Alexander Tadday Kirchhoff Institute for Physics ... - IRTG Heidelberg

Application of Birks' law of 

scintillator nonlinearity in 

Geant4 

Alexander Tadday 

Kirchhoff Institute for Physics 

Heidelberg University 

Alexander Tadday Alexander - IRTG Tadday Meeting - IRTG - Heidelberg Meeting - 05.11.2010

2 

Outline 

• CALICE analogue hadronic calorimeter prototype 

• Birks’ law of scintillator nonlinearity 

• Measurement of Birks’ coefficient (MPIK Heidelberg) 

• Birks’ law in Geant4 

• Conclusion & Discussion 

Alexander Tadday - IRTG Meeting - 05.11.2010

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 (3×3×0.5cm 3 ) 

Wavelength 

shifting fibre 

SiPM 


4 

Birks’ Saturation Formula 

e - 

• Specific energy loss dE/dx is 

high before particle is stopped 

• High ionization density 

dI/dx α dE/dx 

• Quenching: Excited atoms 

can interact and may de-excite radiationless 

• Light yield per unit length dL/dx is reduced for high dE/dx 

• Non-linearity described 

by Birks’ formula: 

scintillator 

dE/dX [MeV/cm] 

3500 

3000 

2500 

2000 

1500 

1000 

500 

0 

0.0005 0.001 0.0015 0.002 

kin energy [MeV] 

Electron collision stopping power 

(Berger-Seltzer eq.) 


Experimental Setup (MPIK Heidelberg) 

5 

• PMT measures light yield 

• Germanium detector measures Energy 

of Compton scattered photon EGe 

• Coincidence trigger PMT and Ge-detector 

• Measured energy range of electrons 

~ 30 - 140 keV 

• Thanks to Christoph Aberle and Stefan 

Wagner for the ability to use the setup 

• Detailed setup description in [1] 

Scintillator 

Germanium 

detector 

137 Cs 

moveable rail 

PMT 


Experimental Setup (MPIK Heidelberg) 

5 

• PMT measures light yield 

• Germanium detector measures Energy 

of Compton scattered photon EGe 

• Coincidence trigger PMT and Ge-detector 

• Measured energy range of electrons 

~ 30 - 140 keV 

• Thanks to Christoph Aberle and Stefan 

Wagner for the ability to use the setup 

• Detailed setup description in [1] 

Scintillator 

Germanium 

detector 

137 Cs 

moveable rail 

PMT 


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: 


7 

kB Measurement (standalone) 

• Experimental data: 

Light-yield as function 

of electron energy 

• Fit with calculated 

Light yield 

➜ Fit parameter kB 

Light yield [a.u.] 

4000 

3500 

3000 

2500 

2000 

1500 

1000 

500 

0 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 

Fit function: Kinetic energy [MeV] 

Fit result: 

kB=0.0151 cm/MeV 

Currently used value: 

kB = 0.007943 cm/MeV 

M. Hirschberg et. al., 

IEEE Trans. Nucl. Sc., Vol. 39, No. 4, 1992 

Data 

Birks' model 

Linear fit (fit range > 0.12MeV) 


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! 


8 


• 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! 


9 


E 

! 

/ 

vis 

E 

! 

1 

0.8 

0.6 

0.4 

0.2 

0 

Curve shows 120keV e - with 

kB=0.0151cm/MeV 

Area under curve 

represents the 

visible energy 

0 0.02 0.04 0.06 0.08 0.1 0.12 

Kinetic energy [MeV] 


9 


Geant4 with default 

settings and 


Visible energy is 

! E 

/ 

vis 

! E 

1 

0.8 

overestimated! Area under curve 

0.6 

0.4 

0.2 

0 



step 2 



step 1 

0 0.02 0.04 0.06 0.08 0.1 0.12 



9 


Geant4 with default 

settings and 


Visible energy is 

Possible solution: 

Use “effective” Birks’ 

coefficient to get the 

correct result 


! E 

/ 

vis 

! E 

1 

0.8 

overestimated! Area under curve 

0.6 

0.4 

0.2 

0 



step 2 



step 1 

0 0.02 0.04 0.06 0.08 0.1 0.12 



10 

effective Birks' coefficient [cm/MeV] 


0.019 

0.018 

0.017 

0.016 

0.015 

0.014 

0.013 

0.012 

10 

-14 

-12 

10 

-10 

10 

-8 

10 

-6 

10 

-4 

10 10 1 

Final range parameter [m] 

qualitatively: 

smaller steps larger steps 

default Geant4 

settings: 

α = 0.2 

Final range = 1mm 

-2 


10 



0.019 

0.018 

0.017 

0.016 

0.015 

0.014 

0.013 

0.012 

10 


-14 

Main disadvantage: 

need different effective Birks’ 

coefficient for different 

parameter configuration 

-12 

10 

-10 

10 

-8 

10 

-6 

10 

-4 

10 10 1 



default Geant4 

settings: 

α = 0.2 

Final range = 1mm 

-2 


11 

• Step-wise integral 

calculation of visible 

energy 

• Use method of Monte 

Carlo integration 

(VEGAS algorithm) 

• Use pre-calculated 

dE/dX to increase 

speed 

Method Improvement 

Default Geant4 Default Geant4 

E 

! 

/ 

vis 

E 

! 

1 

0.8 

0.6 

0.4 

0.2 

0 

0 0.02 0.04 0.06 0.08 0.1 0.12 



12 

• Birks’ coefficient 

independent of final 

range parameter 

(step-size) 

• Residual fluctuation 

from production of 

secondaries (deltaelectrons) 

Method Comparison 


0.019 Default Geant4 

0.018 

0.017 

0.016 

0.015 

0.014 

0.013 

0.012 

10 

-14 

-12 

10 

Integral method 

-10 

10 

-8 

10 

-6 

10 

10 10 1 




Alexander Tadday - IRTG Meeting - 05.11.2010 

-4 

-2

13 

Conclusion & Outlook 

• Measured Birks’ coefficient higher than currently used one 

Measured value: kB = 0.0151cm/MeV (“old”: kB = 0.007943cm/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 


14 

Reference(s) 

• [1] Stefan Wagner, “Ionization Quenching by Low Energy Electrons in the Double Chooz 

Scintillators”, Diploma Thesis (2010) 


Backup 

15

16 

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 

- ρ: Final range (Default value: 1mm) 

- α: dR/R (Default value: 0.2) 

(high energy) 

(low energy) 

➜ Small values of ρ and α result in a small step size 

Alexander Tadday - CALICE Collaboration Meeting - Casablanca - 23.09.2010

17 

[m] 

lim 

S 

! 

0.0035 

0.003 

0.0025 

0.002 

0.0015 

0.001 

0.0005 

Final range 

ρR=1mm 

Step Function 

“slope” 

αR=0.2 

0 

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 

Range [m] 

Alexander Tadday - CALICE Collaboration Meeting - Casablanca - 23.09.2010

Alexander Tadday Kirchhoff Institute for Physics ... - IRTG Heidelberg

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