Difference between revisions of "Collimation geometry for different beam energies"

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  <math>\Theta_K = tan^{-1}\left(\frac{x_1}{286}\right)
 
  <math>\Theta_K = tan^{-1}\left(\frac{x_1}{286}\right)
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                 = tan^{-1}\left(\frac{1}{\sqrt{2}}\ \frac{\Delta_1}{286}\right)
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                 = tan^{-1}\left(\frac{\Delta_1}{\sqrt{2}\ 286}\right)
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                 = tan^{-1}\left(\frac{1}{\sqrt{2}}\ tan(\Theta_C)\right)</math><br>
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                 = tan^{-1}\left(\frac{tan(\Theta_C)}{\sqrt{2}}\right)</math><br>
  
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=25 MeV geometry, <math>\Theta\ /\ 2</math> collimation angle=
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=25 MeV geometry, <math>\Theta / 2</math> collimation angle=
  
  
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=25 MeV and 44 MeV geometry for different collimation angles=
 
=25 MeV and 44 MeV geometry for different collimation angles=
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==general setup==
  
 
[[File:minimum_energy_condition.png|700px]]
 
[[File:minimum_energy_condition.png|700px]]
  
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==calculation==
  
 
{| border="1" cellpadding="10" cellspacing="0"
 
{| border="1" cellpadding="10" cellspacing="0"
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|-
 
|-
 
|25 MeV||<math>\Theta_C / 2</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>2.03^o</math>
 
|25 MeV||<math>\Theta_C / 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||9.18 cm > 8.73 cm||75 cm||7.49 cm > 5.08 cm
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|4.13 cm||6.78 cm||2.92 cm||4.79 cm||9.18 cm||75 cm||7.49 cm
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|-
+
|-'
 
|25 MeV||<math>\Theta_C / 3</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>1.63^o</math>
 
|25 MeV||<math>\Theta_C / 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||8.37 cm < 8.73 cm||111 cm||4.99 cm < 5.08 cm
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|4.13 cm||6.78 cm||1.95 cm||3.20 cm||8.38 cm||111 cm||4.99 cm
 
|-
 
|-
 
|25 MeV||<math>\Theta_C / 4</math>||<math>1.17^o</math>||<math>0.83^o</math>||<math>1.43^o</math>
 
|25 MeV||<math>\Theta_C / 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||7.98 cm < 8.73 cm||136 cm||3.74 cm < 5.08 cm
+
|4.13 cm||6.78 cm||1.46 cm||2.40 cm||7.98 cm||136 cm||3.74 cm
 
|-
 
|-
  
 
|44 MeV||<math>\Theta_C / 2</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>1.16^o</math>
 
|44 MeV||<math>\Theta_C / 2</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>1.16^o</math>
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|2.35 cm||3.85 cm||1.66 cm||2.72 cm||5.21 cm < 8.73 cm||75 cm||4.26 cm < 5.08 cm
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|2.35 cm||3.85 cm||1.66 cm||2.72 cm||5.21 cm||75 cm||4.26 cm
 +
|-
 +
|44 MeV||<math>\Theta_C / 2</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>1.31^o</math>
 +
|2.35 cm||3.85 cm||1.66 cm||3.72 cm||5.71 cm||66 cm||5.03 cm
 
|-
 
|-
 
|44 MeV||<math>\Theta_C / 3</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>0.93^o</math>
 
|44 MeV||<math>\Theta_C / 3</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>0.93^o</math>
−
|2.35 cm||3.85 cm||1.11 cm||1.82 cm||4.76 cm < 8.73 cm||111 cm||2.84 cm < 5.08 cm
+
|2.35 cm||3.85 cm||1.11 cm||1.82 cm||4.76 cm||111 cm||2.84 cm
 
|-
 
|-
 
|44 MeV||<math>\Theta_C / 4</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>0.81^o</math>
 
|44 MeV||<math>\Theta_C / 4</math>||<math>0.67^o</math>||<math>0.47^o</math>||<math>0.81^o</math>
−
|2.35 cm||3.85 cm||0.83 cm||1.36 cm||4.53 cm < 8.73 cm||136 cm||2.13 cm < 5.08 cm
+
|2.35 cm||3.85 cm||0.83 cm||1.36 cm||4.53 cm||136 cm||2.13 cm
 
|}
 
|}
  

Latest revision as of 19:03, 24 May 2012

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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{\Delta_1}{\sqrt{2}\ 286}\right)
                = tan^{-1}\left(\frac{tan(\Theta_C)}{\sqrt{2}}\right)[/math]

25 MeV geometry, [math]\Theta / 2[/math] collimation angle

Vacuum pipe collimator 335 5.png

25 MeV and 44 MeV geometry for different collimation angles

general setup

Minimum energy condition.png

calculation

beam energy [math]\Theta_C / m[/math] [math]\Theta_C[/math] [math]\Theta_K[/math] [math]\alpha[/math] [math]AC[/math] [math]A_1C_1[/math] [math]BD[/math] [math]B_1D_1[/math] [math]A_1D_1[/math] [math]FA[/math] [math]GH[/math]
25 MeV [math]\Theta_C / 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 9.18 cm 75 cm 7.49 cm
25 MeV [math]\Theta_C / 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 8.38 cm 111 cm 4.99 cm
25 MeV [math]\Theta_C / 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 7.98 cm 136 cm 3.74 cm
44 MeV [math]\Theta_C / 2[/math] [math]0.67^o[/math] [math]0.47^o[/math] [math]1.16^o[/math] 2.35 cm 3.85 cm 1.66 cm 2.72 cm 5.21 cm 75 cm 4.26 cm
44 MeV [math]\Theta_C / 2[/math] [math]0.67^o[/math] [math]0.47^o[/math] [math]1.31^o[/math] 2.35 cm 3.85 cm 1.66 cm 3.72 cm 5.71 cm 66 cm 5.03 cm
44 MeV [math]\Theta_C / 3[/math] [math]0.67^o[/math] [math]0.47^o[/math] [math]0.93^o[/math] 2.35 cm 3.85 cm 1.11 cm 1.82 cm 4.76 cm 111 cm 2.84 cm
44 MeV [math]\Theta_C / 4[/math] [math]0.67^o[/math] [math]0.47^o[/math] [math]0.81^o[/math] 2.35 cm 3.85 cm 0.83 cm 1.36 cm 4.53 cm 136 cm 2.13 cm



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