# Presentation: 521369

## Cosmic Conclusions

**David Gerstle**
**LArTPC – Yale University Undergraduate**

- David Gerstle

- 7/11/06

## Outline

- How do we get a particles/m^2/s number?
- Detector location information
- J(>E) (m^2 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

- David Gerstle

- 7/11/06

## Effect of Detector Location

- The two values associated with a location which most affect the flux are the atmospheric depth (g/cm^2) 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 Earth’s magnetic field.  It is closely related to latitude (for the geomagnetic field varies with latitude).
- Soudan: ~990 g/cm^2 at ~400m altitude; ~1.0 GV at 47°N.

- David Gerstle

- 7/11/06

## Need a J(≥E) (m^2 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.

- David Gerstle

- 7/11/06

## Math

- Horizontal Surface:
- Vertical Surface:

- Formula used in spreadsheet

- J(≥E)=

- David Gerstle

- 7/11/06

## Numbers I Use

- Recall Soudan: ~990 g/cm^2 at ~400m altitude; ~1.0 GV at 47°N.
- All citations were found within Grieder, P.K.F. *Cosmic Rays at Earth*. Amsterdam: Elsevier Science, 2001.  A spectacular book.

|   |  |  | n |
| --- | --- | --- | --- |
| muon | J(>0.3 GeV/c) (m^2 s sr)^-1 | 8.87E+01 | 2.16 |
|  | Kranshaar (1949) 53°N, 1.6 GV, 259m |  | Crooks & Rastin (1972) 53°N, >0.35 GeV/c |
| photon | J(>0.5 GeV) (m^2 s sr)^-1 | 9.02E-01 | 3 |
|  | Pugacheva et al., (1973) and Palmatier (1952) |  | Kameda (1960), Beuermann and Wibberenz (1968) |

- Note a factor of ~100 between muon and photon flux FOR THESE values of E

- Photon values are adjusted from photon data

- David Gerstle

- 7/11/06

## Results for >0.3 GeV/c muons and >0.5 GeV photons

- 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(>E) will significantly increase the total photon flux.

| Time bin (s) | Diameter (m) | Height (m) |
| --- | --- | --- |
| 2.00E-03 | 35 | 35 |

|   | Horizontal (m^2 s)^-1 | Horizontal s^-1 | Vertical (m^2 s)^-1 | Vertical s^-1 | TOTAL s^-1 | TOTAL |
| --- | --- | --- | --- | --- | --- | --- |
| muon | 1.34E+02 | 1.29E+05 | 3.25E+01 | 1.25E+05 | 2.54E+05 | 5.08E+02 |
| photon | 1.13E+00 | 1.09E+03 | 2.40E-01 | 9.24E+02 | 2.01E+03 | 4.03E+00 |

- David Gerstle

- 7/11/06

## Are these Muon Numbers Accurate?

- PDG quotes a muon integral flux through a horizontal surface as being ≈ 1 (cm^2 min)^-1 ≈ 170 (m^2 s)^-1
- I calculated ≈ 130 (m^2 s)^-1 for E>0.3 GeV/c.
- The difference is accounted for by recognizing PDG to have used Emin effectively 0 in J(>E).

- 0.3 Gev/c

- Linear Scale

- David Gerstle

- 7/11/06

## Are these Photon Results Accurate?

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

- J(>E)

- dN/dE

- David Gerstle

- 7/11/06

## How does the muon flux affect us?

- Yellow curve is Horizontal and Teal curve is Vertical N(>E)*x(p), where x(p) is the path length of a muon in LAr (from a dE/dx calculation).
- Nhor(>0.3 GeV/c)*x(>p) ≈ 1800 particle meters per meter^2 per second.
- Nvert(>0.3 GeV/c)*x(>p) ≈ 450 particle meters per meter^2 per second.
- 35m by 35m cylindrical detector and 2 millisecond drift-time yields ~7000 particle meters during each live-time.

- David Gerstle

- 7/11/06

## 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. Grieder’s ~$250 book.
- Need to determine the effect of these numbers on the data acquisition system.
- These data are with respect to a Soudan, MN detector—should we consider another surface location?
- Lower latitude and altitude would reduce flux.
- Is there reason to use a different value for E in J(>E) 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?

- David Gerstle

- 7/11/06