Difference between revisions of "Wire angle correspondance"

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(Created page with "=Determining wire-theta correspondance= To associate the hits with the Moller scattering angle theta, the occupancy plots of the drift chamber hits by means of wire numbers and l…")
 
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==Super Layer 1:Layer 6==
 
==Super Layer 1:Layer 6==
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For a hit at layer 2, wire 1 we find the corresponding angle theta in the lab frame to be 5.30 degrees
 
<center>[[File:Superlayer1_layer6_wire1.png]]</center>
 
<center>[[File:Superlayer1_layer6_wire1.png]]</center>
  
  
 +
Examing a hit at layer 2, wire 112 we find the corresponding angle theta in the lab frame to be 40.61 degrees
 +
<center>[[File:Superlayer1_layer6_wire112.png]]</center>
 +
 +
 +
This sets the lower limit:
 +
 +
<center><math>\frac{5.30^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.09250245\ radians\approx 0.025\ radians</math></center>
  
  
<center>[[File:Superlayer1_layer6_wire112.png]]</center>
+
This sets the upper limit:
 +
 
 +
<center><math>\frac{40.61^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.7087782\ radians\approx 0.709\ radians</math></center>
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 +
Taking the difference,
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 +
<center><math>.716457657944-.0872664626\approx\  .616\  radians</math></center>
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 +
 
 +
Dividing by 112, we find
 +
 
 +
<center><math>\frac{.61627575}{112}=.00550246\ radians\approx\ 0.00550\ radians</math></center>
  
 
==Superlayer 2:Layer 1==
 
==Superlayer 2:Layer 1==

Revision as of 20:14, 16 November 2016

Determining wire-theta correspondance

To associate the hits with the Moller scattering angle theta, the occupancy plots of the drift chamber hits by means of wire numbers and layer must be translated using the physical constraints of the detector. Using the data released for the DC:

DC: Drift Chambers(specs)


This gives the detector with a working range of 5 to 40 degrees in Theta for the lab frame, with a resolution of 1m radian.

This sets the lower limit:

[math]\frac{5^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.0872664626\ radians[/math]


This sets the upper limit:

[math]\frac{40^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.698131700798\ radians[/math]

Taking the difference,

[math].698131700798-.0872664626\approx\ .61086523198\ radians[/math]


Dividing by 112, we find

[math]\frac{.61086523198}{112}=.005454153912\ radians\approx\ 0.0055\ radians[/math]

CED Verification

Using CED to verify the angle and wire correlation,

Super Layer 1:Layer 1

For a hit at layer 1, wire 1 we find the corresponding angle theta in the lab frame to be 4.91 degrees

Layer1Wire1Hit.png


For a hit at layer 1, wire 2 we find the corresponding angle theta in the lab frame to be 5.19 degrees

Layer1Wire2.png


Finding the difference between the two wires,

[math]5.19-4.91=.28^{\circ} \frac{\pi\ radians}{180^{\circ}}=0.004886921906\approx\ 0.00489\ radians[/math]

Examing a hit at layer 1, wire 112 we find the corresponding angle theta in the lab frame to be 40.70 degrees

Layer1Wire112.png

This sets the lower limit:

[math]\frac{4.91^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.085695666273\ radians\approx 0.0857\ radians[/math]


This sets the upper limit:

[math]\frac{40.70^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.710349005562\ radians\approx 0.710\ radians[/math]

Taking the difference,

[math].710349005562-.085695666273\approx\ .625\ radians[/math]


Dividing by 112, we find

[math]\frac{.624653339289}{112}=.005577261958\ radians\approx\ 0.00558\ radians[/math]

Noting the difference from the spacing for a single cell, to the entire detector layer

[math]0.00489-0.00558=0.00069\ \approx .001\ radians[/math]

An uncertainty of this magnitude in radians corresponds to an angular uncertainty of

[math].001\ radian\ \frac{180^{\circ}}{\pi\ radians}\approx .0573^{\circ}[/math]

Testing this for a random angle, 78 degrees we find

[math]0.00558\times 78\ = 0.43524\ radians \frac{180^{\circ}}{\pi\ radians}\approx 24.94^{\circ}[/math]

Adding this to the starting angle of 4.91 degrees

[math]4.91^{\circ}+24.94^{\circ}=29.85^{\circ}\pm .0573^{\circ}[/math]

Comparing this to CED at wire 78

Layer1Wire78.png


[math]\Longrightarrow 29.85^{\circ}\pm .0573^{\circ}\approx 29.88^{\circ}[/math]

Super Layer 1:Layer 2

For a hit at layer 2, wire 1 we find the corresponding angle theta in the lab frame to be 5.00 degrees

Superlayer1 layer2 wire1.png


Examing a hit at layer 2, wire 112 we find the corresponding angle theta in the lab frame to be 41.05 degrees

Superlayer1 layer2 wire112.png


This sets the lower limit:

[math]\frac{5.00^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.0872664626\ radians\approx 0.0873\ radians[/math]


This sets the upper limit:

[math]\frac{40.70^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.716457657944\ radians\approx 0.716\ radians[/math]

Taking the difference,

[math].716457657944-..0872664626\approx\ .629\ radians[/math]


Dividing by 112, we find

[math]\frac{.629191195344}{112}=.00561777853\ radians\approx\ 0.00562\ radians[/math]

Super Layer 1:Layer 6

For a hit at layer 2, wire 1 we find the corresponding angle theta in the lab frame to be 5.30 degrees

Superlayer1 layer6 wire1.png


Examing a hit at layer 2, wire 112 we find the corresponding angle theta in the lab frame to be 40.61 degrees

Superlayer1 layer6 wire112.png


This sets the lower limit:

[math]\frac{5.30^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.09250245\ radians\approx 0.025\ radians[/math]


This sets the upper limit:

[math]\frac{40.61^{\circ}}{1}\frac{\pi\ radians}{180^{\circ}}=.7087782\ radians\approx 0.709\ radians[/math]

Taking the difference,

[math].716457657944-.0872664626\approx\ .616\ radians[/math]


Dividing by 112, we find

[math]\frac{.61627575}{112}=.00550246\ radians\approx\ 0.00550\ radians[/math]

Superlayer 2:Layer 1

Superlayer2 layer1 wire1.png



Superlayer2 layer1 wire112.png