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Parameterized Shower Simulation

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									Parameterized Shower Simulation in Lelaps: a
          Comparison with Geant4




     Daniel Birt, Amy Nicholson
                   Overview

• Introduction


• The Models


• Results and Comparison


• Conclusions
                    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.
                       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.
                  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
                    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)
     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


                                                               x



           *G.   Grindhammer and S. Peters, arXiv:hep-ex/0001020v1 (2000)
    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)
     • 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 Geometry
• In our comparison of GEANT4 and Lelaps we use an
electromagnetic calorimeter, two hadron calorimeters, a
luminosity monitor, and a CsI calorimeter.
                                        Layers
• Each detector is divided into
20 radial layers that are 1cm
thick.
• In Lelaps, the detectors are
                                                                                     Slices
composed of slices of equal       Beam Direction
width.                                             Basic layout of the calorimeter

•In GEANT4, slices are of different materials and widths.
• Only layers made of scintillator, silicon, or CsI are sensitive
detectors.
  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.
                 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).
                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.
                 EM Showers: Longitudinal Profiles


                         Cesium Iodide Calorimeter at 10 GeV
         1,700                                                          GEANT4
                                                                        Lelaps
         1,600
         1,500
                           CsI Detector : Longitudinal Profile
         1,400
         1,300
         1,200
         1,100
         1,000
Energy




          900
          800
          700
          600
          500
          400
          300
          200
          100
             0
                 2   4      6     8       10        12   14   16   18    20


                                      Slice index
                           EM Showers: Longitudinal Profiles
                   Large EM Calorimeter at 10 GeV
         800                                              GEANT4
                                                          Lelaps
         750

         700

         650

         600

         550

         500
Energy




         450

         400

         350

         300

         250

         200                                                                      Luminosity Monitor at 10 GeV
         150

         100                                                       700                                                  GEANT4
                                                                                                                        Lelaps
          50
                                                                   650
           0
               5      10    15       20    25   30   35       40   600

                                                                   550

                                 Slice index                       500

                                                                   450

                                                                   400

                                                                   350

                                                                   300

                                                                   250

                                                                   200

                                                                   150

                                                                   100

                                                                    50

                                                                     0
                                                                         5   10      15   20   25   30   35   40   45       50
                             Shower Maximum Positions
                                        Cesium Iodide Calorimeter


                7.5
                         Geant4
                7.0
                6.5      Lelaps
                6.0
                5.5
Slice index




                5.0
                4.5
                4.0
                3.5
                3.0
                2.5
                2.0
                1.5
                1.0
                0.5
                0.0
              - 0.5
                  0.01            0.1            1            10    100   1000

                                                Beam Energy
                         Shower Maximum Positions

                                Large EM Calorimeter
              18
                      Geant4
              16      Lelaps

              14

              12
Slice index




              10

               8

               6

               4

               2

               0
               0.01       0.1      1                 10   100   1000

                                       Beam Energy
                                             Longitudinal: Mean & RMS
                                      Cesium Iodide Mean
              9.0
              8.5      Geant4
              8.0      Lelaps
              7.5
              7.0
              6.5
Slice index




              6.0
              5.5
              5.0
              4.5
              4.0
              3.5
                                                                                            Cesium Iodide RMS
              3.0
              2.5                                                  3.6
              2.0                                                  3.4       Geant4
              1.5                                                  3.2       Lelaps
              1.0                                                  3.0
              0.5                                                  2.8
                0.01            0.1          1         10   100
                                                                   2.6

                                         Beam Energy               2.4
                                                                   2.2
                                                                   2.0
                                                                   1.8
                                                                   1.6
                                                                   1.4
                                                                   1.2
                                                                   1.0
                                                                   0.8
                                                                   0.6
                                                                   0.4
                                                                   0.2
                                                                   0.0
                                                                  - 0.2
                                                                      0.01            0.1        1        10    100
                                            Longitudinal: Mean & RMS
                                     Large EM Mean
              20
              19      Geant4
              18      Lelaps
              17
              16
              15
              14
              13
              12
Slice index




              11
              10
               9
               8
               7
               6
               5                                                                         Large EM RMS
               4
               3
               2
                                                                 7.5
               1
                                                                          Geant4
               0                                                 7.0
               0.01            0.1          1         10   100            Lelaps
                                                                 6.5


