Cosmic Conclusions

1
Cosmic Conclusions
David Gerstle LArTPC Yale University
Undergraduate  
2
Outline

• How do we get a particles/m2/s number?
• Detector location information
• J(gtE) (m2 s sr)-1
• Angular distribution
• Math
• The numbers
• What does that number mean for a given detector
  size and live-time?
• Are these numbers accurate?
• How does the muon flux and track length affect
  us?
• Conclusions and further questions

3
Effect of Detector Location

• The two values associated with a location which
  most affect the flux are the atmospheric depth
  (g/cm2) and geomagnetic cutoff (GV).
• Greater the atmospheric depth, lower the flux.
  The depth is intimately related to the altitude.
• Greater the geomagnetic cutoff value, lower the
  flux. GCV is the least value of kinetic energy
  divided by charge a primary cosmic ray must have
  to get through the Earths magnetic field. It is
  closely related to latitude (for the geomagnetic
  field varies with latitude).
• Soudan 990 g/cm2 at 400m altitude 1.0 GV at
  47N.

4
Need a J(E) (m2 s sr)-1 and Angular
Distribution

• J(E) is the vertical flux of particles above an
  energy E.
• What value of E should we use?
• 0.3 GeV/c muons travel 1m in LAr.
• As this 1m is (probably) the shielding LAr we
  will end up having, 0.3 GeV/c (0.2 GeV KE) is a
  good value for E.
• 0.5 GeV is the lower limit of photon events of
  interest for a detector which is in a beam I
  used this value for photons.
• Generally accepted to be cosn?
• J(E)cosn?, admittedly, is a poor model for the
  shape of J(E,?).
• However, the area (with respect to d?) under
  J(E)cosn? is very close to the area under
  J(E,?), so I have used J(E)cosn?.
• Even though they have different shapes,
  J(E)cosn? is a fine approximation for how we are
  using it.

5
Math
J(E)

• Horizontal Surface
• Vertical Surface

Formula used in spreadsheet
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Numbers I Use
      n
muon J(gt0.3 GeV/c) (m2 s sr)-1 8.87E01 2.16
muon Kranshaar (1949) 53N, 1.6 GV, 259m Kranshaar (1949) 53N, 1.6 GV, 259m Crooks Rastin (1972) 53N, gt0.35 GeV/c
photon J(gt0.5 GeV) (m2 s sr)-1 9.02E-01 3
photon Pugacheva et al., (1973) and Palmatier (1952) Pugacheva et al., (1973) and Palmatier (1952) Kameda (1960), Beuermann and Wibberenz (1968)
Photon values are adjusted from photon data
Note a factor of 100 between muon and photon
flux FOR THESE values of E

• Recall Soudan 990 g/cm2 at 400m altitude
  1.0 GV at 47N.
• All citations were found within Grieder, P.K.F.
  Cosmic Rays at Earth. Amsterdam Elsevier
  Science, 2001. A spectacular book.

7
Results for gt0.3 GeV/c muons and gt0.5 GeV photons
Time bin (s) Diameter (m) Height (m)
2.00E-03 35 35
  Horizontal (m2 s)-1 Horizontal s-1 Vertical (m2 s)-1 Vertical s-1 TOTAL s-1 TOTAL
muon 1.34E02 1.29E05 3.25E01 1.25E05 2.54E05 5.08E02
photon 1.13E00 1.09E03 2.40E-01 9.24E02 2.01E03 4.03E00

• Recall that Horizontal means through a
  horizontal surface and similarly for Vertical.
• Note that as photon energy increases, the flux
  rapidly decreases using a smaller value of E in
  J(gtE) will significantly increase the total
  photon flux.

8
Are these Muon Numbers Accurate?

• PDG quotes a muon integral flux through a
  horizontal surface as being 1 (cm2 min)-1
  170 (m2 s)-1
• I calculated 130 (m2 s)-1 for Egt0.3 GeV/c.
• The difference is accounted for by recognizing
  PDG to have used Emin effectively 0 in J(gtE).

Linear Scale
0.3 Gev/c
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Are these Photon Results Accurate?

• It is key that we know what E value to use
  because the curve is so steep.

dN/dE
J(gtE)
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How does the muon flux affect us?

• Yellow curve is Horizontal and Teal curve is
  Vertical N(gtE)x(p), where x(p) is the path
  length of a muon in LAr (from a dE/dx
  calculation).
• Nhor(gt0.3 GeV/c)x(gtp) 1800 particle meters per
  meter2 per second.
• Nvert(gt0.3 GeV/c)x(gtp) 450 particle meters per
  meter2 per second.
• 35m by 35m cylindrical detector and 2 millisecond
  drift-time yields 7000 particle meters during
  each live-time.

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Conclusions and further Questions

• All calculations were done in Excel the file is
  in the LArTPC DocDB 160 CosmicConclusions.xls
• We might consider buying a copy of Mr. Grieders
  250 book.
• Need to determine the effect of these numbers on
  the data acquisition system.
• These data are with respect to a Soudan, MN
  detectorshould we consider another surface
  location?
• Lower latitude and altitude would reduce flux.
• Is there reason to use a different value for E in
  J(gtE) for muons and/or photons?
• Do we need to accurately model the shape of
  J(E,?)?
• Can we mathematically model the effect of the
  geomagnetic cutoff? Do we need to?