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Update:Geant4 Simulations of the MICE

Beamline –Absolute Normalization

Tom RobertsIllinois Institute of Technology

9/24/03(With thanks to Paul Drumm for great

assistance)

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Updates from 9/24/03 video discussion

• Target intersecting beam: 10 mm2 => 2 mm2

• Layout of beamline added• G4beamline input file added (gives geometrical

details)

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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

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MICE Beamline Layout

ISIS Beam

B2 = 30°

DecaySolenoid,

3 T

B1 = 60°

MICETarget

Q1

Q2

Q3

Diffuser1 Here

Old line(ignore)

Angle = 25°

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G4beamline Input File (1 of 3)# define basic parameters; startEvent comes from the commandlineparam pionP=300.0 muP=200.0 histoFile=$startEvent histoUpdate=100000# sigma<0 means flat distribution, that half-widthbeam rectangular beamWidth=4.22 beamHeight=2 meanMomentum=$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=5.0coil Decay innerRadius=200.0 outerRadius=250.0 length=5000.0solenoid DecayS coilName=Decay current=47.94 color=1,0,0group DecaySolenoid

place DecayS rename=''endgroup

# define shielding. Tubs = tube solidtubs SolenoidBody innerRadius=250 outerRadius=1000 length=5000 kill=1tubs TargetShield innerRadius=101.6 outerRadius=1000 length=1 kill=1

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G4beamline Input File (2 of 3)# define the magnetsparam Q1g=-1.0879963 Q2g=1.2981088 Q3g=-0.61072278idealquad Q1 fieldLength=853.44 fieldRadius=101.6 gradient=$Q1g \

ironRadius=381 ironLength=1104.9 ironColor=0,.6,0 kill=1idealquad Q2 fieldLength=853.44 fieldRadius=101.6 gradient=$Q2g \

ironRadius=381 ironLength=1104.9 ironColor=0,0,.6 kill=1idealquad Q3 fieldLength=853.44 fieldRadius=101.6 gradient=$Q3g \

ironRadius=381 ironLength=1104.9 ironColor=0,.6,0 kill=1mappedmagnet 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=0,1,1asciifile Diffuser1a radius=250 length=1.0 file=$startEvent

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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=2441place Q1 z=3000place Q2 z=4400place Q3 z=5800place B1 z=7855.8 rotation=Y30.0 x=250corner B1c z=8000 rotation=Y60.0place DecaySolenoid z=12200place SolenoidBody z=12200place B2 z=16135 rotation=Y15.8 x=175corner B2c z=16185 rotation=Y31.7place Diffuser1 z=18800place Diffuser1a z=18801

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The Bottom Line

Protons/sec in accelerator: 3.7×1016

Protons/sec intersecting target: 1.7×1012

Pions/sec into beamline accept.: 3.0×106

Pi+ + Mu+ /sec at Diffuser1: 37kMu+/sec at Diffuser1: 25kGood 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.

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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

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The Details (1 of 2)

Rate Computation

Aux. Computation

Beam and Target Rate (estimates by Paul Drumm)Protons in bunch 2.50E+13Bunches per second 1.50E+06Good Target & good RF duty factor 0.0010Beam radius (mm) 37.50Target area (mm^2) 2.00Beam area (mm^2) 4417.86Target/Beam (assumes uniform beam over circle) 0.0005Density factor (account for nonuniform beam) 0.10Protons/sec circulating in accelerator 3.75E+19Protons/sec intersecting target 1.70E+12

Protons => pions into 4pi (LAHET by Paul Drumm)Generated Protons on Target 1.00E+07pions into 4pi sr 53204

Protons => pions into MICE beamline acceptance (norm by Tom Roberts)pions into MICE beamline acceptance 17.96Pions/sec into MICE beamline acceptance 3.05E+06

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The Details (2 of 2)

Pions => Muons through detector, no RF no Absorber (g4beamline by Tom Roberts)Pions generated in MICE beamline acceptance 8.00E+07Pions+Muons at Diffuser1 968914Muons at Diffuser1 667128Muons through detector 5630

Pions+Muons at Diffuser1 per second 3.69E+04Muons at Diffuser1 per second 2.54E+04Muons through detector per Second 215RF Timing Factor 0.25Good Muons per Second 54

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Additional Slides(From my 7/30/03 talk)

The following plots are all at Diffuser1.

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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.

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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

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Momentum at Diffuser1

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P at Q1 for mu+ at Diffuser1

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Mu+ Correlation Matrix (normalized)

X Y dxdz dydz P t

X 1.0000 0.0048 0.7236 0.0169 -0.0840 0.0006

Y 0.0048 1.0000 -0.0280 0.8650 0.0074 -0.0127

dxdz 0.7236 -0.0280 1.0000 -0.0389 -0.4538 0.0121

dydz 0.0169 0.8650 -0.0389 1.0000 0.0081 0.0055

P -0.0840 0.0074 -0.4538 0.0081 1.0000 -0.0157

t 0.0006 -0.0127 0.0121 0.0055 -0.0157 1.0000

P < 250 MeV/c

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Mu+ X vs Y

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Pi+ X vs Y

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Mu+ X vs P

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Pi+ X vs P

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Mu+ X’ vs P

Note whereX’=0 is.

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Pi+ X’ vs P

Note whereX’=0 is.

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Mu+ X vs X’

Note whereX’=0 is.

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Pi+ X vs X’

Note whereX’=0 is.