D. Jason Koskinen FNAL Collab 12/ Geant4 NuMI Monte Carlo Uncertainties

D. Jason Koskinen FNAL Collab 12/2006 2

D. Jason Koskinen FNAL Collab 12/ 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

D. Jason Koskinen FNAL Collab 12/ 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

D. Jason Koskinen FNAL Collab 12/2006 5

D. Jason Koskinen FNAL Collab 12/ d 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 Muon View

D. Jason Koskinen FNAL Collab 12/ Aluminum Core blocks 8 blocks in Absorber Core Machined from 6061-T6 Heavy Duty Aluminum – Density / 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 * cm) * 98.9% = 2.41 g/cm2 – +/ cm * 8 blocks * 98.9% * 2.70 g/cm3 = g/cm2

D. Jason Koskinen FNAL Collab 12/ Steel Core blocks 10 blocks in Absorber Core Flame cut from Continuous Cast Salvage steel – Density /-.001 g/cm3 (9 random samples) – Tolerances are +/-.25 inch – Cooling pipes same as Aluminum Block treatment Uncertainty contribution (g/cm2) – +/-.001 g/cm3 * (10 blocks * cm) * 97.8% =.226 g/cm2 – +/-.635 cm * 10 blocks * 97.8% * g/cm3 = g/cm2

D. Jason Koskinen FNAL Collab 12/ BluBlocks Form Cast by Duratek, INC – Reclaimed steel from demolished building at Oak Ridge lab 88 Duratek BluBlocks – Density /-.35 g/cm3 (21 sheets QC) – Tolerances are +/-.50 inch Uncertainty contribution (g/cm2) – +/-.35 g/cm3 * 530cm = g/cm2 – +/ cm * 4 blocks * 7.25 g/cm3 = g/cm2

D. Jason Koskinen FNAL Collab 12/ Concrete Blocks FNAL concrete blocks with rebar support – Weight /- 50 lbs – 7' x 3' x 3' with.5' and.25' tolerances – 2 recesses for hoist hooks 15” x 7” x 5” – Density is /-.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

D. Jason Koskinen FNAL Collab 12/ Table of Uncertainties (g/cm2) for Data in Muon Monitor 1 Most extra material the muon can travel through

D. Jason Koskinen FNAL Collab 12/ Rock Maquoketa Group - Brainerd Formation – 6 (8) Samples from S-1271 over 10' range ● vertical range of Muon Monitors – /-.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 = g/cm2 (MM1-2) – +/-.04 g/cm3 * 1829 cm = g/cm2 (MM2-3) – Dimension uncertainty will come from survey analysis ● Placeholders are +/- 1.5' for MM1-2 and +/- 1' for MM2-3

D. Jason Koskinen FNAL Collab 12/ 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 * cm = 9.14 g/cm2 (MM1-2) – +/-.2 g/cm3 * cm = 6.1 g/cm2 (MM2-3) – +/ cm * 2.4 g/cm3 = g/cm2 (MM1-2 and 2-3)

D. Jason Koskinen FNAL Collab 12/ Table contributions to uncertainty in g/cm2

D. Jason Koskinen FNAL Collab 12/ 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

D. Jason Koskinen FNAL Collab 12/ 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 GeV Uncertainty in g/cm2 is equivalent to density change

D. Jason Koskinen FNAL Collab 12/

D. Jason Koskinen FNAL Collab 12/

D. Jason Koskinen FNAL Collab 12/

D. Jason Koskinen FNAL Collab 12/ Conclusions Look at uncertainty from survey points Combine uncertainties more constructively Convert g/cm2 uncertainty to Efficiency uncertainty