Beams Document 4896-v2

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Collimation Design using Reduced Courant-Snyder Coordinates

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Bruce C. Brown
Updated by:
Bruce C. Brown
Document Created:
24 Jul 2015, 15:11
Contents Revised:
27 May 2016, 14:59
Metadata Revised:
27 May 2016, 14:59
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24 Jul 2015, 15:30
An effective explanation for the design of a primary-secondary collimator system may employ a diagram in reduced coordinates. We construct such a diagram for the Main Injector collimation system and illustrate how much of the beam which is scattered by the primary collimator is absorbed in the first turn by the nearby secondary collimators. Additional losses are captured in subsequent turns following which some of the initially scattered beam will strike the primary collimator and be rescattered.This note will document the parameters for this system to confirm the various magnitudes and their relationships. We find for an 8-GeV beam that a 3-$\sigma$ horizontal beam size of 9.35 mm is scattered by a 0.25 mm Tungsten blade to give an RMS scattering angle of 371 $\mu$radians giving a size $\sqrt{\beta*50)} \Theta_0$ = 15.95 mm which makes the great effectiveness of the Main Injector collimation system seem quite reasonable.
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Show plot with normalization to sqrt(beta_x/50)
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