Difference between revisions of "Minimum accelerator energy to run experiment"

From New IAC Wiki
Jump to navigation Jump to search
Line 28: Line 28:
 
All energy under this line is good to run experiment for condition above
 
All energy under this line is good to run experiment for condition above
  
=nothing hitting the box going through the collimator condition=
+
=critical collimator line condition=
  
 
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:

Revision as of 03:15, 15 June 2010

Go Back

general setup

Minimum energy condition.png

fitting the collimator size into the hole through the concrete wall

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:

[math]A_1D_1(E,\ \Theta_C/m) = \frac{469}{\sqrt{2}}\tan\left(\frac{0.511}{E}\right)
                              + \frac{469}{2}\tan\left(\frac{1}{m}\frac{0.511}{E}\right)[/math]

To fit the collimator size into the hole through the concrete wall with radius R = 8.73 cm we need to solve equation:

[math]A_1D_1(E,\ \Theta_C/m) = 8.73\ cm[/math]

1) some solutions of this equation for different collimator size m are:

[math]m = 1 \Rightarrow E_{min} = 33.1\ MeV  [/math]
[math]m = 2 \Rightarrow E_{min} = 26.3\ MeV [/math]
[math]m = 4 \Rightarrow E_{min} = 22.8\ MeV [/math]

2) in general for arbitrary collimator size m the solutions are:

Energy condition1.jpeg

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

critical collimator line condition

Also I can express the distance [math]GH[/math] as function of collimator size [math]\Theta_C/m[/math] and electron beam energy E:

Formula cond2.png

If I would like that nothing hitting the 4" box to go through the collimator I need to solve equation:

[math]GH(E,\ \Theta_C/m) = 5.08\ cm[/math]

1) some solutions of this equation for different collimator size m are:

[math]m = 1 \Rightarrow E_{min} = 73.7\ MeV  [/math]
[math]m = 2 \Rightarrow E_{min} = 36.9\ MeV [/math]
[math]m = 4 \Rightarrow E_{min} = 18.4\ MeV [/math]

2) in general for arbitrary collimator size m the solutions are:

Energy condition2.jpeg

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

both solutions above are together

Energy condition12.jpeg

All energy under this linse is good to run experiment for both conditions above


Go Back