Application of Birks' law of scintillator nonlinearity in Geant4. Alexander Tadday Kirchhoff Institute for Physics Heidelberg University
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1 Alexander Tadday Alexander - IRTG Tadday Meeting - IRTG - Heidelberg Meeting Application of Birks' law of scintillator nonlinearity in Geant4 Alexander Tadday Kirchhoff Institute for Physics Heidelberg University
2 2 Outline CALICE analogue hadronic calorimeter prototype Birks law of scintillator nonlinearity Measurement of Birks coefficient (MPIK Heidelberg) Birks law in Geant4 Conclusion & Discussion
3 3 CALICE analogue HCAL Hadronic calorimeter prototype for next e + e - collider Sampling calorimeter with small plastic (polystyrene) tiles as active material Monte Carlo studies Scintillator properties needed Nonlinearity: Birks law Currently Birks coefficient from ZEUS calorimeter scintillator is used Measure kb for the AHCAL scintillator Mirror Plastic scintillator tile ( cm 3 ) Wavelength shifting fibre SiPM
4 4 Birks Saturation Formula e - Specific energy loss de/dx is high before particle is stopped High ionization density di/dx α de/dx scintillator Quenching: Excited atoms can interact and may de-excite radiationless de/dx [MeV/cm] kin energy [MeV] Electron collision stopping power (Berger-Seltzer eq.) Light yield per unit length dl/dx is reduced for high de/dx Non-linearity described by Birks formula:
5 5 Experimental Setup (MPIK Heidelberg) PMT measures light yield Germanium detector measures Energy of Compton scattered photon EGe Germanium detector Coincidence trigger PMT and Ge-detector PMT Measured energy range of electrons ~ kev Scintillator Thanks to Christoph Aberle and Stefan Wagner for the ability to use the setup Detailed setup description in [1] 137 Cs moveable rail
6 5 Experimental Setup (MPIK Heidelberg) PMT measures light yield Germanium detector measures Energy of Compton scattered photon EGe Germanium detector Coincidence trigger PMT and Ge-detector PMT Measured energy range of electrons ~ kev Scintillator Thanks to Christoph Aberle and Stefan Wagner for the ability to use the setup Detailed setup description in [1] 137 Cs moveable rail
7 6 Total Light-Yield We have measured total Light-Yield (LY) Problem: dl/dx not easily measurable divide by de/dx Light-Yield of a particle with energy E0:
8 7 kb Measurement (standalone) Experimental data: Light-yield as function of electron energy Light yield [a.u.] Data Birks' model Linear fit (fit range > 0.12MeV) Fit with calculated Light yield Fit parameter kb Fit function: Kinetic energy [MeV] Fit result: kb= cm/mev Currently used value: kb = cm/mev M. Hirschberg et. al., IEEE Trans. Nucl. Sc., Vol. 39, No. 4, 1992
9 8 Birks coefficient in Geant4 Geant4 is step based: E0 E1 En-1 En=0 dx1 dx2 dxn Steps can t be arbitrarily small because of computational effort Light-Yield in Geant4 (secondaries not considered): Converges only against integral for small steps. This is not the case for default settings in Geant4!
10 8 Birks coefficient in Geant4 Geant4 is step based: E0 E1 En-1 En=0 dx1 dx2 dxn Steps can t be arbitrarily small because of computational effort Light-Yield in Geant4 (secondaries not considered): Converges only against integral for small steps. This is not the case for default settings in Geant4!
11 9 Birks coefficient in Geant4 Curve shows 120keV e - with kb=0.0151cm/mev /!E!E vis Area under curve represents the visible energy Kinetic energy [MeV]
12 9 Birks coefficient in Geant4 Curve shows 120keV e - with kb=0.0151cm/mev step 2 step 1 Geant4 with default settings and kb=0.0151cm/mev Visible energy is overestimated! /!E!E vis Area under curve represents the visible energy Kinetic energy [MeV]
13 9 Birks coefficient in Geant4 Curve shows 120keV e - with kb=0.0151cm/mev step 2 step 1 Geant4 with default settings and kb=0.0151cm/mev Visible energy is overestimated! Possible solution: Use effective Birks coefficient to get the correct result kb=0.0186cm/mev /!E!E vis Area under curve represents the visible energy Kinetic energy [MeV]
14 Birks coefficient in Geant4 effective Birks' coefficient [cm/mev] default Geant4 settings: α = 0.2 Final range = 1mm qualitatively: smaller steps Final range parameter [m] -2 larger steps
15 Birks coefficient in Geant4 effective Birks' coefficient [cm/mev] Main disadvantage: need different effective Birks coefficient for different parameter configuration default Geant4 settings: α = 0.2 Final range = 1mm qualitatively: smaller steps Final range parameter [m] -2 larger steps
16 11 Method Improvement Default Geant4 Default Geant4 Step-wise integral calculation of visible energy Use method of Monte Carlo integration (VEGAS algorithm) /!E!E vis Use pre-calculated de/dx to increase speed Kinetic energy [MeV]
17 12 Method Comparison Birks coefficient independent of final range parameter (step-size) Residual fluctuation from production of secondaries (deltaelectrons) effective Birks' coefficient [cm/mev] qualitatively: smaller steps Default Geant4 Integral method Final range parameter [m] -2 larger steps
18 13 Conclusion & Outlook Measured Birks coefficient higher than currently used one Measured value: kb = cm/MeV ( old : kb = cm/MeV) Default Geant4: Effective Birks coefficient needed in order to describe data correctly (kb is step-size dependent) Integral method allows to calculate precisely the visible energy deposition for each step (kb is step-size independent) To Do Study influence of new kb and new method on simulated particle showers Test performance of integral method
19 14 Reference(s) [1] Stefan Wagner, Ionization Quenching by Low Energy Electrons in the Double Chooz Scintillators, Diploma Thesis (20)
20 Backup 15
21 16 Alexander Tadday - CALICE Collaboration Meeting - Casablanca Step-limitation in GEANT4 Every registered process sets a limit on the the step-size The smallest limit is chosen for each step For ionization process, Stepping function determines the maximum step-size allowed Δxmax (high energy) (low energy) - ρ: Final range (Default value: 1mm) - α: dr/r (Default value: 0.2) Small values of ρ and α result in a small step size
22 17 Alexander Tadday - CALICE Collaboration Meeting - Casablanca Step Function!S lim [m] Final range ρr=1mm slope αr= Range [m]
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