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Parameterized Shower Simulation in Lelaps: a Comparison with Geant4
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Parameterized Shower Simulation Parameterized Shower Simulation in Lelaps: a Comparison with in Lelaps: a Comparison with Geant4 Geant4 Daniel Birt, Amy Nicholson
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Parameterized Shower Simulation in Lelaps: a Comparison with Geant4. 4. Daniel Birt, Amy Nicholson. Overview. Introduction The Models Results and Comparison Conclusions. Introduction. - PowerPoint PPT Presentation
Transcript of Parameterized Shower Simulation in Lelaps: a Comparison with Geant4
Parameterized Shower Simulation in Lelaps: a Parameterized Shower Simulation in Lelaps: a Comparison with Geant4Comparison with Geant4
Daniel Birt, Amy Nicholson
• Introduction
• The Models
• Results and Comparison
• Conclusions
OverviewOverview
• Both Lelaps and GEANT4 are C++ toolkits used for simulating the passage of particles through materials.
• The simulation of particles passing through materials has applications in many fields, including medicine, astronomy, and high-energy physics.
• Physicists are often interested in simulating showers in particle detectors.
IntroductionIntroduction
*S.Agostinelli et al., Nuclear Instruments and Methods A 506 (2003) 250-303.
Introduction: GIntroduction: GEANTEANT44
• GEANT4* is a simulation toolkit that models a particle’s interaction with matter using a wide range of physics processes.
• GEANT4 is typically used to simulate detailed, inhomogeneous detector geometries.
• Individual particles are tracked through a material. These particles create showers of secondary particles, all of which are tracked to zero energy.
•For more information on GEANT4 and source code visit http://geant4.web.cern.ch/geant4/
View http://www.slac.stanford.edu/~wglp09/Lelaps.ppt to learn more about Lelaps
Introduction: LelapsIntroduction: Lelaps
• Lelaps is capable of faster, but less detailed simulations than GEANT4.
• The key to faster simulations with Lelaps is the ability to parameterize particle showers.
• When using shower parameterization in Lelaps, detectors have simple construction and the entire detector is represented as a homogeneous media.
• With shower parameterization, sensitive detector regions are not distinguished.
Introduction: ShowersIntroduction: Showers
A simulation of a shower generated with EGS
(picture from http://www2.slac.stanford.edu/vvc/egs/about/about.html)
• When charged particles travel through matter their energy can be used to generate many other particles creating a shower.
• The shower spreads the incident particle’s energy throughout the material.
Introduction: Shower Parameterization in LelapsIntroduction: Shower Parameterization in Lelaps
• Electromagnetic showers are parameterized using the algorithms of Grindhammer and Peters*
• Longitudinal shower profiles are calculated for each particle of the incident beam.
*G. Grindhammer and S. Peters, arXiv:hep-ex/0001020v1 (2000)
An example longitudinal profile given by the Grindhammer, Peters parameterization
x
Shower Parameterization in Lelaps (continued)Shower Parameterization in Lelaps (continued)
•Radial shower profiles are calculated at steps of one radiation length along the beam direction.
An example radial shower profile given by the parameterization used in Lelaps
radius
Shower Parameterization in Lelaps (continued)Shower Parameterization in Lelaps (continued)
• Hadronic showers are parameterized in much the same way as electomagnetic showers.
• Longitudinal hadronic shower profiles are created using the Bock* parameterization.
• For radial hadronic shower profiles, Lelaps uses the Grindhammer and Peters parameterization but with interaction lengths replacing radiation lengths.
* R.K. Bock, T. Hansl-Kozanecka and T.P. Shah, Nucl. Instr. And Meth. 186 (1981) 533.
The Models: Detector GeometryThe Models: Detector Geometry
Layers
Slices
Basic layout of the calorimeter
• In our comparison of GEANT4 and Lelaps we use an electromagnetic calorimeter, two hadron calorimeters, a luminosity monitor, and a CsI calorimeter.
Beam Direction
• Each detector is divided into 20 radial layers that are 1cm thick.
• In Lelaps, the detectors are composed of slices of equal width.
•In GEANT4, slices are of different materials and widths.
• Only layers made of scintillator, silicon, or CsI are sensitive detectors.
Detector Geometry: Electromagnetic CalorimeterDetector Geometry: Electromagnetic Calorimeter
• The EM calorimeter, for example, in GEANT4 consists of slices of 0.4 cm lead, 0.04 cm air, 0.01 cm Tyvek, 0.1 cm scintillator, 0.01 cm Tyvek, and 0.04 cm air.
