1. 1 Alessandra Casale Università degli Studi di Genova INFN Sezione Genova FT-Cal Prototype Simulations

2. Led housing (teflon) Thickness: 10mm Led housing (teflon) Thickness: 10mm Prototype simulations The model of the calorimeter prototype for these simulations is show in the following picture: 3x3 Lead Tungstate Crystals (15mmx15mmx200mm) 7 StainlessSteel dummies APD housing (PCBoardM) Thickness: 10mm APD housing (PCBoardM) Thickness: 10mm Electronics (Air) Thickness: 50mm Electronics (Air) Thickness: 50mm Copper covering Thichness: 2mm Copper covering Thichness: 2mm 2

3. We used GEMC (GEANT4) to study the prototype response to radiation: The aim of simulations is: To verify the prototype response to cosmic ray and compare it with the measurements. To study the prototype response to electron beam to determine its energetic resolution and to establish the optimal energy range for the JLab test. 3

4. For each event, 3 parameters are involved: “Egen” : the energy generated by the source “Edep” : the energy deposited in the crystal according to GEANT4 “Erec” : the energy reconstructed from light sensors and electronics, that is user defined. In fact it includes the following contributions: the energy to light conversion according to the Light Yield of crystals @18°C, geometrical factors, quantum efficiency of APDs, the gain of APDs and PREAMPs, the charge to ADC channels conversion. 4

5. Simulations with cosmic rays Source: Cosmic Muons APD Threshold: 10 MeV Simulations were performed in a series of steps: 1.Muon beam of 10 GeV with vertex fixed above the prototype going through the 3 central crystals 2.Addition of angular spread: 20 degrees along z-axis and 5 degrees along y-axis 3.Addition of spatial spread: cilindrical muon source with a radius of 3 cm and length of 24 cm fixed above the prototype at a distance of 20 cm 4.Addition of energetic spread: muon energy ranges from 2 GeV to 200 GeV 5

6. Simulations with cosmic rays Source: Cosmic Muons APD Threshold: 10 MeV Simulations were performed in a series of steps: 1.Muon beam of 10 GeV with vertex fixed above the prototype going through the 3 central crystals 6

7. This picture shows the Edep in each cristal: it’s possible to recognize the passage of the cosmic rays through the 3 central crystals The deposited energy Edep shows Landau fluctuations around  16 MeV 7 According with the expected energy, calculated from the mean energy loss in the case of Minimum Ionizing Particles (MIP’s), that cross vertically a crystal: Eexpect = dE/dx(MIP) x crystal thickness = 10.2 MeV/cm [1] x 1.5cm = 15.3MeV [1] Techical Design Report for PANDA EMC According with the expected energy, calculated from the mean energy loss in the case of Minimum Ionizing Particles (MIP’s), that cross vertically a crystal: Eexpect = dE/dx(MIP) x crystal thickness = 10.2 MeV/cm [1] x 1.5cm = 15.3MeV [1] Techical Design Report for PANDA EMC

8. 8 There are not evident differences in shape and width of the distributions: there is no need to implement very accurate descriptions of muon energy and angular distribution. Overlap of Edep of the central crystal @different steps. The Plot is normalized to number of counts and the bin width

9. 9 How much the digitalization affects the signal? This picture shows the overlap distributions of Edep and Erec of the central crystal @Step4: there is not an evident difference. We can conclude that the main contribution to the prototype resolution is the intrinsic fluctuations of the deposit of energy. The contribution of the signal digitalization is negligible.

10. Simulations with electron beam This section consists in: a simulation of 10000 electrons with 500 MeV of energy a simulation of 100000 electrons with energy between 50 MeV and 4 GeV This range matches the energies that could be used in the JLab test. In both cases the beam is centered in the central crystal, it goes through the air and the emission vertex is 100 cm far from the prototype. 10

11. APD Threshold: zero This picture shows the Edep in each crystal: We can note that the central crystal collects 70% of the incident energy. The other 8 crystals collect part of the tails of the electromagnetic shower, corresponding to the 20% of the incident energy. The remaining 10% is lost due to the limited transverse size of the prototype. 11 Simulations with electrons @ 500 MeV

12.  /E≈0.035 Edep Erec Erec-Edep As in the case of cosmic rays, the contribution of digitalization  ((Erec-Edep)/Edep)=  (digi) ≈ 1% is negligible if compared with the resolution of Edep  /E≈0.032 Deposited energy summed over the 9 crystals Reconstructed energy summed over the 9 crystals 12 APD Threshold: zero Simulations with electrons @ 500 MeV

13. Histogram of the difference between the total reconstructed energy and the incident electron energy Erec-Egen Histogram of the difference between the total reconstructed energy and the incident electron energy Erec-Egen as function of electron energy Egen Erec-Egen as function of electron energy Egen 1 1 2 2 3 3 Missing Energy (%) (Erec-Egen )/Egen as function of Egen Missing Energy (%) (Erec-Egen )/Egen as function of Egen 4 4 Resolution  E /E (%) as function of Egen Resolution  E /E (%) as function of Egen Energetic resolution : e - between 50 MeV and 4 GeV APD threshold: 10MeV 13

14. 14 Legend Resolution Edep Resolution Erec Energetic resolution : e - between 50 MeV and 4GeV APD threshold: 10MeV If we compare the energy resolution in the cases of Edep and Erec, we verify that the resolution doesn’t depend significantly on the digitalization but only on the fluctuations of the electromagnetic shower. The energetic resolution is ≈10% at low energy, it improves with the increase of energy to ≈1.5%.

