Parameterized Shower Simulation in Lelaps: a Comparison with Geant4

1. Parameterized Shower Simulation in Lelaps: a Comparison with Geant4 4 Daniel Birt, Amy Nicholson

2. Overview • Introduction • The Models • Results and Comparison • Conclusions

3. Introduction • 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.

4. Introduction: GEANT4 • 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/ *S.Agostinelli et al., Nuclear Instruments and Methods A 506 (2003) 250-303.

5. Introduction: 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. View http://www.slac.stanford.edu/~wglp09/Lelaps.ppt to learn more about Lelaps

6. Introduction: Showers • 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. A simulation of a shower generated with EGS (picture from http://www2.slac.stanford.edu/vvc/egs/about/about.html)

7. x Introduction: 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. An example longitudinal profile given by the Grindhammer, Peters parameterization *G. Grindhammer and S. Peters, arXiv:hep-ex/0001020v1 (2000)

8. radius 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

9. 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.

10. The Models: Detector Geometry • In our comparison of GEANT4 and Lelaps we use an electromagnetic calorimeter, two hadron calorimeters, a luminosity monitor, and a CsI calorimeter. • Each detector is divided into 20 radial layers that are 1cm thick. • In Lelaps, the detectors are composed of slices of equal width. Beam Direction • In GEANT4, slices are of different materials and widths. • Only layers made of scintillator, silicon, or CsI are sensitive detectors.

11. Detector 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.

12. The 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).

13. The 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.

14. EM Showers: Longitudinal Profiles CsI Detector : Longitudinal Profile Cesium Iodide Calorimeter at 10 GeV Energy Slice index

15. EM Showers: Longitudinal Profiles Large EM Calorimeter at 10 GeV Energy Luminosity Monitor at 10 GeV Slice index

16. Shower Maximum Positions Cesium Iodide Calorimeter Slice index Beam Energy

17. Shower Maximum Positions Large EM Calorimeter Slice index Beam Energy

18. Longitudinal: Mean & RMS Cesium Iodide Mean Slice index Cesium Iodide RMS Beam Energy

19. Longitudinal: Mean & RMS Large EM Mean Slice index Large EM RMS Beam Energy

20. Fluctuations: Mean & RMS Cesium Iodide Mean Cesium Iodide RMS Slice index Beam Energy

21. Fluctuations: Mean & RMS Large EM Mean Slice index Large EM RMS Beam Energy

22. EM Showers: Radial Profiles Cesium Iodide Calorimeter Slice 1 Slice 2 Slice 3 30 MeV Slice 1 Slice 8 Slice 18 10 GeV Slice 1 Slice 10 Slice 20 300 GeV

23. Slice 5 Slice 2 Slice 3 Slice 2 Slice 6 Slice 16 Slice 2 Slice 8 Slice 20 EM Showers: Radial Profiles Large EM Calorimeter 30 MeV 10 GeV 300 GeV

24. Hadronic Showers Showers caused by incident hadronic particles (protons, pi-) Lelaps uses the Bock parameterization for longitudinal profiles.

25. Hadronic Showers: Longitudinal Profiles Hadron Calorimeter – Proton Hadron Calorimeter – Pi-

26. Hadronic Showers: Longitudinal Profiles Small Hadron Calorimeter – Pi- Small Hadron Calorimeter – Proton

27. Shower Maximum Position Small Hadron Calorimeter – Protons Slice index Beam Energy Small Hadron Calorimeter – Pi-

28. Longitudinal: Mean & RMS Hadron Calorimeter Mean – Protons Slice index Hadron Calorimeter RMS – Protons Beam Energy

29. Fluctuations: Mean & RMS Hadron Calorimeter Mean – Protons Slice index Hadron Calorimeter RMS – Protons Beam Energy

30. Hadronic Showers: Radial Profiles Hadron Calorimeter – 10 GeV Protons Hadron Slice 1 Hadron Slice 8

31. Conclusions • 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.

32. Conclusions • 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.

33. Acknowledgements • The SULI Program • Our Mentors: • Willy Langeveld • Dennis Wright