1. MCS: Multiple Coulomb Scattering Sophie Middleton

2. Introduction  In MICE Note : MICE0355 ‘ IONIZATION COOLING IN MICE STEP IV’ -Cobb and Carlisle  G4MICE and PDG Moliere, error bars reflect the stated11% accuracy of the theory:  Simulated 10000 muons with p=207MeV/c  At Z<5 significant difference between PDG and G4MICE  G4MICE based on cooling formula->up to 20% deviation

3. Implementation

4. Implementation In MAUS (1)  Used MAUS 0.3.3 and MAUS 0.5.0  Generated tests within the MAUS integration test framework  plotter.py, factory.py, geometry.py, all_tests.py, code_setup.py  Framework allows comparison with ICOOL and other simulation software

5. Thicknesses  Thickness is derived by scaling at a constant value of 0.01685 rad i.e. PDG angle for 63mm LiH ZMaterialThickness/mm 1Liquid Hydrogen576 2Lithium Hydride63 4Beryllium23 6Carbon14 13Aluminum5.8 22Titanium2.3 26Iron1.1 28Nickel1 29Copper1 Beam Parameters for simulations: -muon (-) -207MeV/c -start with 10000 muons

6. Implementation in MAUS (2)  Generate Tests using framework->get set of reference data  Use this to produce 1 D Histogram produced ->get RMS Px->theta= RMS Px/Pz

7. Physics Models

8. MAUS Models  Options MCS or none  Based on GEANT4 which uses Urban Model- based on Lewis Theory  Two versions of GEANT4 looked at:  GEANT4.9.2.p04  GEANT4.9.5.p01

9. ICOOL Physics Models  ICOOL version 3.30 used  RMS calculated for central 99% ->improve statistical stability by removing outliners  ICOOL has several interaction models-set:  Model level for dE/dx =2  Bethe-Bloch with density effect  Model level for multiple scattering =6  Fano (with Rutherford limit)  Also look at SCATLEV=7 ->Tollestrup method  Model level for straggling =5  Restricted energy fluctuations from continuous processes with energy below DCUTx.

10. Results

11. MCS and dependency on step- size  Scattering angle has some dependency on step  MCS in MAUS integration framework is dependent on step size used when step size < material thickness  More apparent for lower Z materials due to method used (i.e. these have larger thickness)

12. MCS dependecy on material in different simulation packages  PDG +/- 11% errors shown along with MAUS and ICOOL simulations  This is the same step-size (1 mm) and scaling as Tim’s plot  Still obvious differences from PDG  Scattering angle dependent on Z of material

13. Discussion  Quantify differences for LiH between models and PDG:  ~17% for MAUS 0.3.3.with G4.9.5.p01  ~8% for MAUS 0.5.0 with G4.9.2.p04  Between 12-8% for ICOOL

14. MCS dependency on GEANT4 version  Results show that GEANT4.9.5.p01 appears more consistent with PDG  MCS based on Lewis theory in GEANT4  Urban Model, based on Lewis Theory.  Uses model functions to determine angular & spatial distributions  Parameterises tail and centre separately  Main difference: G4UrbanMCSModel9.5->improved tail sampling, simplified geom path length if true path length ~range, added protection against numerical problems of sampling scattering with small steps at high energy to avoid back-reflection  Step length dependency corrected in g4.9.5.p01

15. Conclusions

16.  From the plots the GEANT4.9.5.p01 in MAUS version 0.5.0 appears to best fit the PDG value within errors  Main differences occur for lower Z materials  Next Stage in my analysis will be to use the MARS code to do the same  After MCS study I will look at energy loss models

17. MARS Code  Set of Monte Carlo programs for simulation of harmonic and electromagnetic cascades  Standalone->Not GEANT4 based  SAMCS model used  MCS modeled from the Moliere distribution with nuclear form-factors included