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

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[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]
 
[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]
  
−
=Some measurements of 90 experimental degree exit port=
+
=90<math>^o</math> exit port measurements=
  
−
[[File:exit_port1.png]]<br><br>
+
[[File:exit_port1.png|800px]]<br><br>
  
 +
=Critical and Kicker angles=
  
−
=Critical angle and displacement calculations=
+
[[File:Beam_up_down.png|800px]]<br>
  
−
<math>\Theta = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{44\ MeV} = 0.67\ ^o</math><br>
+
<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><br>
  
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=Kicker angle and displacement calculations=
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=General collimator setup=
  
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==1 foot = 30.48 cm==
+
[[File:minimum_energy_condition.png|800px]]
  
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==accelerator's side wall==
+
<math>AC = 286\cdot\tan(\Theta_K)\ cm</math><br>
 +
<math>A_1C_1 = (286 +183)\cdot\tan(\Theta_K)\ cm</math>
  
−
  <math>\Delta = 286\ cm\ *\ \tan(0.67^o) = 3.34\ cm</math>  
+
<math>BD = 286\cdot\tan(\Theta_C/m)\ cm</math><br>
 +
<math>B_1D_1 = (286 + 183)\cdot\tan(\Theta_C/m)\ cm</math><br>
  
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  <math>x^2+x^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ cm</math>
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<math>\alpha = \frac{A_1D_1 - AB}{183} = \frac{(A_1C_1 + C_1D_1/2) - (AC - B_1D_1/2)}{183}</math>
  
−
  <math>\Delta = 2.36\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.47\ ^o</math>
+
  <math>FA = AB/\tan(\alpha)\ cm</math><br>
−
 
+
  <math>GH = (286 - FA)\cdot\tan(\alpha)\ cm</math>
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==detector's side wall==
 
−
 
 
−
  <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm</math>
 
−
 
 
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  <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm</math>
 
−
 
 
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=Off-axis collimation geometry=
 
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[[File:beam_up_down5.png]]<br>
 
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=Vacuum pipe location (<math> \Theta_c/2</math>)=
 
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==collimator location==
 
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1) center position:
 
−
 
 
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  <math>286\ cm \cdot \tan (0.47) = 2.35\ cm</math> (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm</math>  (wall 2)
 
−
 
 
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2) collimator diameter:
 
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  <math>\Theta_c/2 = 0.67^o/2 = 0.335^o</math>
 
−
 
 
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  <math>286\ cm \cdot \tan (0.335) = 1.67\ cm</math>  (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (0.335) = 2.74\ cm</math>  (wall 2)
 
−
 
 
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==collimator critical angle==
 
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  <math> AB = AC - BD/2 = (2.35 - 1.67/2)\ cm = 1.52\ cm </math><br>
 
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  <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 2.74/2)\ cm = 5.22\ cm </math><br>
 
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  <math> ED_1 = A_1D_1 - A_1E = (5.22 - 1.52)\ cm = 3.70\ cm </math>
 
−
 
 
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from triangle <math>BED_1</math>:
 
−
 
 
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  <math> \tan (\alpha) = \frac{3.70\ cm}{183\ cm} \Rightarrow \alpha = 1.16^o</math>
 
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==minimal distance from the wall==
 
−
 
 
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from triangle FAB:
 
−
 
 
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  <math> FA = \frac{AB}{\tan (1.16^o)} = \frac{1.52\ cm}{\tan (1.16^o)} = 75\ cm </math>
 
−
 
 
−
 
 
−
 
 
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=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)<br>
 
−
  <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)<br>
 
−
  <math>(286 + 183)\ cm \cdot \tan (0.168) = 1.38\ cm</math>  (wall 2)
 
−
 
 
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==collimator critical angle==
 
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  <math> AB = AC - BD/2 = (2.35 - 0.84/2)\ cm = 1.93\ cm </math><br>
 
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  <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>
 
−
 
 
−
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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from triangle FAB:
 
−
 
 
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  <math> FA = \frac{AB}{\tan (0.82^o)} = \frac{1.93\ cm}{\tan (0.82^o)} = 135\ cm </math>
 
  
 
=Funny pictures...=
 
=Funny pictures...=
  
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==how it looks (<math> \Theta_c/2</math>)==
+
==how it looks (<math> \Theta_c/2</math>, pipe 3")==
  
 
[[File:vacuum_pipe_collimator_0.335_2.png]]<br>
 
[[File:vacuum_pipe_collimator_0.335_2.png]]<br>
  
−
==how it looks 1 (<math> \Theta_c/4</math>)==
+
==how it looks 1 (<math> \Theta_c/4</math>, pipe 3")==
  
 
[[File:vacuum_pipe_collimator_0.168_2.png]]<br>
 
[[File:vacuum_pipe_collimator_0.168_2.png]]<br>
  
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==how it looks 2 (<math> \Theta_c/4</math>)==
+
==how it looks 2 (<math> \Theta_c/4</math>, pipe 3")==
  
 
[[File:vacuum_pipe_collimator_168_1.png]]<br>
 
[[File:vacuum_pipe_collimator_168_1.png]]<br>
−
 
−
 
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==how it looks 3 (<math> \Theta_c/2</math>, pipe (2 1/2)" and then pipe 4")==
 
−
 
−
[[File:vacuum_pipe_collimator_335_3.png]]<br>
 
  
 
==how it looks 4 (<math> \Theta_c/2</math>, pipe (2 1/2)" and then pipe 4")==
 
==how it looks 4 (<math> \Theta_c/2</math>, pipe (2 1/2)" and then pipe 4")==

Latest revision as of 22:49, 20 June 2010

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

Exit port1.png

Critical and Kicker angles

Beam up down.png

[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]

General collimator setup

Minimum energy condition.png 

[math]AC = 286\cdot\tan(\Theta_K)\ cm[/math]

[math]A_1C_1 = (286 +183)\cdot\tan(\Theta_K)\ cm[/math]

[math]BD = 286\cdot\tan(\Theta_C/m)\ cm[/math]

[math]B_1D_1 = (286 + 183)\cdot\tan(\Theta_C/m)\ cm[/math]


[math]\alpha = \frac{A_1D_1 - AB}{183} = \frac{(A_1C_1 + C_1D_1/2) - (AC - B_1D_1/2)}{183}[/math]

[math]FA = AB/\tan(\alpha)\ cm[/math]

[math]GH = (286 - FA)\cdot\tan(\alpha)\ 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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