MCS Multiple Coulomb Scattering Sophie Middleton Introduction In

MCS: Multiple Coulomb Scattering Sophie Middleton

Introduction Ü In MICE Note : MICE 0355 ‘IONIZATION COOLING IN MICE STEP IV’ -Cobb and Carlisle Ü G 4 MICE and PDG Moliere, error bars reflect the stated 11% accuracy of theory: Ü Simulated 10000 muons with p=207 Me. V/c Ü At Z<5 significant difference between PDG and G 4 MICE Ü G 4 MICE based on cooling formula->up to 20% deviation

Implementation

Implementation In MAUS (1) Ü Used MAUS 0. 3. 3 and MAUS 0. 5. 0 Ü Generated tests within the MAUS integration test framework Ü plotter. py, factory. py, geometry. py, all_tests. py, code_setup. py Ü Framework allows comparison with ICOOL and other simulation software

Thicknesses Ü Thickness is derived by scaling at a constant value of 0. 01685 rad i. e. PDG angle for 63 mm Li. H Z Material Thickness/mm 1 Liquid Hydrogen 576 2 Lithium Hydride 63 4 Beryllium 23 6 Carbon 14 Beam Parameters for simulations: 13 Aluminum 5. 8 22 Titanium 2. 3 26 Iron 1. 1 -muon (-) -207 Me. V/c -start with 10000 muons 28 Nickel 1 29 Copper 1

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

Physics Models

MAUS Models Ü Options MCS or none Ü Based on GEANT 4 which uses Urban Model-based on Lewis Theory Ü Two versions of GEANT 4 looked at: Ü GEANT 4. 9. 2. p 04 Ü GEANT 4. 9. 5. p 01

ICOOL Physics Models Ü ICOOL version 3. 30 used Ü RMS calculated for central 99% ->improve statistical stability by removing outliners Ü ICOOL has several interaction models-set: Ü Model level for d. E/dx =2 Ü Bethe-Bloch with density effect Ü Model level for multiple scattering =6 Ü Fano (with Rutherford limit) Ü Also look at SCATLEV=7 ->Tollestrup method Ü Model level for straggling =5 Ü Restricted energy fluctuations from continuous processes with energy below DCUTx.

Results

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

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

Discussion Ü Quantify differences for Li. H between models and PDG: Ü ~17% for MAUS 0. 3. 3. with G 4. 9. 5. p 01 Ü ~8% for MAUS 0. 5. 0 with G 4. 9. 2. p 04 Ü Between 12 -8% for ICOOL

MCS dependency on GEANT 4 version Ü Results show that GEANT 4. 9. 5. p 01 appears more consistent with PDG Ü MCS based on Lewis theory in GEANT 4 Ü Urban Model, based on Lewis Theory. Ü Uses model functions to determine angular & spatial distributions Ü Parameterises tail and centre separately Ü Main difference: G 4 Urban. MCSModel 9. 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 Ü Step length dependency corrected in g 4. 9. 5. p 01

Conclusions

Conclusions Ü From the plots the GEANT 4. 9. 5. p 01 in MAUS version 0. 5. 0 appears to best fit the PDG value within errors Ü Main differences occur for lower Z materials Ü Next Stage in my analysis will be to use the MARS code to do the same Ü After MCS study I will look at energy loss models

MARS Code Ü Set of Monte Carlo programs for simulation of harmonic and electromagnetic cascades Ü Standalone->Not GEANT 4 based Ü SAMCS model used Ü MCS modeled from the Moliere distribution with nuclear form-factors included