# Activity 3: Alignment Tolerances and Uncertainties

### Goals

Today you will explore alignment-related flux uncertainties. You will compare simulations of 'nominal' beams and those with alignment/focusing parameters shifted and look at the impact on fluxes at the near and far detector. Good luck!

### Instructions

1. Prepare a work area
• Create a new working area for todays activity
• Copy the tarball of flux files to your working area and unpack it (see the Day 1 instructions for unpacking tarballs).
• Download the python template you'll be working with today.
2. The files you are working with today contain histograms of neutrino energy spectra for the nominal ("EngineeredOptimized") lbnf design and with various alignment parameters shifted. Studying alignment effects requires large statistics samples, and the ntuples for these samples take up too much disk space and time to analyze for this exercise, hence the histograms that have been made for you. Open one of the files and familiarize yourself the histograms. There are files for the near and far detector, and within each file you'll find oscillated and unoscillated fluxes for six neutrino flavors (electron, muon and tau neutrinos and their antineutrino partners). You'll also find histograms of neutral current and charged event rates (flux * cross section, basically).
3. Run your template script to compare the nominal flux with a horn current shifted flux:
``````
python day3.py
```
```
4. Look at the output
``````
display unc.png
```
```
This shows the fractional change in flux when we vary the horn current from the nominal value (293 kA) by 2 kA. If 2 kA is our uncertainty on the horn current, this fractional difference is what we take to be the uncertainty due to the horn current on the neutrino flux.
5. Plot the flux uncertainty (in a manner similar to the horn current example) due to the following effects:
• Horn Water Layer thickness (nominal = 0 mm, varied = 0.5mm)
• Decay pipe radius (nominal = 2.0 m, varied = 1.9 m)
• Horn 1 Transverse offset (nominal = centered horn, varied = entire horn shifted 0.5 mm in x and 0.5 mm in y)
• Horn 1 transverse tilt (nominal = centered horn, varied = upstream end tilted 0.5 mm in x and 0.5 mm in y; downstream end tilted -0.5 mm in x and -0.5 mm in y)
• Horn 2 Transverse offset (nominal = centered horn, varied = entire horn shifted 0.5 mm in x and 0.5 mm in y)
• Horn 2 transverse tilt (nominal = centered horn, varied = upstream end tilted 0.5 mm in x and 0.5 mm in y; downstream end tilted -0.5 mm in x and -0.5 mm in y)
• Horn 3 Transverse offset (nominal = centered horn, varied = entire horn shifted 0.5 mm in x and 0.5 mm in y)
• Horn 3 transverse tilt (nominal = centered horn, varied = upstream end tilted 0.5 mm in x and 0.5 mm in y; downstream end tilted -0.5 mm in x and -0.5 mm in y)
• Target Transverse offset (nominal = centered, varied = entire target shifted 0.5 mm in x and 0.5 mm in y)
• Target transverse tilt (nominal = centered, varied = upstream end tilted 0.5 mm in x and 0.5 mm in y; downstream end tilted -0.5 mm in x and -0.5 mm in y)
• Target longitudinal offset (nominal = nominal position; varied = shifted downstream by 1 mm)
• Beam sigma (nominal = 2.7 mm; varied = 2.8 mm)
• Beam Transverse position (nominal = centered; varied = shifted 0.5 mm in x and y)
• Target density (nominal = 1.78 g/cm3, varied = 1.8156 g/cm3)
• Question 14: Provide uncertainties on muon neutrino flux versus energy due to the above sources of misalignments
6. Question 15: Which alignment parameters have the biggest impact on the neutrino flux?
7. The "baffle scraping" uncertainty is estimated slightly differently than the uncertainties considered above. To estimate this uncertainty, we point a pencil beam directly at the baffle (beam shifted by 9 mm in x), and assume that at most 0.25% of the beam is directed at the baffle. So do the following
8. Question 16: Plot the "Baffle Scraping" flux, compared to the nominal (centered) flux.
9. Scale the baffle flux by 0.0025 and add it to the nominal flux.
10. Take the ratio to the nominal flux; this is the "baffle scraping" flux uncertainty.
11. Question 17: Provide the baffle scraping uncertainty plot.
12. The 0.25% comes from very early calculations in NuMI and may be quite different for DUNE. How large would the uncertainty be if it were 2%?
13. Question 18: Provide the baffle scraping uncertainty plot, assuming up to 2% of the beam might scrape the baffle
14. Question 19: Assuming that all of the variations described above are the complete error budget for LBNF alignment uncertainties, plot total fractional flux uncertainty due to alignment effects, versus neutrino energy. Note that the ratios above are actually one plus the uncertainty, so you should subtract off one before you add everything in quadrature.
15. Bonus Question 3: What is the alignment flux uncertainty at the near detector? What differences are there from the uncertainty at the far detector?
16. Bonus Question 4: What is the total alignment uncertainties on the near/far flux ratio?
17. Bonus Question 5: Make the plots above for muon antineutrinos and electron neutrinos. How do the alignment uncertainties for these flavors different than for muon neutrinos?
18. Bonus Question 6: Are there other alignment uncertainties you can think of that should be considered, other than those considered above?