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>
  
−
=Kicker angle and displacement calculations=
+
=General collimator setup=
  
−
==1 foot = 30.48 cm==
+
[[File:minimum_energy_condition.png|800px]]
  
−
==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>
  
−
  <math>x^2+x^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ 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>\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>
  
−
==detector's side wall==
+
=Funny pictures...=
  
−
  <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm</math>
+
==how it looks (<math> \Theta_c/2</math>, pipe 3")==
  
−
  <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm</math>
+
[[File:vacuum_pipe_collimator_0.335_2.png]]<br>
  
−
=Off-axis collimation geometry=
+
==how it looks 1 (<math> \Theta_c/4</math>, pipe 3")==
  
−
[[File:beam_up_down5.png]]<br>
+
[[File:vacuum_pipe_collimator_0.168_2.png]]<br>
  
−
=Vacuum pipe location (only the kicker angle)=
+
==how it looks 2 (<math> \Theta_c/4</math>, pipe 3")==
  
−
==collimator location==
+
[[File:vacuum_pipe_collimator_168_1.png]]<br>
  
−
1) center position
+
==how it looks 4 (<math> \Theta_c/2</math>, pipe (2 1/2)" and then pipe 4")==
  
−
  <math>286\ cm \cdot \tan (0.47) = 2.35\ cm</math>  (wall 1)<br>
+
need to adjust to converter position
−
  <math>(286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm</math>  (wall 2)
 
  
−
2) assume diameter is <math>\Theta_c/2 = 0.67^o/2 = 0.335^o</math>
+
[[File:vacuum_pipe_collimator_335_4.png]]<br>
  
−
  <math>286\ cm \cdot \tan (0.335) = 1.67\ cm</math>  (wall 1)<br>
 
−
  <math>(286 + 183)\ cm \cdot \tan (0.335) = 2.74\ cm</math>  (wall 2)
 
  
−
==collimator critical angle==
+
==how it looks 5 (<math> \Theta_c/2</math>, box 3"x4" and then pipe 4")==
  
−
  <math> AB = AC - BD/2 = (2.35 - 1.67/2)\ cm = 1.52\ cm </math><br>
+
need to adjust to converter position
−
  <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 2.74/2)\ cm = 5.22\ cm </math><br>
 
−
  <math> ED_1 = A_1D_1 - AB = (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>
+
[[File:vacuum_pipe_collimator_335_5.png]]<br>
−
 
 
−
==minimal distance from the wall==
 
−
 
 
−
1) from triangle QAB:
 
−
 
 
−
  <math> QA = \frac{AB}{\tan (1.16^{\circ })} = \frac{1.52\ cm}{\tan (1.16^{\circ })} = 75\ cm </math>
 
−
 
 
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3) from triangles OPR and QPR:
 
−
 
 
−
  <math> OQ = OA - QA = (286 - 75)\ cm = 211\ cm </math>
 
−
 
 
−
  <math> OR\cdot \tan (0.67^{\circ }) = (211 - OR)\cdot \tan (1.16^{\circ }) \Rightarrow</math><br>
 
−
  <math> OR = 211 cm\cdot \frac{tan (1.16^{\circ })}{tan (0.16^{\circ }) + tan (0.67^{\circ })} = 134\ cm</math>
 
−
 
 
−
  <math> RQ = OQ - RQ = (211-134)\ cm = 77\ cm </math>
 
−
 
 
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  <math> PR = 134\cdot \tan (0.67^{\circ }) = 1.57\ cm</math>
 
−
 
 
−
4) minimal distance:
 
−
 
 
−
  <math> OR = 134\ cm\ \ (vacuum\ pipe\ length) </math>
 
−
 
 
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  <math> RA = OA - OR = (286 - 134)\ cm = 152\ cm\ \ (from\ the\ wall\ to\ the\ pipe) </math>
 
−
 
 
−
==collimator and pipe geometry==
 
−
 
 
−
[[File:vacuum_pipe_collimator.png]]<br>
 
−
 
 
−
 
 
−
=Vacuum pipe location (kicker angle + multiple scattering angle)=
 
−
 
−
1) take multiple scattering angle <math> \Theta = 0.27^o</math>
 
−
 
 
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  <math> 0.47^o \longrightarrow (0.47^o - 0.27^o) = 0.20^o</math>
 
−
 
 
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  <math> RQ = 211\cdot \frac{tan (0.20^o)}{tan (0.20^o) + tan (1.16^o)} = 31\ cm</math>
 
−
 
 
−
4) minimal distance:
 
−
 
 
−
  RA = RQ + QA = (31 + 75) cm = 106 cm (from the wall to the vacuum pipe)
 
−
 
 
−
  OR = OA + RA = (286 + 106) cm = 180 cm (vacuum pipe length)
 
  
  
  
 
[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]

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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