• The scintillator slices are the sensitive regions.
• This unit is repeated 40 times along the longitudinal axis of the calorimeter.
• In Lelaps, the EM calorimeter is made of slices that are 0.6 cm wide and composed of 66% lead, 13.2% air, 3.3% Tyvek, and 16.5% scintillator.
The Models: BeamsThe Models: Beams
• We ran events in all five detectors at energies ranging from 30 MeV to 300 GeV.
• In each event, a particle is sent through the detector
• For the EM calorimeters (CsI, EM, luminosity monitor) we used electrons.
• For the hadron calorimeters we used protons and pions.
• We ran approximately 1000 events for each particle at each energy (fewer events for the most time consuming simulations).
The Models: DataThe Models: Data
• In both GEANT4 and Lelaps we created histograms showing …
• the energy deposited in each slice for every detector at every energy.
• the energy deposited in each layer of every slice for each case.
• the fluctuations in the mean of the longitudinal profile for each event.
EM Showers: Longitudinal ProfilesEM Showers: Longitudinal Profiles
CsI Detector : Longitudinal Profile
Slice index
2 4 6 8 10 12 14 16 18 200
100
200
300
400
500
600
700
800
900
1,000
1,100
1,200
1,300
1,400
1,500
1,600
1,700Lelaps
GEANT4
Ene
rgy
Cesium Iodide Calorimeter at 10 GeV
EM Showers: Longitudinal ProfilesEM Showers: Longitudinal Profiles
5 10 15 20 25 30 35 400
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800Lelaps
GEANT4
5 10 15 20 25 30 35 40 45 500
50
100
150
200
250
300
350
400
450
500
550
600
650
700Lelaps
GEANT4
Large EM Calorimeter at 10 GeV
Luminosity Monitor at 10 GeV
Slice index
Ene
rgy
Shower Maximum PositionsShower Maximum Positions
Cesium Iodide Calorimeter
Beam Energy
Sli
ce in
dex
0.01 0.1 1 10 100 1000- 0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Lelaps
Geant4
Shower Maximum PositionsShower Maximum Positions
Large EM Calorimeter
Sli
ce in
dex
Beam Energy 0.01 0.1 1 10 100 10000
2
4
6
8
10
12
14
16
18
Lelaps
Geant4
Longitudinal: Mean & RMSLongitudinal: Mean & RMS
0.01 0.1 1 10 1000.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
Lelaps
Geant4
Cesium Iodide Mean
0.01 0.1 1 10 100- 0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
Lelaps
Geant4
Cesium Iodide RMS
Sli
ce in
dex
Beam Energy
Longitudinal: Mean & RMSLongitudinal: Mean & RMSLarge EM Mean
0.01 0.1 1 10 1000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Lelaps
Geant4
Large EM RMSSli
ce in
dex
Beam Energy
0.01 0.1 1 10 1000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Lelaps
Geant4
Fluctuations: Mean & RMSFluctuations: Mean & RMS
0.01 0.1 1 10 1000.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
Lelaps
Geant4
Cesium Iodide Mean
0.01 0.1 1 10 1000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Lelaps
Geant4
Cesium Iodide RMS
Beam Energy
Sli
ce in
dex
Fluctuations: Mean & RMSFluctuations: Mean & RMS
0.01 0.1 1 10 1000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Lelaps
Geant4
0.01 0.1 1 10 1000.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
Lelaps
Geant4
Large EM Mean
Large EM RMSSli
ce in
dex
Beam Energy
EM Showers: Radial ProfilesEM Showers: Radial Profiles
5 10 15 200
50
100
150Lelaps
GEANT4
5 10 15 200.0
0.5
1.0
1.5Lelaps
GEANT4
5 10 15 200.00.10.20.30.40.50.6
Lelaps
GEANT4
5 10 15 200
5,000
10,000
15,000Lelaps
GEANT4
5 10 15 200
200
400
600Lelaps
GEANT4
5 10 15 200.0
0.5
1.0
1.5
2.0Lelaps
GEANT4
5 10 15 200
50
100
150
200Lelaps
GEANT4
5 10 15 200
50
100
150Lelaps
GEANT4
5 10 15 200
10
20
30
40Lelaps
GEANT4
30 MeV
10 GeV
300 GeV
Slice 20
Slice 1
Slice 1
Slice 2
Slice 8
Slice 10
Slice 3
Slice 18
Slice 1
Cesium Iodide Calorimeter
EM Showers: Radial Profiles
5 10 15 200
2,500
5,000
7,500
10,000Lelaps
GEANT4
5 10 15 200
100
200
300
400Lelaps
GEANT4
5 10 15 200.0
0.2
0.4
0.6
0.8Lelaps
GEANT4
5 10 15 200
2,500
5,000
7,500
10,000Lelaps
GEANT4
5 10 15 200
200
400
600Lelaps
GEANT4
5 10 15 200.00.20.40.60.81.01.2
Lelaps
GEANT4
5 10 15 200
50
100
150Lelaps
GEANT4
5 10 15 200
20
40
60
80Lelaps
GEANT4
5 10 15 200
5
10
15Lelaps
GEANT4 Slice 2
Slice 2
Slice 2
Slice 3
Slice 6
Slice 8
Slice 5
Slice 16
Slice 20
30 MeV
10 GeV
300 GeV
Large EM Calorimeter
Hadronic ShowersHadronic Showers
Showers caused by incident hadronic particles (protons, pi-)
Lelaps uses the Bock parameterization for longitudinal profiles.
