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

From New IAC Wiki
Jump to navigation Jump to search
Line 9: Line 9:
 
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:
 
   
 
   
  <math>A_1D_1(E,\ \Theta_C/m) = \frac{469}{2}\tan(\frac{0.511}{E}) + \frac{469}{sqrt{2}}\tan(\frac{1}{m}\frac{0.511}{E})<math>
+
  <math>A_1D_1(E,\ \Theta_C/m) = \frac{469}{2}\tan(\frac{0.511}{E}) + \frac{469}{sqrt{2}}\tan(\frac{1}{m}\frac{0.511}{E})<\math>
  
 
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 22:00, 14 June 2010

Go Back

general setup

Minimum energy condition.png

fitting the collimator size into the hole in 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}{2}\tan(\frac{0.511}{E}) + \frac{469}{sqrt{2}}\tan(\frac{1}{m}\frac{0.511}{E})\lt \math\gt 

The minimum energy of accelerator (MeV) is limited by fitting the collimator size \lt math\gt 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

GH = 5.08 cm condition

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 under this line is good to run experiment for condition above

both conditions above are together

Plot energy bothcondition.jpeg

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


Go Back