June 13, 2003 1

Geant4 Simulations of the MICE Beamline

Tom Roberts

Illinois Institute of Technology

June13, 2003

June 13, 2003 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.

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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

Pole

Solution RegionSolution RegionSolution Region

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RAL Type I bending Magnet Model

Bend Type 1 (pole half-length=457, Eff-half-length=519)

B fields

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 200 400 600 800 1000

By on AxisBz Halfway up

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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=1,0,0tubs SolenoidBody innerRadius=250 outerRadius=1000 length=5000 kill=1group DecaySolenoid length=5000

place DecayS z=0place SolenoidBody z=0

endgroup

idealquad default ironRadius=381 ironLength=1104.9 kill=1idealquad 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,.6idealquad 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=3000place Q2 z=4400place Q3 z=5800place B1 z=7855.8 rotation=Y30 x=250corner B1c z=8000 rotation=Y60place DecaySolenoid z=12200place B2 z=16135 rotation=Y15.8 x=175corner B2c z=16185 rotation=Y31.7place MICEdiffuser1 z=18840

Group Elements together

A corner in the centerlineY60 is a 60° rotation around Y;

Multiple rotations: Y60,Z45,X90

Kill=1 makes a Perfect Shield.

“tubs” is Geant4-speak for atube or cylinder

A detector generates an NTuple

The beam and physicsspecifications are omitted for clarity, asis other basic stuff.

Every elementhas a name

Color is R,G,BOmitted=invisible

A solenoid is a coil plus a currentThe coil has a sharable map

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MICE Beamline layout

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Pictures of Simulated TracksColors of Tracks:

Green pi+

Blue mu+

White e+

Other particles are killed.

Colors of Objects:

Green Focusing Quad

Blue Defocusing Quad

Yellow Bending Magnet

Red Decay Solenoid

White Wide 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).

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Good Muon

June 13, 2003 9

π+ μ+ e+

Positrons are quite rare.

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Pion

There are also a gazillion protons.

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There are many ways for muons to miss

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There are many ways for muons to miss

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There are many ways for muons to miss

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But some are just lucky

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Pions – Beam Loss position along Centerline

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Pions at the MICE Z Position

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Muons at the MICE Z Position

June 13, 2003 18

Protons at the MICE Z Position

June 13, 2003 19

Pion Momentum at the MICE Z position

June 13, 2003 20

Muon Momentum at the MICE Z Position

June 13, 2003 21

Proton Momentum at the MICE Z Position

Scale is different – this is quite similar to the π+ momentum distribution.

June 13, 2003 22

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.