Hadronic Showers: Longitudinal ProfilesHadronic Showers: Longitudinal Profiles
10 20 30 40 50 60 70 80 90 100 110 1200
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300Lelaps
GEANT4
10 20 30 40 50 60 70 80 90 100 110 1200
50
100
150
200
250
300
350
400
450
500Lelaps
GEANT4
Hadron Calorimeter – Proton
Hadron Calorimeter – Pi-
Hadronic Showers: Longitudinal ProfilesHadronic Showers: Longitudinal Profiles
5 10 15 20 25 30 350
50
100
150
200
250
300
350
400
450
500
550
600Lelaps
GEANT4
5 10 15 20 25 30 350
50
100
150
200
250
300
350
400
450
500
550
600
650Lelaps
GEANT4
Small Hadron Calorimeter – Pi-
Small Hadron Calorimeter – Proton
Shower Maximum PositionShower Maximum Position
0.01 0.1 1 10 100 10000
2
4
6
8
10
12
14
16
18
geant4
lelaps
0.01 0.1 1 10 100 10000
2
4
6
8
10
12
14
16
18
geant4
lelaps
Small Hadron Calorimeter – Protons
Beam Energy
Sli
ce in
dex
Small Hadron Calorimeter – Pi-
Longitudinal: Mean & RMSLongitudinal: Mean & RMS
0.01 0.1 1 10 1000
5
10
15
20
25
30
35
40
45
50
55
Lelaps
Geant4
0.01 0.1 1 10 100- 2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Lelaps
Geant4
Hadron Calorimeter Mean – Protons
Hadron Calorimeter RMS – ProtonsSli
ce in
dex
Beam Energy
Fluctuations: Mean & RMSFluctuations: Mean & RMS
0.01 0.1 1 10 1000
5
10
15
20
25
30
35
40
45
50
55
Lelaps
Geant4
0.01 0.1 1 10 1000
2
4
6
8
10
12
14
16
18
20
22
24
Lelaps
Geant4
Sli
ce in
dex
Beam Energy
Hadron Calorimeter Mean – Protons
Hadron Calorimeter RMS – Protons
Hadronic Showers: Radial ProfilesHadronic Showers: Radial Profiles
2 4 6 8 10 12 14 16 18 200
5
10
15
20
25
30
35
40
45
50
55
60
65
70Lelaps
GEANT4
2 4 6 8 10 12 14 16 18 20- 10
0
10
20
30
40
50
60
70
80
90
100
110
120
130Lelaps
GEANT4
Hadron Slice 1
Hadron Slice 8
Hadron Calorimeter – 10 GeV Protons
ConclusionsConclusions
• The data produced by Lelaps corresponds best with that of Geant4 under the following conditions:
• In non-segmented calorimeters
• With beam energies above 300 MeV
• For electromagnetic interactions
• The longitudinal profiles correspond better than the radial profiles.
ConclusionsConclusions
• Lelaps gives sufficiently accurate results for some of the most important aspects of a simulation.
• Lelaps will never be as accurate as GEANT4, however in some instances one may be willing to sacrifice precision for time.
• Tuning the parameterization could possibly improve the accuracy of Lelaps.
AcknowledgementsAcknowledgements
• The SULI Program
• Our Mentors:
• Willy Langeveld
• Dennis Wright
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