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Beam Optics of the TTF2

Beam Optics of the TTF2. Nina Golubeva DESY. Beam optics from the BC2 up to the undulators. • General introduction to linear optics: – constraints for different sections – matching between sections (flexibility, chromatic behaviour)

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Beam Optics of the TTF2

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  1. Beam Optics of the TTF2 Nina Golubeva DESY

  2. Beam optics from the BC2 up to the undulators • General introduction to linear optics: – constraints for different sections – matching between sections (flexibility, chromatic behaviour) • Chromatic properties • Effect of the transverse space charge (after BC3) Transverse beam dynamics

  3. BC2 bunch compressor FODO cells (μx,y=45°) ACC2 & ACC3 BC3 bunch compressor ACC4, ACC5, TB_ACC6, TB_ACC7 COLLIMATOR (with the dogleg) FODO in TB_SEED UNDULATOR · Beam waist and small β between two last dipoles (CSR effects) · L = 1.9 m => βmax ~ 3.5 m · Matching (BC2, BC3) is ƒ (E, Eacc, …) · Beam waist and small β between two last dipoles (CSR effects) · Matching (BC3, COLL) is f (E, Eacc, …) · β (dogleg) ~ 5 m, 2 sextupoles, 4 Collimators: β(CT1&2) > 20m · μx,y = 45º => βmax ~ 17 m · <β> ~ 4.5 m Layout & properties & constraints

  4. Linear optics BC2 BC3 COL MAD code no RF focusing ACC2&3 ACC4&5 β~40m FODO FODO UND βx=6m βx~2m

  5. Linear optics: transverse focusing of RF cavities Elegant code, M.Borland Twiss parameters at the entrance of BC3 and COLL sections are fixed: Matching (BC2, BC3) = ƒ (E, Eacc) Matching(BC3, COLL) = f (E, Eacc) Example: E0 (BC2) = 130 MeV E(BC3) = 380 MeV Ef (COL) = 445 MeV ACC2 & ACC3: Φ = 80º, Eacc = 15 MV/m ACC4: Φ = 90º, Eacc = 8 MV/m ACC5: Switch off

  6. BC2 section BC2 FODO ACC1 • 2 quads of ACC1 • 3 quads in the front of BC2 • 5 quads between BC2 and FODO lattice • FODO cells => => BC2 area as a matching section to FODO lattice is flexible to beam parameters from injector

  7. Collimation system TESLA Report 2003-17 Collimator section • Protection of undulators (transv. & energy collimation) • Protection against off-energy and mis-steered beams CT1 CT2 CE 4 copper collimators: Recommended apertures radii: R(CT1) = 2 mm R(CT2) = 2 mm R(CE1) = 6 mm R(CE2) = 2 mm |ΔE/E0| > 3% will be stopped Lcol = 50 cm L = 50 cm

  8. Chromatic properties TrackFMN code, V.Balandin • All matching sections • (esp. from small/large to large/small β-functions): • • are optimized taking into account the chromatic effects • • tuned to let the particles with the energy offset less • ±3% pass through with small distortion of beam • parameters • 2. Collimator section with the dogleg: • • second order dispersion is suppressed by 2 sextupoles • • particles with the energy offset less ±1.5% pass through • with small distortion of beam parameters The total optics has an energy acceptance of about ±1.5%.

  9. Chromatic properties Section between BC3 and COLL Collimator section (final) -1.5% Initial Sext. off +1.5% 3 ellipses: -3%, 0%, +3% 3 ellipses: -1.5%, 0%, +1.5% Sext. on Final E = 380 MeV E = 445 MeV

  10. Effect of transverse space charge TrackFMN code, V.Balandin ¤ Beam line after last bunch compressor BC3: after ACC4 module to undulators ¤ Beam parameters: E0 = 450 MeV Î = (0.5 – 3) kA εn = 2 mm mrad TrackFMN : • 2D Poisson equation solver • 4D particle tracking (x, Px, y, Py)

  11. Transverse space charge after BC3 statistical horizontal β-functions Î = 3 kA hor Î = 2 kA ver Î = 1 kA Î=0 mismatch at und. entrance = 0.5 (γ0 βi – 2 α0αi + β0 βi) 3 kA 2 kA Simulations: Np = 10^5 - 10^6 Grid: 128 – 512 Nsp-kick / elem = 2 – 20 1 kA 0 kA Results for the total beam

  12. Transverse space charge after BC3 Vertical plane Statistical β-functions Current: 0, 1, 2, 3 kA

  13. Transverse space charge after BC3 initial: ACC4 exit final: undulator entrance 1 σ 2 σ Î=0 Red: 10 000 particles, Gaussian distr. Green (I=0) & Blue (I=2kA): test particles: – do not contribute in space charge forces – are tracked in space charge field of the main beam Î=2kA CPU time = 90 sec (grid: 256x256, Nsp/elem=5)

  14. • Linear optics: * BC2 area is working as matching section between injector and FODO lattice * large β-functions in sections between BC2&BC3 and BC3&COLLIMATOR * optics of COLLIMATOR section is assumed to be fixed • Energy acceptance: |ΔE/E0| is about ±1.5% • Particles with |ΔE/E0| > 3% are stopped by collimators • Error and misalignment analysis • Detailed studies of the space charge effects, ƒ(E, Î, εn), (optics less sensitive to the space charge effect ?) • … Summary & next steps

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