1. TJR 9/24/031 Update: Geant4 Simulations of the MICE Beamline – Absolute Normalization Tom Roberts Illinois Institute of Technology 9/24/03 (With thanks to Paul Drumm for great assistance)

2. TJR 9/24/032 Updates from 9/24/03 video discussion Target intersecting beam: 10 mm 2 => 2 mm 2 Layout of beamline added G4beamline input file added (gives geometrical details)

3. TJR 9/24/033 Goals Compute the absolute normalization of the beamline –Mu/sec at Diffuser1 –Good Mu/sec through the MICE detector –Singles rates in the beamline Generate lots of muons at Diffuser1 to use in optimization studies of the MICE detector

4. TJR 9/24/034 MICE Beamline Layout ISIS Beam B2 = 30° Decay Solenoid, 3 T B1 = 60° MICE Target Q1 Q2 Q3 Diffuser1 Here Old line (ignore) Angle = 25°

5. TJR 9/24/035 G4beamline Input File (1 of 3) # define basic parameters; startEvent comes from the commandline param pionP=300.0 muP=200.0 histoFile=$startEvent histoUpdate=100000 # sigma<0 means flat distribution, that half-width beam rectangular beamWidth=4.22 beamHeight=2 meanMomentum=$pionP particle=pi+\ sigmaXp=-0.0143 sigmaYp=-0.0369 sigmaP=-55 nEvents=100000000 # define the decay solenoid; put into a group so it can be rotated (all other elements # can be rotated on their own) coil default material=Cu dR=5.0 dZ=5.0 coil Decay innerRadius=200.0 outerRadius=250.0 length=5000.0 solenoid DecayS coilName=Decay current=47.94 color=1,0,0 group DecaySolenoid place DecayS rename='' endgroup # define shielding. Tubs = tube solid tubs SolenoidBody innerRadius=250 outerRadius=1000 length=5000 kill=1 tubs TargetShield innerRadius=101.6 outerRadius=1000 length=1 kill=1

6. TJR 9/24/036 G4beamline Input File (2 of 3) # define the magnets param Q1g=-1.0879963 Q2g=1.2981088 Q3g=-0.61072278 idealquad Q1 fieldLength=853.44 fieldRadius=101.6 gradient=$Q1g \ ironRadius=381 ironLength=1104.9 ironColor=0,.6,0 kill=1 idealquad Q2 fieldLength=853.44 fieldRadius=101.6 gradient=$Q2g \ ironRadius=381 ironLength=1104.9 ironColor=0,0,.6 kill=1 idealquad Q3 fieldLength=853.44 fieldRadius=101.6 gradient=$Q3g \ ironRadius=381 ironLength=1104.9 ironColor=0,.6,0 kill=1 mappedmagnet B1 mapname=RALBend1 Bfield=-0.9646 \ fieldWidth=660.4 fieldHeight=152 fieldLength=2000 fieldColor='' \ ironLength=1397 ironHeight=1320 ironWidth=1981 ironColor=1,1,0 kill=1 mappedmagnet B2 mapname=RALBend1 Bfield=-0.3512 \ fieldWidth=660.4 fieldHeight=152 fieldLength=2000 fieldColor='' \ ironLength=1397 ironHeight=1320 ironWidth=1981 ironColor=1,1,0 kill=1 # define detectors (tracks which intersect them are put into an NTuple) detector Diffuser1 radius=250 length=1.0 color=0,1,1 asciifile Diffuser1a radius=250 length=1.0 file=$startEvent

7. TJR 9/24/037 G4beamline Input File (2 of 3) # Place the defined elements into the beamline. # The z coordinate is the centerline of the beamline; x=beam left, y=up. # Each corner bends the beamline appropriately (Y30 => rotate around y by 30 degrees) place TargetShield z=2441 place Q1 z=3000 place Q2 z=4400 place Q3 z=5800 place B1 z=7855.8 rotation=Y30.0 x=250 corner B1c z=8000 rotation=Y60.0 place DecaySolenoid z=12200 place SolenoidBody z=12200 place B2 z=16135 rotation=Y15.8 x=175 corner B2c z=16185 rotation=Y31.7 place Diffuser1 z=18800 place Diffuser1a z=18801

8. TJR 9/24/038 The Bottom Line Protons/sec in accelerator:3.7×10 16 Protons/sec intersecting target:1.7×10 12 Pions/sec into beamline accept.:3.0×10 6 Pi + + Mu + /sec at Diffuser1:37k Mu + /sec at Diffuser1:25k Good Mu + /sec through the detector:54 All of these “per sec” occur during the 1 ms per second when our target is in the beam and our RF is active.

9. TJR 9/24/039 Comparison to the MICE proposal Mu + /sec at Diffuser1: –MICE Proposal: 3,000 –This computation: 25,000 Major differences: –700 MeV/c protons → 800 MeV/c –Target geometry: Height = 2 mm → 10 mm –Diffuser1 geometry: r=20 cm → 25 cm Diffuser1-B2 = 3 m → 2 m These differences account for a factor of ~6

10. TJR 9/24/0310 The Details (1 of 2)

11. TJR 9/24/0311 The Details (2 of 2)

12. TJR 9/24/0312 Additional Slides (From my 7/30/03 talk) The following plots are all at Diffuser1.

13. TJR 9/24/0313 MICE Beam Layout and Tune Layout from “LAYOUT-MICE 14May03” –Bend 1 is 60°, Bend 2 is 30° –Target to Diffuser1 is 18.8 m Quad (Type IV) and Bending Magnet (Type I) parameters are from RAL drawings and tables. Fringe fields for Bending Magnets were computed via Laplace’s equation; quads are ideal (no fringe fields). Bend 1 is tuned for 300 MeV/c pions Bend 2 is tuned for 200 MeV/c muons Quads are tuned for maximum mu/pi ratio at Diffuser1 (using minuit) – the triplet is configured DFD (~20% better than FDF) Target re-oriented so a long edge is along the beam.

14. TJR 9/24/0314 Input Beam Pi+ beam 200 MeV/c < P < 400 MeV/c (uniform) dxdz and dydz generated to cover Q1 aperture (uniform) Target is 10 mm high, 10*cos(25°) mm wide (uniform) All materials kill tracks instantly, without secondaries

15. TJR 9/24/0315 Momentum at Diffuser1

16. TJR 9/24/0316 P at Q1 for mu+ at Diffuser1

17. TJR 9/24/0317 Mu+ Correlation Matrix (normalized) XYdxdzdydzPt X 1.00000.00480.72360.0169-0.08400.0006 Y 0.00481.0000-0.02800.86500.0074-0.0127 dxdz 0.7236-0.02801.0000-0.0389-0.45380.0121 dydz 0.01690.8650-0.03891.00000.00810.0055 P -0.08400.0074-0.45380.00811.0000-0.0157 t 0.0006-0.01270.01210.0055-0.01571.0000 P < 250 MeV/c

18. TJR 9/24/0318 Mu+ X vs Y

19. TJR 9/24/0319 Pi+ X vs Y

20. TJR 9/24/0320 Mu+ X vs P

21. TJR 9/24/0321 Pi+ X vs P

22. TJR 9/24/0322 Mu+ X’ vs P Note where X’=0 is.

23. TJR 9/24/0323 Pi+ X’ vs P Note where X’=0 is.

24. TJR 9/24/0324 Mu+ X vs X’ Note where X’=0 is.

25. TJR 9/24/0325 Pi+ X vs X’ Note where X’=0 is.