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

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[[File:Beam_up_down.png]]<br>
 
[[File:Beam_up_down.png]]<br>
  
==Critical and Kicker angle==
+
==Critical and Kicker angles==
  
 
  <math>\Theta_C = \frac{m_ec^2}{E}</math>
 
  <math>\Theta_C = \frac{m_ec^2}{E}</math>
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                       = tan^-1\left(\frac{1}{\sqrt{2}}\ tan(\Theta_C)\right)</math><br>
 
                       = tan^-1\left(\frac{1}{\sqrt{2}}\ tan(\Theta_C)\right)</math><br>
  
==Kicker angle and displacements on the wall==
+
==Collimator location==
  
   <math>\Delta_1 = 286\ cm\ \tan(\Theta_C) = 3.34\ cm</math> <br>
+
   <math>\Delta_1 = 286\ cm\ \tan(\Theta_C)<br>
   <math>x_1^2+x_1^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ cm</math><br>
+
   <math>\Delta_2 = (286 + 183)\ cm\ \tan(\Theta_C)<br>
  <math>\Delta = 2.36\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.47\ ^o</math><br>
 
  
   <math>\Delta_2 = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm</math><br>
+
   <math>x_1 = 286\ cm \ \tan(\Theta_K)</math><br>
   <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm</math>
+
   <math>x_1 = (286 +183)\ cm \ \tan(\Theta_K)</math><br>
 +
 
 +
==Collimator critical angle==
 +
 
 +
  <math>\alpha = </math>
  
 
=Vacuum pipe location (<math> \Theta_c/2</math>)=
 
=Vacuum pipe location (<math> \Theta_c/2</math>)=

Revision as of 22:18, 20 June 2010

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90[math]^o[/math] exit port geometry

Exit port1.png

Off-axis collimation geometry

Beam up down.png

Critical and Kicker angles

[math]\Theta_C = \frac{m_ec^2}{E}[/math]
[math]\Theta_K = tan^-1\left(\frac{x_1}{286}\right)
                       = tan^-1\left(\frac{1}{\sqrt{2}}\ \frac{\Delta_1}{286}\right)
                       = tan^-1\left(\frac{1}{\sqrt{2}}\ tan(\Theta_C)\right)[/math]

Collimator location

  [math]\Delta_1 = 286\ cm\ \tan(\Theta_C)\lt br\gt 
   \lt math\gt \Delta_2 = (286 + 183)\ cm\ \tan(\Theta_C)\lt br\gt 

   \lt math\gt x_1 = 286\ cm \  \tan(\Theta_K)[/math]
[math]x_1 = (286 +183)\ cm \ \tan(\Theta_K)[/math]

Collimator critical angle

 [math]\alpha = [/math]

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]


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/4 = 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]

Funny pictures...

how it looks ([math] \Theta_c/2[/math], pipe 3")

Vacuum pipe collimator 0.335 2.png

how it looks 1 ([math] \Theta_c/4[/math], pipe 3")

Vacuum pipe collimator 0.168 2.png

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

Vacuum pipe collimator 168 1.png

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

need to adjust to converter position

Vacuum pipe collimator 335 4.png


how it looks 5 ([math] \Theta_c/2[/math], box 3"x4" and then pipe 4")

need to adjust to converter position

Vacuum pipe collimator 335 5.png


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