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| | [[File:min_energy.png|1000px]] | | [[File:min_energy.png|1000px]] |
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| − | critical angle:<br>
| + | <math> \Theta_C = \frac{0.511\ MeV}{E\ MeV}\frac{180}{\pi} </math> critical angle<br> |
| − | <math> \Theta_C = \frac{0.511\ MeV}{E\ MeV}\frac{180}{\Pi} </math> | |
| − | | |
| − | displacements on the wall:<br> | |
| | <math> \Delta = 286\ \tan(\Theta_C) </math><br> | | <math> \Delta = 286\ \tan(\Theta_C) </math><br> |
| − | <math> x = \frac{\Delta}{\sqrt{2}}</math> | + | <math> x = \frac{\Delta}{\sqrt{2}}</math><br> |
| − | | + | <math> r = \frac{1}{2}286\ \tan{\frac{\Theta_C}{2}} <math> collimator radius |
| − | assume diameter of collimator is <math>\Theta/2</math>
| |
| − | <math> r = \frac{1}{2}286\ \tan{\frac{\Theta_C}{2}} <math> | |
| | | | |
| | =25 MeV geometry= | | =25 MeV geometry= |
Revision as of 22:48, 11 June 2010
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Minimum accelerator energy to run experiment
[math] \Theta_C = \frac{0.511\ MeV}{E\ MeV}\frac{180}{\pi} [/math] critical angle
[math] \Delta = 286\ \tan(\Theta_C) [/math]
[math] x = \frac{\Delta}{\sqrt{2}}[/math]
[math] r = \frac{1}{2}286\ \tan{\frac{\Theta_C}{2}} \lt math\gt collimator radius
=25 MeV geometry=
==critical angle==
\lt math\gt \Theta_C = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{25\ MeV} = 1.17\ ^o[/math]
kicker angle
[math]\Delta_1 = 286\ cm\ *\ \tan(1.17^o) = 5.84\ cm[/math]
[math]x^2+x^2 = 5.84^2\ cm \ \ \Rightarrow\ \ x = 4.13\ cm[/math]
[math]\Delta_2 = 4.13\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{4.13}{286}\right) = 0.827\ ^o[/math]
geometry ([math] \Theta_c/2[/math])
collimator center position
[math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math] (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math] (wall 2)
collimator diameter
[math]286\ cm \cdot \tan (1.17/2) = 2.92\ cm[/math] (wall 1)
[math](286 + 183)\ cm \cdot \tan (1.17/2) = 4.79\ cm[/math] (wall 2)
collimator critical angle
[math] AB = AC - BD/2 = (4.13 - 2.92/2)\ cm = 2.67\ cm [/math]
[math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 4.79/2)\ cm = 9.165\ cm [/math]
[math]\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(9.165 - 2.67)\ cm}{183\ cm} \Rightarrow \alpha = 2.033^o[/math]:
minimal distance from the wall ([math] \Theta_c/2[/math])
[math]\bigtriangleup FAB \Rightarrow FA = \frac{AB}{\tan (2.033^o)} = \frac{2.67\ cm}{\tan (2.033^o)} = 75\ cm [/math]
geometry ([math] \Theta_c/4[/math])
collimator center position
[math]286\ cm \cdot \tan (0.827) = 4.13\ cm[/math] (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm[/math] (wall 2)
collimator diameter
[math]286\ cm \cdot \tan (1.17/4) = 1.46\ cm[/math] (wall 1)
[math](286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm[/math] (wall 2)
collimator critical angle
[math] AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ cm [/math]
[math] A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm [/math]
[math]\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o[/math]:
minimal distance from the wall ([math] \Theta_c/4[/math])
[math]\bigtriangleup FAB \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm [/math]
Funny 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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