Difference between revisions of "Geometry (25 MeV LINAC exit port)"

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1) center position:
 
1) center position:
  
−
   <math>286\ cm \cdot \tan (0.47) = 2.35\ cm</math>  (wall 1)<br>
+
   <math>286\ cm \cdot \tan (0.827) = 4.13\ cm</math>  (wall 1)<br>
−
   <math>(286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm</math>  (wall 2)
+
   <math>(286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm</math>  (wall 2)
  
 
2) collimator diameter:
 
2) collimator diameter:
 
    
 
    
−
  <math>\Theta_c/4 = 0.67^o/4 = 0.168^o</math>
+
   <math>286\ cm \cdot \tan (1.17/4) = 1.46\ cm</math>  (wall 1)<br>
−
 
+
   <math>(286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm</math>  (wall 2)
−
   <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==
 
==collimator critical angle==
  
−
   <math> AB = AC - BD/2 = (2.35 - 0.84/2)\ cm = 1.93\ cm </math><br>
+
   <math> AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ 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> A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm </math><br>
−
  <math> ED_1 = A_1D_1 - AB = (4.54 - 1.93)\ cm = 2.61\ cm </math>
 
 
    
 
    
−
from triangle <math>BED_1</math>:
+
  <math>\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o</math>:
−
 
 
−
  <math> \tan (\alpha) = \frac{2.61\ cm}{183\ cm} \Rightarrow \alpha = 0.82^o</math>
 
  
 
==minimal distance from the wall==
 
==minimal distance from the wall==
  
−
from triangle FAB:
+
   <math>\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm </math>
−
 
 
−
   <math> FA = \frac{AB}{\tan (0.82^o)} = \frac{1.93\ cm}{\tan (0.82^o)} = 135\ cm </math>
 
  
 
=Funny pictures...=
 
=Funny pictures...=

Revision as of 06:00, 11 June 2010

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Critical angle

[math]\Theta_C = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{25\ MeV} = 1.17\ ^o[/math]

Kicker angle

  [math]\Delta_1 = 286\ cm\ *\ \tan(1.17^o) = 5.84\ cm[/math] 

  [math]x^2+x^2 = 5.84^2\ cm \ \ \Rightarrow\ \  x = 4.13\ cm[/math] 

  [math]\Delta_2 = 4.13\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.827\ ^o[/math]

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

collimator location

1) center position: 

  [math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math]  (wall 2)

2) collimator diameter: 

  [math]286\ cm \cdot \tan (1.17/2) = 2.92\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (1.17/2) = 4.79\ cm[/math]  (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (4.13 - 2.92/2)\ cm = 2.67\ cm [/math]

  [math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 4.79/2)\ cm = 9.165\ cm [/math]

 
  [math]\bigtriangleup BED_1  \Rightarrow \tan (\alpha) = \frac{(9.165 - 2.67)\ cm}{183\ cm} \Rightarrow \alpha = 2.033^o[/math]:

minimal distance from the wall

  [math]\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (2.033^o)} = \frac{2.67\ cm}{\tan (2.033^o)} = 75\ cm [/math]

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

collimator location

1) center position: 

  [math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math]  (wall 2)

2) collimator diameter: 

  [math]286\ cm \cdot \tan (1.17/4) = 1.46\ cm[/math]  (wall 1)

  [math](286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm[/math]  (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ cm [/math]

  [math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm [/math]

 
  [math]\bigtriangleup BED_1  \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o[/math]:

minimal distance from the wall

  [math]\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm [/math]

Funny pictures...

how it looks 1 ([math] \Theta_c/2[/math], box 3"x4" and then pipe 4")

File:Vacuum pipe collimator .png

how it looks 2 ([math] \Theta_c/4[/math], box 3"x4" and then pipe 4")

File:Vacuum pipe collimator .png


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