorimeter. As well, the parameters q , q and q are obtainedindividually for different layers and for different nuclei.With the prime energy estimation of each saturated crystal after the left-right correction, we obtain a prime estimation of the total energy deposit E dep , whichis the sum of energy deposits in all crystals including the saturated one(s). By E dep , we obtain η UD ,j for a further correction: E Sat ,j = η UD ,j − η UD ,j × ( E Left ,j + E Right ,j + E Up ,j + E Down ,j ) . (4)If more than one saturated crystals exist in different layers, they would becorrected one by one globally. The correction of Eq.(4) can be performed itera-tively, with updated E Sat ,j (s) and E dep . The results converge quickly after fewiterations (three times in application).
4. Performance
The performance of this two-step correction method is illustrated in Fig.6using high energy MC helium nuclei. The Fig.6( a ) shows the ratio of the cor-rected energy deposit ( E cor ) to the simulated one ( E simu ). The result proves9 atio0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 N u m be r o f E v en t s simu /E digi E simu /E cor E MC Helium (a) S i m u / E C o r E MC Helium
Incident Energy [TeV]20 40 60 80 100 120 140 160 180 200 U n c e r t a i n t y (b) θ [ deg ] s i m u / E c o r E MC Helium (c)
Figure 6: The performance of the correction method of MC saturated helium nuclei withincident energies above 10 TeV. (a) : The distributions of E digi /E simu (blue) and E cor /E simu (red). (b) : The E cor /E simu ratio versus incident energy and the uncertainties ( ± σ ) fromthe correction. (c) : The E cor /E simu ratio versus incident zenith angle θ . that this method can well correct the energy deposits of saturated events. The E cor /E simu ratios for different incident energies of MC helium data are shownin Fig.6( b ). We find that the performance of the correction is effective for allenergies up to 200 TeV, and the uncertainty due to the correction is ∼ η LR and η LR , by considering the dependence on theincident trajectory. For one reason, the wide distributions of the correction vari-ables are primarily due to the randomness of the hadronic shower development,rather than the incident trajectory. For another, the correction variables onlyhave an effective dependence on the hit position for on-aixs events with a smallincident zenith angle, however, the accepted particles of DAMPE are mostlyoblique-incident with a zenith angle varying from 0 to 50 degree. As shown inFig.6( c ), the correction is actually independent with the incident zenith angle.To validate the correction method with the flight data, we select high energyproton and helium candidates which are not saturated but close to the upperlimit (see Fig.1). We require that the events should have at least one BGOcrystal with energy deposits higher than 0 . × E thr , where E thr represents themeasurement threshold of the corresponding crystal. Then we artificially re-move the energy deposit(s) of such BGO crystal(s) to produce pseudo saturatedevents. The performances of the correction for the pseudo saturated proton10 atio0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 N u m be r o f E v en t s meas /E pseudo E meas /E cor E Flight Data (Proton)
Total Energy Deposit [TeV]20 30 40 50 60 70 80 90 100 m ea s / E c o r E Flight Data (Proton)
Figure 7:
Left : The distributions of E pseudo /E meas (blue) and E cor /E meas (red) for pseudosaturated proton candidates with total energy deposits above 20 TeV. Right : The E cor /E meas ratio versus total energy deposit for pseudo saturated proton candidates in the flight data. Ratio0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 N u m be r o f E v en t s meas /E pseudo E meas /E cor E Flight Data (Helium)
Total Energy Deposit [TeV]20 30 40 50 60 70 80 90 100 m ea s / E c o r E Flight Data (Helium)
Figure 8:
Left : The distributions of E pseudo /E meas (blue) and E cor /E meas (red) for pseudosaturated helium candidates with total energy deposits above 20 TeV. Right : The E cor /E meas ratio versus total energy deposit for pseudo saturated helium candidates in the flight data. candidates and helium candidates are shown in Fig.7 and Fig.8, respectively.Despite the limited statistics, exported results indicate that the E cor /E meas ra-tio shows a good independence with the total energy deposit. For most of thepseudo saturated events, the energy deposit is properly corrected with respectto the measured one. However, it shows that a few events are slightly over-corrected. This happens because the pseudo saturated events are all under thesaturation threshold, but the parameters we used for the corrections are derivedwith real saturated MC protons and heliums separately.Finally in Fig.9 we show the comparisons among digitized (with saturation),11orrected, and simulated energies for MC protons and helium nuclei. As can beseen in this plot, the saturation effect becomes more and more important withthe increase of incident energy above 50 TeV. The correction is thus necessaryfor the calculation of the energy response matrix which is relevant to the spectralmeasurements of CR nuclei. For the proton spectrum analysis up to 100TeV inRef. [21], the correction has been applied for rare saturated proton candidatesin the flight data. E ne r g y D epo s i t[ G e V ] MC Proton
MC TruthDigitizedCorrected
Incident Energy [GeV] R a t i o E ne r g y D epo s i t[ G e V ] MC Helium
MC TruthDigitizedCorrected
Incident Energy [GeV] R a t i o Figure 9: The digitized energies (blue dots) and corrected energies (red dots) compared withthe incident energies (black squares) for MC protons ( left ) and helium nuclei ( right ). Thebottom panels show the ratios of E digi /E simu (blue dots) and E cor /E simu (red dots).
5. Conclusions
In order to extend the energy measurements of the DAMPE for hadronicCRs to sub-PeV energy ranges, the BGO readout saturation effect has beenstudied based on detailed MC simulation data. Through combining the energyinformation of neighbouring BGO crystals and the longitudinal shower devel-opment, we proposed a two-step correction method to reconstruct the energydeposit of saturated crystals. The first step is to use the left and right energydeposits of the saturated crystal to get a prime estimation of the saturated crys-tals. Then the longitudinal shower development is further taken into accountto improve the correction. The correction parameters are obtained for different12ucleonic species. The performance of the correction method is illustrated usingMC helium nuclei and also helium candidates in flight data, which show that theenergy deposits of saturated crystals can be well reconstructed. The correctionis expected to be very helpful in the measurements of the CR spectra at veryhigh energies.One caveat of the correction method is that it applies only for the case withno adjacent saturated crystals within the same layer. The events with two ormore adjacent crystals of the same layer get saturated are very rare, but existingin the flight data. The correction for such events would be more complicatedand uncertain. We leave such a study in future works. Acknowledgments.
This work is supported by the National Key Research and Development Pro-gram of China (Grant No. 2016YFA0400200), and the National Natural ScienceFoundation of China (Grant Nos. 11722328, 11773085, U1738205, U1738207,11851305), and the 100 Talents Program of Chinese Academy of Sciences.
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