Minimum accelerator energy to run experiment: Difference between revisions
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=general setup= | =general setup= | ||
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I can express the distance <math>A_1D_1</math> as function of collimator size <math>\Theta_C/m</math> and electron beam energy E: | I can express the distance <math>A_1D_1</math> as function of collimator size <math>\Theta_C/m</math> and electron beam energy E: | ||
[[File: | [[File:formula_cond11.png]] | ||
To fit the collimator size into the hole through the concrete wall with radius R = 8.73 cm we need to solve equation: | To fit the collimator size into the hole through the concrete wall with radius R = 8.73 cm we need to solve equation: | ||
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Also I can express the distance <math>GH</math> as function of collimator size <math>\Theta_C/m</math> and electron beam energy E: | Also I can express the distance <math>GH</math> as function of collimator size <math>\Theta_C/m</math> and electron beam energy E: | ||
[[File: | [[File:formula_cond21.png]] | ||
If I would like that nothing hitting the 4" box to go through the collimator I need to solve equation: | If I would like that nothing hitting the 4" box to go through the collimator I need to solve equation: | ||
Latest revision as of 19:03, 24 May 2012
general setup
fitting the collimator size into the hole through the concrete wall
I can express the distance [math]\displaystyle{ A_1D_1 }[/math] as function of collimator size [math]\displaystyle{ \Theta_C/m }[/math] and electron beam energy E:
To fit the collimator size into the hole through the concrete wall with radius R = 8.73 cm we need to solve equation:
[math]\displaystyle{ A_1D_1(E,\ \Theta_C/m) = 8.73\ cm }[/math]
1) some solutions of this equation for different collimator sizes m are:
[math]\displaystyle{ m = 1 \Rightarrow E_{min} = 33.1\ MeV }[/math]
[math]\displaystyle{ m = 2 \Rightarrow E_{min} = 26.3\ MeV }[/math]
[math]\displaystyle{ m = 4 \Rightarrow E_{min} = 22.8\ MeV }[/math]
2) in general for arbitrary collimator size m the solutions are:
All energies above this line is good to run experiment for condition above
critical collimator line condition
Also I can express the distance [math]\displaystyle{ GH }[/math] as function of collimator size [math]\displaystyle{ \Theta_C/m }[/math] and electron beam energy E:
If I would like that nothing hitting the 4" box to go through the collimator I need to solve equation:
[math]\displaystyle{ GH(E,\ \Theta_C/m) = 5.08\ cm }[/math]
1) some solutions of this equation for different collimator sizes m are:
[math]\displaystyle{ m = 1 \Rightarrow E_{min} = 73.7\ MeV }[/math]
[math]\displaystyle{ m = 2 \Rightarrow E_{min} = 36.9\ MeV }[/math]
[math]\displaystyle{ m = 4 \Rightarrow E_{min} = 18.4\ MeV }[/math]
2) in general for arbitrary collimator size m the solutions are:
All energies above this line is good to run experiment for condition above
both solutions are together
All energies above this lines is good to run experiment for both conditions above