Minimum accelerator energy to run experiment

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condition 1: fitting the collimator size into the hole

Min energy.png

The minimum energy of accelerator (MeV) is limited by fitting the collimator size [math]r_2[/math] into the hole R = 8.73 cm:

[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) for arbitrary collimator size [math]\Theta_C/2[/math]:

Plot energy collimatorsize.jpeg

All energy under this line is good to run experiment for condition above

condition 2: F1A = 286 cm

1) assuming the collimator diameter is [math]\Theta_C[/math]

[math] E_{min} = 73.7\ MeV  [/math]

2) assuming the collimator diameter is [math]\Theta_C/2[/math]

[math] E_{min} = 36.9\ MeV  [/math]

3) assuming the collimator diameter is [math]\Theta_C/4[/math]

[math] E_{min} = 18.4\ MeV  [/math]

4) for arbitrary collimator size [math]\Theta_C/m[/math]:

Plot energy F1A.jpeg

All energy above this line is good to run experiment

both conditions above are together

Plot energy bothcondition.jpeg

All energy above this lines is good to run experiment


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