Geometry (44 MeV LINAC exit port)

From New IAC Wiki
Jump to navigation Jump to search

Go Back

Some measurements of 90 experimental degree exit port

Exit port1.png


Critical angle and displacement calculations

[math]\Theta = \frac{m_ec^2}{E_{beam}} = \frac{0.511\ MeV}{44\ MeV} = 0.67\ ^o[/math]


Kicker angle and displacement calculations

1 foot = 30.48 cm

accelerator's side wall

  [math]\Delta = 286\ cm\ *\ \tan(0.67^o) = 3.34\ cm[/math] 
  [math]x^2+x^2 = 3.34^2\ cm \ \ \Rightarrow\ \  x = 2.36\ cm[/math]
  [math]\Delta = 2.36\ cm \ \ \Rightarrow\ \ \tan^{-1}\left(\frac{2.36}{286}\right) = 0.47\ ^o[/math]

detector's side wall

  [math]\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.67^o) = 5.48\ cm[/math]
  [math]\Delta = (286\ cm + 183\ cm)\ *\ \tan(0.47^o) = 3.85\ cm[/math]

Off-axis collimation geometry

Beam up down5.png

Vacuum pipe location (only the kicker angle)

collimator location

1) center position

  [math]286\ cm \cdot \tan (0.47) = 2.35\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.47) = 3.85\ cm[/math] (wall 2)

2) assume collimator diameter is [math]\Theta_c/2 = 0.67^o/2 = 0.335^o[/math]

  [math]286\ cm \cdot \tan (0.335) = 1.67\ cm[/math]  (wall 1)
[math](286 + 183)\ cm \cdot \tan (0.335) = 2.74\ cm[/math] (wall 2)

collimator critical angle

  [math] AB = AC - BD/2 = (2.35 - 1.67/2)\ cm = 1.52\ cm [/math]
[math] A_1D_1 = A_1C_1 + B_1D_1/2 = (3.85 + 2.74/2)\ cm = 5.22\ cm [/math]
[math] ED_1 = A_1D_1 - A_1E = (5.22 - 1.52)\ cm = 3.70\ cm [/math]

from triangle [math]BED_1[/math]:

  [math] \tan (\alpha) = \frac{3.70\ cm}{183\ cm} \Rightarrow \alpha = 1.16^o[/math]

minimal distance from the wall

1) from triangle QAB:

  [math] QA = \frac{AB}{\tan (1.16^o)} = \frac{1.52\ cm}{\tan (1.16^o)} = 75\ cm [/math]

3) from triangles OPR and QPR:

  [math] OQ = OA - QA = (286 - 75)\ cm = 211\ cm [/math]
  [math] OR\cdot \tan (0.67^o)) = (211 - OR)\cdot \tan (1.16^o) \Rightarrow[/math]
[math] OR = 211 cm\cdot \frac{tan (1.16^o)}{tan (1.16^o) + tan (0.67^o)} = 134\ cm[/math]
  [math] RQ = OQ - RQ = (211-134)\ cm = 77\ cm [/math]
  
  [math] PR = 134\cdot \tan (0.67^o) = 1.57\ cm[/math]

4) minimal distance:

  [math] OR = 134\ cm\ \ (vacuum\ pipe\ length) [/math]
  [math] RA = OA - OR = (286 - 134)\ cm = 152\ cm\ \ (from\ the\ wall\ to\ the\ pipe) [/math]

collimator and pipe geometry

Vacuum pipe collimator2.png

Vacuum pipe location (kicker + multiple scattering angle angles)

1) take multiple scattering angle [math] \Theta = 0.27^o[/math]

  [math] 0.67^o \longrightarrow (0.67^o - 0.27^o) = 0.40^o[/math]
  [math] OR = 211 cm\cdot \frac{tan (1.16^o)}{tan (1.16^o) + tan (0.40^o)} = 157\ cm[/math]
  [math] RQ = OQ - RQ = (211-157)\ cm = 54\ cm [/math]
  
  [math] PR = 157\cdot \tan (0.40^o) = 1.09\ cm[/math]

4) minimal distance:

  [math] OR = 157\ cm\ \ (vacuum\ pipe\ length) [/math]
  [math] RA = OA - OR = (286 - 157)\ cm = 129\ cm\ \ (from\ the\ wall\ to\ the\ pipe) [/math]


Go Back