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

2. Introduction The Models Results and Comparison Conclusions Overview

3. Both Lelaps and G EANT 4 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. Introduction

4. * S.Agostinelli et al., Nuclear Instruments and Methods A 506 (2003) 250-303. Introduction: G EANT 4 G EANT 4 * is a simulation toolkit that models a particle’s interaction with matter using a wide range of physics processes. G EANT 4 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 G EANT 4 and source code visit http://geant4.web.cern.ch/geant4/

5. View http://www.slac.stanford.edu/~wglp09/Lelaps.ppt to learn more about Lelaps Introduction: Lelaps Lelaps is capable of faster, but less detailed simulations than G EANT 4. 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.

6. Introduction: 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.

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

8. 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

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 G EANT 4 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 G EANT 4, 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 G EANT 4 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 G EANT 4 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 Slice indexEnergy Cesium Iodide Calorimeter at 10 GeV

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

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

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

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

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

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

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

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

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

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 Beam Energy Slice index Small Hadron Calorimeter – Pi-

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

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

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

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 G EANT 4, 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