15. 15 Study of resolution as function of the APD threshold With electrons between 50 MeV and 4 GeV Study of resolution as function of the APD threshold With electrons between 50 MeV and 4 GeV This picture shows the resolution in logarithmic scale for different cases: Edep APDThr= 0MeV represents the ideal limit Erec APDThr= 0MeV there is not evident difference with the previous case Erec APDThr= 10MeV there is a little difference with the previous cases Erec APDThr= 20MeV there is a more significant difference and a worsening of the resolution: we can note the effect of threshold on the signal

16. 16 Summary We have simulated the response of the FT-Cal Prototype to cosmic rays and electrons with energy up to 4 GeV. COSMIC RAYS: 1.The most likely deposited energy is about 16 MeV, above the minimum measureable energy. 2.Effects related to the energy and angular distributions of muons are expected to be negligible with respect to the intrinsic fluctuation. 3.The intrinsic fluctuations of deposited energy are expected to be dominant over the digitalization effects. ELECTRON BEAM: 1.The transverse fluctuations in the energy deposition are dominant over the digitalization effects. 2.Energy losses varies from 20% @50MeV to 10% @1GeV (APDthr=10MeV). 3.Resolution varies from 10% @50MeV to 1.5% @ 4GeV (APDthr=10MeV). 4.Effects of the threshold start to be evident for thr of 20MeV.

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18. With the increase of APD threshold we have decrease of the average enegy collected worsening of resolution  /E, extract from a gaussian fit 18 APD threshold= 0 MeV Mean value= 437 MeV  /E(%)≈ 3.5 APD threshold= 10 MeV Mean value= 416 MeV  /E(%)≈ 4.14 APD threshold= 20MeV Mean value= 392 MeV  /E(%)≈5.16 Study of resolution as function of the APD threshold with electrons @500MeV Overlap of Erec summed over the 9 crystals @different APD threshold

19. Edep (Mev) x x 240 γ/MeV Light yield @18° ½ Light distribution in the crystal 1/1.2 Geometrical loss factor 1/2.25 APD area 0.75 APD quantum efficiency Electron-hole pairs of APD = = For APD gain = 250 @18° ∂G/ ∂V= 10% [V -1 ]For ΔV=30mV we have ΔG=3 10 -3 ∂G/ ∂T= -5% [K -1 ]For ΔT=0.1°C we have ΔG=5 10 -3 ΔGtotal = 6 10 -3 (summed in quadrature) For APD gain = 250 @18° ∂G/ ∂V= 10% [V -1 ]For ΔV=30mV we have ΔG=3 10 -3 ∂G/ ∂T= -5% [K -1 ]For ΔT=0.1°C we have ΔG=5 10 -3 ΔGtotal = 6 10 -3 (summed in quadrature) + + Poisson Distribution to describe the fluctuations of e-h pairs Poisson Distribution to describe the fluctuations of e-h pairs x x 250 APD gain + + APD gain fluctuations due to supply voltage and temperature changes = = Electrons of APD signal + + PREAMP noise (input equivalent electrons: gaussian with RMS of 4500 electrons) x x 2500 PREAMP gain Electron charge (pC) 20 The charge to QDC channel conversion Turned QDC channels = = Edep =0.1 MeV  3.3 e-h pairs  8.3*10 2 electrons  6.67 QCD channel To convert the final turned QDC channels into Erec, it is necessary to divide this number by each previous factor without considering the fluctuation terms. A numeric example: 19

20. 20 How much the digitalization affects the signal? This picture shows the overlap distributions of Edep and Erec of the central crystal @Step4: there is not an evident difference. We can conclude that the main contribution to the prototype resolution is the intrinsic fluctuations of the deposit of energy. The contribution of the signal digitalization is negligible.

21. An other way to demonstrate the negligible of digitalization is to study how the fluctuation terms influence the signal. We list them: Poisson fluctuation of electron-hole pairs on the photo-sensitive cathode of APD APD gain changes due to supply voltage and temperature changes PREAMP noise (input equivalent electrons: gaussian with RMS of 4500 electrons) To do this, we implemented this simulation with a series of steps: Step 1.None of fluctuation terms Step 2.Only Poisson fluctuations Step 3.Poisson + APD gain fluctuations Step 4.Poisson + APD gain + PREAMP noise 21 Study of digitalization with electrons @ 500 MeV APD Threshold: zero

22. We compared the Erec summed over all 9 crystals in each step. If we overlap these graphs we can note that the resolution doesn’t change significantly. This demonstrates that the intrinsic resolution of the e.m. shower dominates over the digitalization fluctuations. 22 Study of digitalization with electrons @ 500 MeV APD Threshold: zero

23. Without copper With copper 23 Erec @ 500MeV

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