Minimum accelerator energy to run experiment
condition 1: fitting the collimator size into the hole
The minimum energy of accelerator (MeV) is limited by fitting the collimator size [math]\displaystyle{ r_2 }[/math] into the hole R = 8.73 cm:
[math]\displaystyle{ x_2 + r_2 = R }[/math]
1) Assuming the collimator diameter is [math]\displaystyle{ \Theta_C }[/math]:
[math]\displaystyle{ \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]\displaystyle{ \Theta_C/2 }[/math]:
[math]\displaystyle{ \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]\displaystyle{ \Theta_C/4 }[/math]:
[math]\displaystyle{ \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]\displaystyle{ \Theta_C/2 }[/math]:
All energy above this line is good to run experiment for condition above
condition 2: F1A = 286 cm
1) assuming the collimator diameter is [math]\displaystyle{ \Theta_C }[/math]
[math]\displaystyle{ E_{min} = 73.7\ MeV }[/math]
2) assuming the collimator diameter is [math]\displaystyle{ \Theta_C/2 }[/math]
[math]\displaystyle{ E_{min} = 36.9\ MeV }[/math]
3) assuming the collimator diameter is [math]\displaystyle{ \Theta_C/4 }[/math]
[math]\displaystyle{ E_{min} = 18.4\ MeV }[/math]
4) for arbitrary collimator size [math]\displaystyle{ \Theta_C/m }[/math]:
All energy above this line is good to run experiment
both conditions above are together
All energy above this lines is good to run experiment