d. jason koskinen fnal collab 12/2006 1 geant4 numi monte carlo uncertainties

D. Jason Koskinen FNAL Collab 12/2006 1

Geant4 NuMI Monte CarloUncertainties


The end goal of calculating the flux from Muon Monitor data relies upon ongoing work in the following areas:

GNuMI Monte Carlo reweighting for muons (provides muon distribution at End Cap)

Muon Monitor calibration and data consistency

G4NuMI Monte Carlo uncertainties in Muon Flux

Fitting Muon Monitor data to Monte Carlo


Uncertainties

Density/Geometry– 8 Aluminum Absorber Core blocks

– 10 Steel Absorber Core blocks

– BluBlocks

● Recesses for crane– Concrete in shielding

● Recesses for crane– Rock between Muon Alcoves

Geometry– Steel plates in gaps between Core and BluBlock shielding

– Excavated wall depth


3d Absorber in 2d view– Density g/cm3 g/cm2

– A – Absorber Core● Covers 32.1%● Al and Stl blocks

– B – Gaps● 5.3%

– C – BluBlocks● 60%

– H2O pipes● 2.6%

Excluding tilt

A

B

C

H20 pipes

Muon View


Aluminum Core blocks8 blocks in Absorber Core

Machined from 6061-T6 Heavy Duty Aluminum– Density 2.70 +/- 0.01 g/cm3

– Tolerances are +/- .5 inch

Cooling pipes– Constitutes ~2.2% of block volume for 32 pipes

● Avg. Aluminum block has 32/2 pipes, 1.1% volume

– Dealt w/ in separate analysis

Uncertainty contribution (g/cm2)– +/- .01 g/cm3 * (8 blocks * 30.48 cm) * 98.9% = 2.41 g/cm2

– +/- 1.27 cm * 8 blocks * 98.9% * 2.70 g/cm3 = 27.13 g/cm2


Steel Core blocks

10 blocks in Absorber Core

Flame cut from Continuous Cast Salvage steel– Density 7.842 +/-.001 g/cm3 (9 random samples)


– Cooling pipes same as Aluminum Block treatment

Uncertainty contribution (g/cm2)– +/- .001 g/cm3 * (10 blocks * 23.11 cm) * 97.8% = .226 g/cm2

– +/- .635 cm * 10 blocks * 97.8% * 7.842 g/cm3 = 48.70 g/cm2


BluBlocks

Form Cast by Duratek, INC– Reclaimed steel from demolished building at Oak Ridge

lab

88 Duratek BluBlocks– Density 7.25 +/-.35 g/cm3 (21 sheets QC)


Uncertainty contribution (g/cm2)– +/- .35 g/cm3 * 530cm = 185.05 g/cm2

– +/- 1.27 cm * 4 blocks * 7.25 g/cm3 = 36.83 g/cm2


Concrete Blocks

FNAL concrete blocks with rebar support– Weight 10150 +/- 50 lbs

– 7' x 3' x 3' with .5' and .25' tolerances

– 2 recesses for hoist hooks 15” x 7” x 5”

– Density is 2.61 +/- .02 g/cm3

Uncertainty contribution (g/cm2)– +/- .02 g/cm3 * 91.5 cm = 1.83 g/cm2

– +/- .635 cm * 1 block * 2.61 g/cm3 = 1.66 g/cm2


Density % Dimensions % TotalAl Core 2.41 0.37 27.13 4.12 658.37Steel Core 0.23 0.01 48.70 2.91 1675.77BluBlocks 185.30 4.50 36.82 0.89 4114Concrete 1.83 0.77 1.65 0.69 238.28Gaps ???? ???? 1171

Table of Uncertainties (g/cm2) for Data in Muon Monitor 1

Most extra material the muon can travel through


RockMaquoketa Group - Brainerd Formation– 6 (8) Samples from S-1271 over 10' range

● vertical range of Muon Monitors

– 2.79 +/-.04 g/cm3

– ~40' of rock between MM1 and MM2, and ~60' of rock between MM2 and MM3

Uncertainty contribution (g/cm2)– +/- .04 g/cm3 * 1219 cm = 48.77 g/cm2 (MM1-2)

– +/- .04 g/cm3 * 1829 cm = 73.15 g/cm2 (MM2-3)

– Dimension uncertainty will come from survey analysis

● Placeholders are +/- 1.5' for MM1-2 and +/- 1' for MM2-3


Shokrete

Conrete sprayed onto walls– 2.4 +/- .2 g/cm3

● Bounded by Decay Tunnel backfill(2.22 g/cm3) and FNAL concrete blocks (2.61 g/cm3)

– 4” was the Shokrete target thickness w/ a 3” uncertainty because of surface undulation

Uncertainty contribution (g/cm2)– +/- .2 g/cm3 * 45.72 cm = 9.14 g/cm2 (MM1-2)

– +/- .2 g/cm3 * 30.48 cm = 6.1 g/cm2 (MM2-3)

– +/- 15.24 cm * 2.4 g/cm3 = 36.58 g/cm2 (MM1-2 and 2-3)


Table contributions to uncertainty in g/cm2 Density % Dimensions % Total % AreaAl Core 2.41 0.37 27.13 4.12 658.37 16.1Steel Core 0.23 0.01 48.70 2.91 1675.77 16.1BluBlocks 185.30 4.50 36.82 0.89 4114 60Gaps ???? ???? ???? ???? 1171 5.32H2O ???? ???? ???? ???? 1901 2.6Concrete 1.83 0.77 1.65 0.69 238.28MM1-2 Rock 48.77 1.41 43.10 1.25 3447.9 Shockrete 9.14 12.49 36.58 50.01 73.15MM2-3 Rock 73.15 1.41 32.04 0.62 5171.85 Shokrete 6.10 12.51 36.58 75.01 48.77

MM1 MM2 MM3Total 3194.2 6715.25 15130.06uncertainty 149.385 286.98 434.85


Uncertainty to Flux

The flux is the integrated muon distribution in each Muon Alcove 1, 2, 3. To get each distribution an efficiency plots of muons at the end of the Decay Pipe is multiplied by a provided(Zarko) distribution at the end of the Decay Pipe.

The uncertainty in efficiency is directly related to energy loss which is in turn directly related to material between the end of the Decay Pipe and the Muon Alcoves


Efficiency Plots

Metric to examine the effect that changes to the G4NuMI MC have on muon flux is to look at an 'Efficiency'– E = (# muon traversing muon monitor (1,2,3))/(#

muons produced)

– 30,000 muons

– mono-energetic muon beam uniformally distributed across Decay Pipe End Cap

– Samples at 1-120 GeV

Uncertainty in g/cm2 is equivalent to density change


Conclusions

Look at uncertainty from survey points

Combine uncertainties more constructively

Convert g/cm2 uncertainty to Efficiency uncertainty

d. jason koskinen fnal collab 12/2006 1 geant4 numi monte carlo uncertainties

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