Minimum accelerator energy to run experiment: Difference between revisions
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The minimum energy of accelerator (MeV) is limited by fitting the collimator size <math>r_2</math> into the hole R = 8.73 cm: | The minimum energy of accelerator (MeV) is limited by fitting the collimator size <math>r_2</math> into the hole R = 8.73 cm: | ||
Revision as of 21:39, 14 June 2010
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 under 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 under this line is good to run experiment for condition above
both conditions above are together
All energy under this linse is good to run experiment for both conditions above