                                        Beam Energy              6.0

                                                                 5.5

                                                                 5.0

                                                                 4.5

                                                                 4.0

                                                                 3.5

                                                                 3.0

                                                                 2.5

                                                                 2.0

                                                                 1.5

                                                                 1.0

                                                                 0.5

                                                                 0.0
                                                                   0.01            0.1     1       10   100
                                            Fluctuations: Mean & RMS
                            Cesium Iodide Mean
              9.0
                       Geant4
              8.5
                       Lelaps
              8.0
              7.5
              7.0
              6.5
Slice index




              6.0
              5.5
              5.0                                                             Cesium Iodide RMS
              4.5
              4.0
              3.5
                                                               1.9                                      Geant4
              3.0
                                                               1.8                                      Lelaps
              2.5
                                                               1.7
              2.0                                              1.6
              1.5                                              1.5
              1.0                                              1.4
              0.5                                              1.3
                0.01            0.1     1           10   100
                                                               1.2
                                                               1.1

                                      Beam Energy              1.0
                                                               0.9
                                                               0.8
                                                               0.7
                                                               0.6
                                                               0.5
                                                               0.4
                                                               0.3
                                                               0.2
                                                               0.1
                                                               0.0
                                                                 0.01   0.1         1       10    100
                                         Fluctuations: Mean & RMS

                                     Large EM Mean
              20
              19      Geant4
              18      Lelaps
              17
              16
              15
              14
Slice index




              13
              12
              11
              10
               9
               8
               7                                                             Large EM RMS
               6
               5
               4                                              4.4                                 Geant4
               3                                              4.2                                 Lelaps
               2                                              4.0
               1                                              3.8
               0                                              3.6
               0.01            0.1       1         10   100
                                                              3.4
                                                              3.2

                                     Beam Energy              3.0
                                                              2.8
                                                              2.6
                                                              2.4
                                                              2.2
                                                              2.0
                                                              1.8
                                                              1.6
                                                              1.4
                                                              1.2
                                                              1.0
                                                              0.8
                                                              0.6
                                                              0.4
                                                              0.2
                                                                0.01   0.1     1       10   100
                                  EM Showers: Radial Profiles
                                                   Cesium Iodide Calorimeter

          40            Slice 1      GEANT4          2.0             Slice 2       GEANT4        0.6       Slice 3      GEANT4
                                     Lelaps                                        Lelaps        0.5                    Lelaps
          30                                         1.5
                                                                                                 0.4
30 MeV    20                                         1.0                                         0.3
                                                                                                 0.2
          10                                         0.5
                                                                                                 0.1
           0                                         0.0                                         0.0
                   5       10      15     20                   5        10        15        20         5        10     15        20



          150          Slice 1       GEANT4          600           Slice 8         GEANT4        1.5       Slice 18     GEANT4
                                     Lelaps                                        Lelaps                               Lelaps
          100                                        400                                         1.0
10 GeV
           50                                        200                                         0.5

               0                                       0                                         0.0
                   5        10      15        20               5        10        15        20         5        10     15        20



          200           Slice 1      GEANT4          15,000         Slice 10       GEANT4        150        Slice 20    GEANT4
                                     Lelaps                                        Lelaps                               Lelaps
          150
                                                     10,000                                      100
300 GeV   100
                                                      5,000                                       50
           50
               0                                           0                                       0
                   5        10      15        20                    5        10    15       20         5        10     15        20
                             EM Showers: Radial Profiles
                                                 Large EM Calorimeter

          15       Slice 2         GEANT4        1.2           Slice 3         GEANT4        0.8       Slice 5          GEANT4
                                   Lelaps        1.0                           Lelaps                                   Lelaps
                                                                                             0.6
          10                                     0.8
30 MeV                                           0.6                                         0.4
           5                                     0.4
                                                                                             0.2
                                                 0.2
           0                                     0.0                                         0.0
                   5        10    15    20                 5        10        15        20             5       10      15        20



          80       Slice 2         GEANT4        600           Slice 6         GEANT4        400       Slice 16         GEANT4
                                   Lelaps                                      Lelaps                                   Lelaps
          60                                                                                 300
                                                 400
10 GeV    40                                                                                 200
                                                 200
          20                                                                                 100
           0                                       0                                           0
                   5        10    15    20                 5        10        15        20             5       10      15        20



