Difference between revisions of "Geometry (25 MeV LINAC exit port)"

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[[File:plot_energy_collimatorsize.jpeg]]
 
[[File:plot_energy_collimatorsize.jpeg]]
  
=Consider 25 MeV geometry=
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=25 MeV geometry=
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{| border="1" cellpadding="20" cellspacing="0"
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|-
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|<math>\Theta_{critical}</math>
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||<math>\Theta_{kicker}</math>
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||<math>\Theta_{collimator}</math>
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||<math>AC</math>
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||<math>A_1C_1</math>
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||<math>BD</math>
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||<math>B_1D_1</math>
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|-
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|20 MeV || <math>90^o</math> || <math>94.38^o</math> || <math>600\ \mu b</math>
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|| <math>63\ \mu b/sr</math> || <math>40\cdot 10^{-4}\ sr</math> || <math>4.2\cdot 10^{-4}</math> 
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|-
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|40 MeV || <math>90^o</math> || <math>96.06^o</math> || <math>350\ \mu b</math>
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|| <math>23\ \mu b/sr</math> || <math>40\cdot 10^{-4}\ sr</math> || <math>2.6\cdot 10^{-4}</math> 
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|-
 +
|}
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==critical angle==
 
==critical angle==

Revision as of 05:20, 13 June 2010

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Minimum accelerator energy to run experiment

Min energy.png

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])

[math]x_2 + r_2 = R[/math]

1) Assuming the collimator diameter is [math]\Theta_C[/math]:

[math]\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
       \frac{1}{2}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) = 8.73 \Rightarrow E_{min} = 33.1\ MeV  [/math]

2) Assuming the collimator diameter is [math]\Theta_C/2[/math]:

[math]\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
       \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]

3) Assuming the collimator diameter is [math]\Theta_C/4[/math]:

[math]\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
       \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]

4) In general:

Plot energy collimatorsize.jpeg

25 MeV geometry

[math]\Theta_{critical}[/math] [math]\Theta_{kicker}[/math] [math]\Theta_{collimator}[/math] [math]AC[/math] [math]A_1C_1[/math] [math]BD[/math] [math]B_1D_1[/math]
20 MeV [math]90^o[/math] [math]94.38^o[/math] [math]600\ \mu b[/math] [math]63\ \mu b/sr[/math] [math]40\cdot 10^{-4}\ sr[/math] [math]4.2\cdot 10^{-4}[/math]
40 MeV [math]90^o[/math] [math]96.06^o[/math] [math]350\ \mu b[/math] [math]23\ \mu b/sr[/math] [math]40\cdot 10^{-4}\ sr[/math] [math]2.6\cdot 10^{-4}[/math]


critical angle

[math]\Theta_C = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{25\ MeV} = 1.17\ ^o[/math]

kicker angle

  [math]\Delta_1 = 286\ cm\ *\ \tan(1.17^o) = 5.84\ cm[/math] 
[math]x^2+x^2 = 5.84^2\ cm \ \ \Rightarrow\ \ x = 4.13\ cm \Rightarrow\ \ \tan^{-1}\left(\frac{4.13}{286}\right) = 0.827\ ^o[/math]

geometry ([math] \Theta_c/2[/math])

collimator center position

  [math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math] (wall 2)

collimator diameter

  [math]286\ cm \cdot \tan (1.17/2) = 2.92\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (1.17/2) = 4.79\ cm[/math] (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (4.13 - 2.92/2)\ cm = 2.67\ cm [/math]
[math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 4.79/2)\ cm = 9.165\ cm [/math]
[math]\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(9.165 - 2.67)\ cm}{183\ cm} \Rightarrow \alpha = 2.033^o[/math]:

minimal distance from the wall ([math] \Theta_c/2[/math])

  [math]\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (2.033^o)} = \frac{2.67\ cm}{\tan (2.033^o)} = 75\ cm [/math]

geometry ([math] \Theta_c/4[/math])

collimator center position

  [math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math] (wall 2)

collimator diameter

  [math]286\ cm \cdot \tan (1.17/4) = 1.46\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm[/math] (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ cm [/math]
[math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm [/math]
[math]\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o[/math]:

minimal distance from the wall ([math] \Theta_c/4[/math])

  [math]\bigtriangleup FAB  \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm [/math]

Funny pictures...

how it looks 1 ([math] \Theta_c/2[/math], box 3"x4" and then pipe 4")

File:Vacuum pipe collimator .png

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

File:Vacuum pipe collimator .png


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