Geometry (25 MeV LINAC exit port)

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Minimum accelerator energy to run experiment

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:

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]\frac{\Theta_{critical}}{2}[/math]	[math]1.17^o[/math]	[math]0.83^o[/math]	[math]2.03^o[/math]	4.13	6.78	2.92	4.79
[math]\frac{\Theta_{critical}}{4}[/math]	[math]1.17^o[/math]	[math]0.82^o[/math]	[math]1.43^o[/math]	4.13	6.78	1.46	2.40

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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