Geometry (25 MeV LINAC exit port)

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Minimum accelerator energy to run experiment

condition 1: fitting the collimator size into the hole

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

condition 2: F1A = 286 cm

All energy above this line is good to run experiment

both conditions above are 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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