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Minimum accelerator energy to run experiment
[math]x_2 + r_2 \leq R[/math] condition
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) for arbitrary collimator size:
All energy above this line is good to run experiment
[math]F_1A \lt = 286\ cm[/math] condition
All energy above this line is good to run experiment
both condition above just together
All energy above this lines is good to run experiment
25 MeV geometry
geometry calculation
| 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]F_1F[/math]
|
| [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 |
143 cm
|
| [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 |
203 cm
|
geometry 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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