          150                      GEANT4        10,000                        GEANT4        10,000                     GEANT4
                       Slice 2                                 Slice 8                                     Slice 20
                                   Lelaps                                      Lelaps                                   Lelaps
                                                  7,500                                       7,500
          100
300 GeV                                           5,000                                       5,000
           50
                                                  2,500                                       2,500
               0                                       0                                           0
                   5         10   15        20                  5        10    15       20                 5      10    15       20
     Hadronic Showers
Showers caused by incident hadronic
particles (protons, pi-)


Lelaps uses the Bock parameterization
for longitudinal profiles.
                Hadronic Showers: Longitudinal Profiles
            Hadron Calorimeter – Proton
300                                                             GEANT4
                                                                Lelaps
280

260

240

220

200

180

160

140

120

100

 80

 60
                                                                                          Hadron Calorimeter – Pi-
 40

 20                                                                                                                                      GEANT4
                                                                          500
  0                                                                                                                                      Lelaps
      10   20    30   40   50   60   70   80   90   100   110       120
                                                                          450


                                                                          400


                                                                          350


                                                                          300


                                                                          250


                                                                          200


                                                                          150


                                                                          100


                                                                           50


                                                                            0
                                                                                10   20   30   40   50   60   70   80   90   100   110       120
          Hadronic Showers: Longitudinal Profiles
          Small Hadron Calorimeter – Pi-
600                                             GEANT4
                                                Lelaps
550

500

450

400

350

300

250

200

150

100
                                                                    Small Hadron Calorimeter – Proton
 50

  0                                                       650                                            GEANT4
      5       10     15     20     25      30        35                                                  Lelaps
                                                          600

                                                          550

                                                          500

                                                          450

                                                          400

                                                          350

                                                          300

                                                          250

                                                          200

                                                          150

                                                          100

                                                           50

                                                            0
                                                                5        10     15    20     25     30        35
                                     Shower Maximum Position
                      Small Hadron Calorimeter – Protons
              18
                      lelaps
              16      geant4


              14
Slice index




              12

              10

               8

               6

               4

               2

               0
               0.01            0.1    1            10           100                  1000


                                     Beam Energy
                                                                           Small Hadron Calorimeter – Pi-
                                                        18
                                                                      lelaps
                                                        16            geant4

                                                        14

                                                        12

                                                        10

                                                         8

                                                         6

                                                         4

                                                         2

                                                         0
                                                         0.01                  0.1          1   10      100   1000
                                       Longitudinal: Mean & RMS
                         Hadron Calorimeter Mean – Protons
              55
                      Geant4
              50      Lelaps
              45

              40
Slice index




              35

              30

              25

              20

              15                                                      Hadron Calorimeter RMS – Protons
              10
                                                              32
               5                                              30
                                                                      Geant4
                                                              28
                                                                      Lelaps
               0
               0.01            0.1      1          10   100   26
                                                              24
                                     Beam Energy              22
                                                              20
                                                              18
                                                              16
                                                              14
                                                              12
                                                              10
                                                               8
                                                               6
                                                               4
                                                               2
                                                               0
                                                              -2
                                                               0.01            0.1   1   10      100
                                     Fluctuations: Mean & RMS
                      Hadron Calorimeter Mean – Protons
              55
                      Geant4
              50      Lelaps

              45

              40
Slice index




              35

              30

              25

              20

              15




                                                                      Hadron Calorimeter RMS – Protons
              10

               5

               0
               0.01            0.1     1           10   100   24
                                                                       Geant4
                                                              22
                                     Beam Energy                       Lelaps
                                                              20

                                                              18

                                                              16

                                                              14

                                                              12

                                                              10

                                                               8

                                                               6

                                                               4

                                                               2

                                                               0
                                                               0.01             0.1   1    10      100
                    Hadronic Showers: Radial Profiles
                                  Hadron Calorimeter – 10 GeV Protons

70                                               GEANT4

65
                 Hadron Slice 1                  Lelaps


60

55

50

45

40

35

30

25

20

15

10
                                                          130                                                GEANT4
 5
                                                          120
                                                                             Hadron Slice 8                  Lelaps

 0
     2   4   6      8   10   12   14   16   18     20     110

                                                          100

                                                           90

                                                           80

                                                           70

                                                           60

                                                           50

                                                           40

                                                           30

                                                           20

                                                           10

                                                            0

                                                          - 10
                                                                 2   4   6      8   10   12   14   16   18     20
                      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.
                   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.
            Acknowledgements
• The SULI Program
• Our Mentors:
  • Willy Langeveld
  • Dennis Wright

								
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