Difference between revisions of "Geometry (44 MeV LINAC exit port)"

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[[File:vacuum_pipe_collimator2.png]]<br>
 
[[File:vacuum_pipe_collimator2.png]]<br>
  
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=Vacuum pipe location (kicker + multiple scattering angle angles)=
 
−
 
−
1) take multiple scattering angle <math> \Theta = 0.27^o</math>
 
  
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  <math> 0.67^o \longrightarrow (0.67^o - 0.27^o) = 0.40^o</math>
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=Vacuum pipe location (<math> \Theta_c/4</math>)=
  
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  <math> OR = 211 cm\cdot \frac{tan (1.16^o)}{tan (1.16^o) + tan (0.40^o)} = 157\ cm</math>
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==collimator location==
  
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   <math> RQ = OQ - RQ = (211-157)\ cm = 54\ cm </math>
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1) center position:
 +
 
 +
   <math>286\ cm \cdot \tan (0.47) = 2.35\ cm</math>  (wall 1)<br>
 +
  <math>(286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm</math> (wall 2)
 +
 
 +
2) collimator diameter:
 
    
 
    
−
   <math> PR = 157\cdot \tan (0.40^o) = 1.09\ cm</math>
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   <math>\Theta_c/2 = 0.67^o/4 = 0.168^o</math>
 +
 
 +
  <math>286\ cm \cdot \tan (0.168) = 0.84\ cm</math>  (wall 1)<br>
 +
  <math>(286 + 183)\ cm \cdot \tan (0.168) = 1.38\ cm</math>  (wall 2)
 +
 
 +
==collimator critical angle==
 +
 
 +
  <math> AB = AC - BD/2 = (2.35 - 0.84/2)\ cm = 1.93\ cm </math><br>
 +
  <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 1.38/2)\ cm = 4.54\ cm </math><br>
 +
  <math> ED_1 = A_1D_1 - AB = (4.54 - 1.93)\ cm = 2.61\ cm </math>
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 +
from triangle <math>BED_1</math>:
 +
 
 +
  <math> \tan (\alpha) = \frac{2.61\ cm}{183\ cm} \Rightarrow \alpha = 0.82^o</math>
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==minimal distance from the wall==
  
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4) minimal distance:
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from triangle FAB:
  
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   <math> OR = 157\ cm\ \ (vacuum\ pipe\ length) </math>
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   <math> FA = \frac{AB}{\tan (0.82^o)} = \frac{1.93\ cm}{\tan (0.82^o)} = 135\ cm </math>
  
−
  <math> RA = OA - OR = (286 - 157)\ cm = 129\ cm\ \ (from\ the\ wall\ to\ the\ pipe) </math>
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==collimator and pipe geometry==
  
 +
[[File:vacuum_pipe_collimator2.png]]<br>
  
  
 
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Revision as of 18:00, 25 May 2010

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Some measurements of 90 experimental degree exit port

Exit port1.png


Critical angle and displacement calculations

[math]\Theta = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{44\ MeV} = 0.67\ ^o[/math]


Kicker angle and displacement calculations

1 foot = 30.48 cm

accelerator's side wall

  [math]\Delta = 286\ cm\ *\ \tan(0.67^o) = 3.34\ cm[/math] 

  [math]x^2+x^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ cm[/math]

  [math]\Delta = 2.36\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.47\ ^o[/math]

detector's side wall

  [math]\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm[/math]

  [math]\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm[/math]

Off-axis collimation geometry

Beam up down5.png

Vacuum pipe location ([math] \Theta_c/2[/math])

collimator location

1) center position: 

  [math]286\ cm \cdot \tan (0.47) = 2.35\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm[/math]  (wall 2)

2) collimator diameter: 

  [math]\Theta_c/2 = 0.67^o/2 = 0.335^o[/math]

  [math]286\ cm \cdot \tan (0.335) = 1.67\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.335) = 2.74\ cm[/math]  (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (2.35 - 1.67/2)\ cm = 1.52\ cm [/math]

  [math] A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 2.74/2)\ cm = 5.22\ cm [/math]

  [math] ED_1 = A_1D_1 - A_1E = (5.22 - 1.52)\ cm = 3.70\ cm [/math]

from triangle [math]BED_1[/math]: 

  [math] \tan (\alpha) = \frac{3.70\ cm}{183\ cm} \Rightarrow \alpha = 1.16^o[/math]

minimal distance from the wall

from triangle FAB: 

  [math] FA = \frac{AB}{\tan (1.16^o)} = \frac{1.52\ cm}{\tan (1.16^o)} = 75\ cm [/math]

collimator and pipe geometry

Vacuum pipe collimator2.png


Vacuum pipe location ([math] \Theta_c/4[/math])

collimator location

1) center position: 

  [math]286\ cm \cdot \tan (0.47) = 2.35\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm[/math]  (wall 2)

2) collimator diameter: 

  [math]\Theta_c/2 = 0.67^o/4 = 0.168^o[/math]

  [math]286\ cm \cdot \tan (0.168) = 0.84\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.168) = 1.38\ cm[/math]  (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (2.35 - 0.84/2)\ cm = 1.93\ cm [/math]

  [math] A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 1.38/2)\ cm = 4.54\ cm [/math]

  [math] ED_1 = A_1D_1 - AB = (4.54 - 1.93)\ cm = 2.61\ cm [/math]

from triangle [math]BED_1[/math]: 

  [math] \tan (\alpha) = \frac{2.61\ cm}{183\ cm} \Rightarrow \alpha = 0.82^o[/math]

minimal distance from the wall

from triangle FAB: 

  [math] FA = \frac{AB}{\tan (0.82^o)} = \frac{1.93\ cm}{\tan (0.82^o)} = 135\ cm [/math]

collimator and pipe geometry

Vacuum pipe collimator2.png


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