Difference between revisions of "Geometry (25 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]
  
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=Minimum accelerator energy to run experiment=
 
  
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[[File:min_energy.png|1000px]]
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=general setup=
  
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The minimum energy of accelerator (MeV) is limited by fitting the collimator (<math>r_2</math>) into the hole (<math>R = 8.73\ cm</math>)
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[[File:minimum_energy_condition.png]]
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<math>x_2 + r_2 = R</math>
 
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1) Assuming the collimator diameter is <math>\Theta_C</math>:
 
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<math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
 
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      \frac{1}{2}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) = 8.73 \Rightarrow E_{min} = 33.1\ MeV  </math>
 
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2) Assuming the collimator diameter is <math>\Theta_C/2</math>:
 
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<math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
 
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      \frac{1}{2}\ (286+183)\ \tan\left(\frac{1}{2}\ \frac{0.511}{E_{min}}\right) = 8.73 \Rightarrow E_{min} = 26.3\ MeV  </math>
 
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3) Assuming the collimator diameter is <math>\Theta_C/4</math>:
 
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<math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
 
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      \frac{1}{2}\ (286+183)\ \tan\left(\frac{1}{4}\ \frac{0.511}{E_{min}}\right) = 8.73 \Rightarrow E_{min} = 22.8\ MeV  </math>
 
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4) In general:
 
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[[File:plot_energy_collimatorsize.jpeg]]
 
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=25 MeV geometry=
 
  
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=geometry calculation=
  
 
{| border="1" cellpadding="20" cellspacing="0"
 
{| border="1" cellpadding="20" cellspacing="0"
 
|-
 
|-
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||<math>collimator diameter</math>
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!width=40|beam energy
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||<math>\Theta_{critical}</math>
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!width=40|collimator diameter
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||<math>\Theta_{kicker}</math>
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|<math>\Theta_{critical}</math>
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||<math>\alpha_{collimator}</math>
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|<math>\Theta_{kicker}</math>
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||<math>AC</math>
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|<math>\alpha_{collimator}</math>
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||<math>A_1C_1</math>
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|<math>AC</math>
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||<math>BD</math>
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|<math>A_1C_1</math>
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||<math>B_1D_1</math>
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|<math>BD</math>
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|<math>B_1D_1</math>
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|<math>FA</math>
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|<math>GH</math>
 
|-
 
|-
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||<math>\frac{\Theta_{critical}}{2}</math>||<math>1.17^o</math>||<math>0.82^o</math>||<math>2.03^o</math>||4.13||6.78||2.92||4.79
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|25 MeV||<math>\frac{\Theta_{critical}}{2}</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>2.03^o</math>
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|4.13 cm||6.78 cm||2.92 cm||4.79 cm||75 cm||7.49 cm
 
|-
 
|-
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||<math>1.17^o</math>||<math>0.82^o</math>||<math>\frac{\Theta_{critical}}{2}</math>||4.13||6.78||2.92||4.79
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|25 MeV||<math>\frac{\Theta_{critical}}{3}</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>1.63^o</math>
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|4.13 cm||6.78 cm||1.95 cm||3.20 cm||111 cm||4.99 cm
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|-
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|25 MeV||<math>\frac{\Theta_{critical}}{4}</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>1.43^o</math>
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|4.13 cm||6.78 cm||1.46 cm||2.40 cm||136 cm||3.74 cm
 
|-
 
|-
 
|}
 
|}
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==critical angle==
 
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<math>\Theta_C = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{25\ MeV} = 1.17\ ^o</math><br>
 
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==kicker angle==
 
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  <math>\Delta_1 = 286\ cm\ *\ \tan(1.17^o) = 5.84\ cm</math> <br>
 
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  <math>x^2+x^2 = 5.84^2\ cm \ \ \Rightarrow\ \  x = 4.13\ cm
 
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  \Rightarrow\ \ \tan^{-1}\left(\frac{4.13}{286}\right) = 0.827\ ^o</math><br>
 
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==geometry (<math> \Theta_c/2</math>)==
 
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===collimator center position===
 
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  <math>286\ cm \cdot \tan (0.827) = 4.13\ cm</math>  (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm</math>  (wall 2)
 
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===collimator diameter===
 
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  <math>286\ cm \cdot \tan (1.17/2) = 2.92\ cm</math>  (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (1.17/2) = 4.79\ cm</math>  (wall 2)
 
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===collimator critical angle===
 
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  <math> AB = AC - BD/2 = (4.13 - 2.92/2)\ cm = 2.67\ cm </math><br>
 
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  <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 4.79/2)\ cm = 9.165\ cm </math><br>
 
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  <math>\bigtriangleup BED_1  \Rightarrow \tan (\alpha) = \frac{(9.165 - 2.67)\ cm}{183\ cm} \Rightarrow \alpha = 2.033^o</math>:
 
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===minimal distance from the wall (<math> \Theta_c/2</math>)===
 
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  <math>\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (2.033^o)} = \frac{2.67\ cm}{\tan (2.033^o)} = 75\ cm </math>
 
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==geometry (<math> \Theta_c/4</math>)==
 
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===collimator center position===
 
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  <math>286\ cm \cdot \tan (0.827) = 4.13\ cm</math>  (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm</math>  (wall 2)
 
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===collimator diameter===
 
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  <math>286\ cm \cdot \tan (1.17/4) = 1.46\ cm</math>  (wall 1)<br>
 
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  <math>(286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm</math>  (wall 2)
 
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===collimator critical angle===
 
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  <math> AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ cm </math><br>
 
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  <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm </math><br>
 
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  <math>\bigtriangleup BED_1  \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o</math>:
 
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===minimal distance from the wall (<math> \Theta_c/4</math>)===
 
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  <math>\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm </math>
 
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==Funny pictures...==
 
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===how it looks 1 (<math> \Theta_c/2</math>, box 3"x4" and then pipe 4")===
 
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[[File:vacuum_pipe_collimator_.png]]<br>
 
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===how it looks 2 (<math> \Theta_c/4</math>, box 3"x4" and then pipe 4")===
 
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[[File:vacuum_pipe_collimator_.png]]<br>
 
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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]

Latest revision as of 17:50, 20 June 2010

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general setup

Minimum energy condition.png

geometry calculation

beam energy collimator diameter [math]\Theta_{critical}[/math] [math]\Theta_{kicker}[/math] [math]\alpha_{collimator}[/math] [math]AC[/math] [math]A_1C_1[/math] [math]BD[/math] [math]B_1D_1[/math] [math]FA[/math] [math]GH[/math]
25 MeV [math]\frac{\Theta_{critical}}{2}[/math] [math]1.17^o[/math] [math]0.83^o[/math] [math]2.03^o[/math] 4.13 cm 6.78 cm 2.92 cm 4.79 cm 75 cm 7.49 cm
25 MeV [math]\frac{\Theta_{critical}}{3}[/math] [math]1.17^o[/math] [math]0.83^o[/math] [math]1.63^o[/math] 4.13 cm 6.78 cm 1.95 cm 3.20 cm 111 cm 4.99 cm
25 MeV [math]\frac{\Theta_{critical}}{4}[/math] [math]1.17^o[/math] [math]0.83^o[/math] [math]1.43^o[/math] 4.13 cm 6.78 cm 1.46 cm 2.40 cm 136 cm 3.74 cm


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