Collimation geometry for different beam energies

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Critical and Kicker angles

[math]\Theta_C = \frac{m_ec^2}{E}[/math]

[math]\Theta_K = tan^{-1}\left(\frac{x_1}{286}\right)
                = tan^{-1}\left(\frac{1}{\sqrt{2}}\ \frac{\Delta_1}{286}\right)
                = tan^{-1}\left(\frac{1}{\sqrt{2}}\ tan(\Theta_C)\right)[/math]

General collimator setup

[math]AC = 286\cdot\tan(\Theta_K)\ cm[/math]

[math]A_1C_1 = (286 +183)\cdot\tan(\Theta_K)\ cm[/math]

[math]BD = 286\cdot\tan(\Theta_C/m)\ cm[/math]

[math]B_1D_1 = (286 + 183)\cdot\tan(\Theta_C/m)\ cm[/math]

[math]\alpha = \frac{A_1D_1 - AB}{183} = \frac{(A_1C_1 + C_1D_1/2) - (AC - B_1D_1/2)}{183}[/math]

[math]FA = AB/\tan(\alpha)\ cm[/math]

[math]GH = (286 - FA)\cdot\tan(\alpha)\ cm[/math]

geometry calculation

beam energy	collimator diameter	$\Theta_{critical}$	$\Theta_{kicker}$	$\alpha_{collimator}$	$AC$	$A_1C_1$	$BD$	$B_1D_1$	$A1D1$	$FA$	$GH$
25 MeV	$\frac{\Theta_{critical}}{2}$	$1.17^o$	$0.83^o$	$2.03^o$	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
25 MeV	$\frac{\Theta_{criicalt}}{3}$	$1.17^o$	$0.83^o$	$1.63^o$	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
25 MeV	$\frac{\Theta_{critical}}{4}$	$1.17^o$	$0.83^o$	$1.43^o$	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
44 MeV	$\frac{\Theta_{critical}}{2}$	$0.67^o$	$0.47^o$	$1.16^o$	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
44 MeV	$\frac{\Theta_{critical}}{3}$	$0.67^o$	$0.47^o$	$0.93^o$	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
44 MeV	$\frac{\Theta_{critical}}{4}$	$0.67^o$	$0.47^o$	$0.81^o$	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

Funny pictures...

how it looks ($\Theta_c/2$, pipe 3")

how it looks 1 ($\Theta_c/4$, pipe 3")

how it looks 2 ($\Theta_c/4$, pipe 3")

how it looks 4 ($\Theta_c/2$, pipe (2 1/2)" and then pipe 4")

need to adjust to converter position

how it looks 5 ($\Theta_c/2$, box 3"x4" and then pipe 4")

need to adjust to converter position

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