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 setup

geometry calculation

beam energy	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]A1D1[/math]	[math]FA[/math]	[math]GH[/math]
25 MeV	[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	9.18 cm > 8.73 cm	75 cm	7.49 cm > 5.08 cm
25 MeV	[math]\frac{\Theta_{criicalt}}{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
25 MeV	[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	7.98 cm < 8.73 cm	136 cm	3.74 cm < 5.08 cm
44 MeV	[math]\frac{\Theta_{critical}}{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 < 8.73 cm	75 cm	4.26 cm < 5.08 cm
44 MeV	[math]\frac{\Theta_{critical}}{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
44 MeV	[math]\frac{\Theta_{critical}}{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

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