How to test the rates

By making plots of trk_mc_d and trk_mc_z the sizes of the mu-, trt-, sct- and pixvolumes are obtained. The rate measured in these volumes should be proportional to their relative size.

The files used to determine these values are:

• muVol_noField_all.aan.root
• trtVol_noField_all.aan.root
• sctVol_noField_all.aan.root
• pixVol_noField_all.aan.root

MUON VOLUME

-- MathieuBlom - 29 Jun 2007

• plots of the trk_mc_d and trk_mc_z for the muon volume. Data taken from muVol_noField_all.aan.root:
  

• I have estimated the dimensions of the muon volume to be 4 x 20 m. There are two strange dips at + and - 5. Probably this has something to do with endcaps.

TRT VOLUME

• plots of the trk_mc_d and trk_mc_z for the TRT volume. Data taken from trtVol_noField_all.aan.root::
  

* I have estimated the dimensions of the TRT volume to be 2 x 1.8 m.

SCT VOLUME

• plots of the trk_mc_d and trk_mc_z for the SCT volume. Data taken from sctVol_noField_all.aan.root::
  

* I have estimated the dimensions of the SCT volume to be between 1.8 x 2 m and 2.2 x 2 m.

PIXEL VOLUME

• plots of the trk_mc_d and trk_mc_z for the pixel volume. Data taken from pixVol_noField_all.aan.root::
  

* I have estimated the dimensions of the pixel volume to be 0.5 x 7 m.

Table of combined values:

VOL	d	z	opp
Mu	4 m	20 m	80 m^2
TRT	2 m	1.8 m	3.9 m^2
SCT	1.8 - 2.2 m	2 m	3.9 - 4.4 m^2
Pix	0.5 m	7 m	3.5 m^2

Relative rates

Compared to the muon volume:

• Rate of the muon volume: 3139 Hz
• TRT/Mu = 4.9 % --> 154 Hz
• SCT/Mu = 4.9 - 5.5 % --> 154 - 173 Hz
• Pix/Mu = 4.4 % --> 138 Hz

Compared to the SCT volume:

• Rate of the SCT volume: 12 Hz
• TRT/SCT = 89 - 100 % --> 11 - 12 Hz
• Pix/SCT = 80 - 90 % --> 10 -11 Hz

Compared to the TRT volume:

• Rate of the TRT volume: 27 Hz
• Pix/TRT = 90 % --> 24 Hz

Discussion

The real rates are:

• Mu --> 3139 Hz
• SCT --> Hz
• TRT --> 27 Hz
• Pixel --> 34 Hz

if we compare these values with the expected rate, we see that:

• real values are all much lower than expected based on the relative muon rate.
• TRT and SCT have different rates although they have approximately the same size.
• Real rate of the pixel volume is 5 - 6 times smaller than one would expect based on the ratio of the pixel and muon volumes, and significantly higher then expected based on the ratio of the TRT or SCT/Pixel volumes

Relative rates for the files with an improved muon volume

In the files above the demand was made that there was a hit in the colorimeter. This has been fixed and so a better size for the muon volume is found:

• d = 26 m
• z = 40 m
• opp = 1040 M^2

The data used to find these dimensions comes from:

• Erange225MeV.digfix.aan.root
• Erange1GeV.digfix.aan.root
• Erange10GeV.digfix.aan.root

The plots of the data are shown below:

• plots of trk_mc_d and z for the file: Erange225MeV.digfix.aan.root:
  

• plots of trk_mc_d and z for the file: Erange1GeV.digfix.aan.root:
  

• plots of trk_mc_d and z for the file: Erange10GeV.digfix.aan.root:
  

This new size means that the realtive rates which involve the muon volume go down by a factor 13. This leaves us with:

	relative rate	real rate
Mu	-	3139
TRT/Mu	12	27
SCT/Mu	12 - 13	12
Pix/Mu	11	34

We see that this works very well for the SCT rate. The TRT and pixel rates are a little higer in real life, but the obtained numbers are much better than before. It works quit well!

---

I have calculated the rates in three ways:

• the relative rates proportional to the sizes of the volumes before LVL1 trigger (shown above).
• the rates proportional to the sizes of the volme after the LVL1 trigger.
• the fraction of events that past a certain volume within the boundaries of a smaller volume.

It seems that for an energy of 10 GeV 17.17% of the cosmics have a hit in the muon volume. This reduces the rate from 3139 to 539 Hz. The relative rates obtained in this way are shown in the table. All these rates are found in the table beneath:

	rate from relative size before LVL1 trigger	after LVL1 trigger	fraction of MU volume	real rate
Mu	3139	539	3139	3139
TRT/Mu	12	26.4	13.5	27
SCT/Mu	12-13	26.4-29.7	12.7-15.7	12
Pix/Mu	11	23.7	3.4	34