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| | [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] | | [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] |
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| − | =Minimum accelerator energy to run experiment=
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| − | [[File:min_energy.png|1000px]]
| + | =general setup= |
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| − | 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>)
| + | [[File:minimum_energy_condition.png]] |
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| − | <math>x_2 + r_2 = R</math>
| + | =geometry calculation= |
| − | | |
| − | 1) Assuming the collimator diameter is <math>\Theta_C</math>:
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| − | <math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
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| − | \frac{1}{2}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) = 8.73 \Rightarrow E_{min} = 33.1\ MeV </math>
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| − | 2) Assuming the collimator diameter is <math>\Theta_C/2</math>:
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| − | <math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
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| − | \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>
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| − | 3) Assuming the collimator diameter is <math>\Theta_C/4</math>:
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| − | | |
| − | <math>\frac{1}{\sqrt{2}}\ (286+183)\ \tan\left(\frac{0.511}{E_{min}}\right) +
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| − | \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>
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| − | | |
| − | 4) In general:
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| − | [[File:plot_energy_collimatorsize.jpeg]]
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| − | | |
| − | =Consider 25 MeV geometry=
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| − | | |
| − | ==critical angle==
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| − | | |
| − | <math>\Theta_C = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{25\ MeV} = 1.17\ ^o</math><br>
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| − | | |
| − | ==kicker angle==
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| − | | |
| − | <math>\Delta_1 = 286\ cm\ *\ \tan(1.17^o) = 5.84\ cm</math> <br>
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| − | <math>x^2+x^2 = 5.84^2\ cm \ \ \Rightarrow\ \ x = 4.13\ cm</math> <br>
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| − | <math>x = 4.13\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{4.13}{286}\right) = 0.827\ ^o</math><br>
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| − | | |
| − | ==geometry (<math> \Theta_c/2</math>)==
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| − | | |
| − | ===collimator center position===
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| − | | |
| − | <math>286\ cm \cdot \tan (0.827) = 4.13\ cm</math> (wall 1)<br>
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| − | <math>(286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm</math> (wall 2)
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| − | | |
| − | ===collimator diameter===
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| − |
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| − | <math>286\ cm \cdot \tan (1.17/2) = 2.92\ cm</math> (wall 1)<br>
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| − | <math>(286 + 183)\ cm \cdot \tan (1.17/2) = 4.79\ cm</math> (wall 2)
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| − | | |
| − | ===collimator critical angle===
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| − | | |
| − | <math> AB = AC - BD/2 = (4.13 - 2.92/2)\ cm = 2.67\ cm </math><br>
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| − | <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 4.79/2)\ cm = 9.165\ cm </math><br>
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| − | <math>\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(9.165 - 2.67)\ cm}{183\ cm} \Rightarrow \alpha = 2.033^o</math>:
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| − | | |
| − | ===minimal distance from the wall (<math> \Theta_c/2</math>)===
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| − | <math>\bigtriangleup FAB \Rightarrow FA = \frac{AB}{\tan (2.033^o)} = \frac{2.67\ cm}{\tan (2.033^o)} = 75\ cm </math>
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| − | | |
| − | ==geometry (<math> \Theta_c/4</math>)==
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| − | | |
| − | ===collimator center position===
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| − | | |
| − | <math>286\ cm \cdot \tan (0.827) = 4.13\ cm</math> (wall 1)<br>
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| − | <math>(286 + 183)\ cm \cdot \tan (0.827) = 6.77\ cm</math> (wall 2)
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| − | | |
| − | ===collimator diameter===
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| − |
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| − | <math>286\ cm \cdot \tan (1.17/4) = 1.46\ cm</math> (wall 1)<br>
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| − | <math>(286 + 183)\ cm \cdot \tan (1.17/4) = 2.39\ cm</math> (wall 2)
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| − | | |
| − | ===collimator critical angle===
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| − | | |
| − | <math> AB = AC - BD/2 = (4.13 - 1.46/2)\ cm = 3.4\ cm </math><br>
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| − | <math> A_1D_1 = A_1C_1 + B_1D_1/2 = (6.77 + 2.39/2)\ cm = 7.965\ cm </math><br>
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| − | <math>\bigtriangleup BED_1 \Rightarrow \tan (\alpha) = \frac{(7.965 - 3.4)\ cm}{183\ cm} \Rightarrow \alpha = 1.429^o</math>:
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| − | | |
| − | ===minimal distance from the wall (<math> \Theta_c/4</math>)===
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| − | | |
| − | <math>\bigtriangleup FAB \Rightarrow FA = \frac{AB}{\tan (1.429^o)} = \frac{3.4\ cm}{\tan (1.429^o)} = 136\ cm </math>
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| − | | |
| − | ==Funny pictures...==
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| − | | |
| − | ===how it looks 1 (<math> \Theta_c/2</math>, box 3"x4" and then pipe 4")===
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| − | [[File:vacuum_pipe_collimator_.png]]<br>
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| − | | |
| − | ===how it looks 2 (<math> \Theta_c/4</math>, box 3"x4" and then pipe 4")===
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| − | [[File:vacuum_pipe_collimator_.png]]<br>
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| | + | {| border="1" cellpadding="20" cellspacing="0" |
| | + | |- |
| | + | !width=40|beam energy |
| | + | !width=40|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>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||75 cm||7.49 cm |
| | + | |- |
| | + | |25 MeV||<math>\frac{\Theta_{critical}}{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||111 cm||4.99 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||136 cm||3.74 cm |
| | + | |- |
| | + | |} |
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| | [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] | | [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] |
