1. June 13, 20031 Geant4 Simulations of the MICE Beamline Tom Roberts Illinois Institute of Technology June13, 2003

2. 2 Introducing the g4beamline Program A general tool for simulating beamlines, using Geant4 5.1p1. All problem-specific aspects of the simulation are given in a simple ASCII file. The basic idea is to define elements, and then to place them into the system (perhaps multiple times). Centerline coordinates can be used, simplifying layout for beamline-like configurations. –Centerline coordinates are piecewise-straight, with the z axis down the nominal centerline of the beamline. –The centerline coordinates {x,y,z} rotate at a corner (bending magnet), as do all elements placed after the corner. By default, objects are simply lined up along the centerline; specific locations and rotations can also be given. The complexity of the description matches the complexity of the problem.

3. June 13, 20033 The MICE Beamline Simulation Decay Solenoid: –Accurate magnetic map computed via infinitely-thin sheets –Map parameters (# sheets,nR,nZ,dR,dZ,length) are determined automatically, given the required accuracy (0.0002 relative accuracy used) Quadrupole Magnets: –Perfect and constant block fields used. –No fringe fields. Bending Magnets: –Fringe field computation - Laplace’s Equation for magnetic potential –Assume infinitely-wide –Computation done using Excel, 1 mm grid –Solution extended in Y and Z via symmetry Pole Solution Region

4. June 13, 20034 RAL Type I bending Magnet Model

5. June 13, 20035 micebeam.in (Input to g4beamline) coil Decay innerRadius=200.0 outerRadius=250.0 length=5000.0 material=Cu solenoid DecayS coilName=Decay current=47.94 color=1,0,0 tubs SolenoidBody innerRadius=250 outerRadius=1000 length=5000 kill=1 group DecaySolenoid length=5000 place DecayS z=0 place SolenoidBody z=0 endgroup idealquad default ironRadius=381 ironLength=1104.9 kill=1 idealquad Q1 fieldLength=863.6 fieldRadius=101.6 gradient=2.0 ironColor=0,.6,0 idealquad Q2 fieldLength=863.6 fieldRadius=101.6 gradient=-3.0 ironColor=0,0,.6 idealquad Q3 fieldLength=863.6 fieldRadius=101.6 gradient=0.8 ironColor=0,.6,0 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 detector MICEdiffuser1 radius=250 length=1.0 color=0,1,1 place Q1 z=3000 place Q2 z=4400 place Q3 z=5800 place B1 z=7855.8 rotation=Y30 x=250 corner B1c z=8000 rotation=Y60 place DecaySolenoid z=12200 place B2 z=16135 rotation=Y15.8 x=175 corner B2c z=16185 rotation=Y31.7 place MICEdiffuser1 z=18840 Group Elements together A corner in the centerline Y60 is a 60° rotation around Y; Multiple rotations: Y60,Z45,X90 Kill=1 makes a Perfect Shield. “tubs” is Geant4-speak for a tube or cylinder A detector generates an NTuple The beam and physics specifications are omitted for clarity, as is other basic stuff. Every element has a name Color is R,G,B Omitted=invisible A solenoid is a coil plus a current The coil has a sharable map

6. June 13, 20036 MICE Beamline layout

7. June 13, 20037 Pictures of Simulated Tracks Colors of Tracks: Greenpi+ Bluemu+ Whitee+ Other particles are killed. Colors of Objects: GreenFocusing Quad BlueDefocusing Quad YellowBending Magnet RedDecay Solenoid WhiteWide detector at MICE Z Position The target is at the lower left, with protons not shown – if they were shown they would head 25 degrees down to the lower right. The detector at MICE diffuser1 is much larger than the experimental acceptance, so I can see what’s out there. For quads and the solenoid, only the ends are shown. These pictures are 2-d plan views (not 3-d as the previous picture).

8. June 13, 20038 Good Muon

9. June 13, 20039 π +  μ +  e + Positrons are quite rare.

10. June 13, 200310 Pion There are also a gazillion protons.

11. June 13, 200311 There are many ways for muons to miss

12. June 13, 200312 There are many ways for muons to miss

13. June 13, 200313 There are many ways for muons to miss

14. June 13, 200314 But some are just lucky

15. June 13, 200315 Pions – Beam Loss position along Centerline

16. June 13, 200316 Pions at the MICE Z Position

17. June 13, 200317 Muons at the MICE Z Position

18. June 13, 200318 Protons at the MICE Z Position

19. June 13, 200319 Pion Momentum at the MICE Z position

20. June 13, 200320 Muon Momentum at the MICE Z Position

21. June 13, 200321 Proton Momentum at the MICE Z Position Scale is different – this is quite similar to the π + momentum distribution.

22. June 13, 200322 Conclusions Visualization is essential to verify the layout is correct. g4beamline is a flexible and useful tool for simulations like this. The MICE detector will have significant backgrounds from the beamline – not to mention strays that cannot be accurately modeled, and of course Cosmic Rays. We need to compute normalized fluxes for protons, pions, and muons. Diffuser1 is clearly not needed to “spread out the beam”; Diffuser2 is still required to break the angle-position correlation.