View source for Geometry (44 MeV LINAC exit port)

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=Some measurements of 90 experimental degree exit port=

[[File:exit_port1.png]]<br><br>


=Critical angle and displacement calculations=

<math>\Theta = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{44\ MeV} = 0.67\ ^o</math><br>


=Kicker angle and displacement calculations=

==1 foot = 30.48 cm==

==accelerator's side wall==

   <math>\Delta = 286\ cm\ *\ \tan(0.67^o) = 3.34\ cm</math> 

   <math>x^2+x^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ cm</math>

   <math>\Delta = 2.36\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.47\ ^o</math>

==detector's side wall==

   <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm</math>

   <math>\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm</math>

=Off-axis collimation geometry=

[[File:beam_up_down5.png]]<br>

=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)<br>
   <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)<br>
   <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><br>
   <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 - 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>

==how it looks (<math> \Theta_c/2</math>)==

[[File:vacuum_pipe_collimator_0.335_2.png]]<br>

=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)

==collimator critical angle==

   <math> AB = AC - BD/2 = (2.35 - 0.84/2)\ cm = 1.93\ 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> 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>

==how it looks (<math> \Theta_c/4</math>)==

[[File:vacuum_pipe_collimator_0.168_2.png]]<br>


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