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Simulation of LHC Beam Collimation: Analysis of Beam Dynamics and Collimator Efficiency

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This study presents a comprehensive simulation of the Large Hadron Collider (LHC) beam collimation process, focusing on four critical locations: the Beam Collimator (BC), secondary Collimator (SCOL), tertiary Collimator (TCOL), and the RF accelerating system. We analyze particle dynamics through linear transfer matrices and investigate halo generation, absorption mechanics, and the impact of different crystal parameters on channeling efficiency. Our results reveal significant beam losses and the importance of maintaining optimal crystal orientations to reduce these losses effectively.

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Simulation of LHC Beam Collimation: Analysis of Beam Dynamics and Collimator Efficiency

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  1. Simulation of the LHCbeam collimation -------------------------------------------- RF • Four points along the ring were considered: BC - crystal SCOL – secondary collimator TCOL – tertiary collimator RF – accelerating system voltage • • • BC TCOL SCOL Particle coordinates – (x, x′, y, y′, l, δ) Four linear 6-D transfer matrices M(6,6) were used to transport particles between BC → SCOL SCOL → TCOL TCOL → RF RF → BC

  2. Simulation of the LHC beam collimation (horizontal) -------------------------------------------- BC positions: TCP.A6L7.B1, s= 19795.1844 xbc=6σx=1.557 mm (7 TeV/c) → 5.949 mm (0.45 TeV/c) SCOL positions: TCSG.6R7.B1, s=20140.5234, xscol=7σx=2.88 mm (7 TeV/c) → 10.01 mm (0.45 TeV/c) TCOL position: TCLA.B6R7.B1, s=20178.4634 RF position: in the middle of the cavities, s=9996.79 with lattice parameters interpolated with voltage summed LHC beam emittanceε=0.5×10-9 m·rad for 7 TeV/c ε=7.3×10-9 m·rad for 0.45 TeV/c

  3. LHC azimuths characterization --------------------------------- Start point → BC azimuth Halo generation Halo particles begin hit BC after some turn numbers Due to increase of particle oscillation amplitudes Final points → (1) absorption in SCOL (2) Inelastic interactions in BC TCOL azimuth → halo registration RF azimuth → change of particle momentum due to RF voltage V

  4. Peculiarities of the LHC beam collimation -------------------------------------------- Different distances from the orbit for collimators For crystal collimator Δbc=xbc(0.45 TeV/c) – xbc(7 TeV/c) = 4.392 mm Corresponding change of beam envelope direction ΔXP = (αx/βx)·Δbc= 62.38 µrad -------------------------- Critical channeling angle for (110) Si bent with R=60 m θcb=9.89 μrad (0.45 TeV/c) → 1.96 μrad (7 TeV/c) Multiple Coulomb scattering in 3 mm Si θms=5.91 μrad (0.45 TeV/c) → 0.38 μrad (7 TeV/c) Ratio of coherent to incoherent scattering θcb/θms= 1.67 (0.45 TeV/c) → 5.17 (7 TeV/c) -------------------------- Inelastic nuclear cross-section σin = 507 mb (0.45 TeV/c) → 567.5 mb (7 TeV/c)

  5. Impact parameters and angles for the first hits ------------------------------------- With betatron amplitude increase per turn as in the SPS 0.45 TeV/c 7TeV/c QH=64.31 ΔXP ≈ 1 μrad QH=64.28 ΔXP ≈ 10 μrad Different phase point density

  6. Impact parameters with SCOL for perfect alignment ------------------------------------- 0.45 TeV/c 7TeV/c

  7. Impact parameters with BC for amorphous orientation ------------------------------------- Before extraction (blue) and inelastic interactions in crystal (red) 0.45 TeV/c 7TeV/c The whole crystal works Only crystal surface works

  8. Impact parameters with BC for VR orientation ------------------------------------- 0.45 TeV/c 7TeV/c In both cases the whole crystal works

  9. Channeling efficiency and beam losses ------------------------------------- 0.45 TeV/c 7TeV/c Efficiency is larger than 80% in the range of 25 µrad and 5 µrad, respectively Losses in AM 18% and 75%, respectively

  10. Crystal imperfections: miscut and torsion ------------------------------------- Miscut angle: 60 µrad Loss increase for θo=0, ΔL= 180% Channeling reduction for θo=0, ΔPch=0.7% 1 µrad/mm → ΔL=24% , ΔPch=0.27% Crystal torsion: 2 µrad/mm →ΔL=39% , ΔPch=0.6%

  11. Optimal crystal parameters - ? ------------------------------- L=3 mm, α=40 µrad, R=75 m→ ΔL=-9.4% , ΔPch=0.8% L=3 mm, α=50 µrad, R=60 m → L=4 mm, α=50 µrad, R=80 m → ΔL=0 , ΔPch=0.28% Impact parameters with SCOL for α=40 µrad

  12. Conclusions ---------- 1. Very large beam losses 75% occur in AM crystal (mainly in its surface) Avoid AM-orientations for 7 TeV/c Keep crystal in CH or VR modes 2. Range of 80% channeling: 25 µrad (0.45 TeV/c) and 5-6 µrad (7 TeV/c) 90% channeling: 20 µrad and 3 µrad 3. Effects of crystal imperfections will be sufficiently small when miscut angle ≤ 50 µrad and torsion ≤ 1 µrad/mm 4. Optimal crystal parameters : L=3-4 mm at α=50 µrad 5. Main problem is goniometer fast and accurate and reproducible crystal orientations

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