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Transport formalism

Transport formalism. Linear matrix elements. Second order matrix elements. Truncated maps. Violation of the symplectic condition !. Lie algebraic treatment. Dragt-Finn factorization :. generators. [A. Dragt et al., Ann. Rev. Nucl. Part. Sci. 38 (1988) 455]. Linear matrix.

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Transport formalism

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  1. Transport formalism Linear matrix elements Second order matrix elements Truncated maps Violation of the symplectic condition !

  2. Lie algebraic treatment Dragt-Finn factorization : generators [A. Dragt et al., Ann. Rev. Nucl. Part. Sci. 38 (1988) 455] Linear matrix produces Tijkand higher order terms (sextupole effects) produces third order and higher order terms (octupoles effects) Numerical methods for nonlinear optimization : PARTICLE TRACKING, Dynamic aperture scans, particle spectra…

  3. Tracking codes:Simulations to show the feasibility Entrance: IP: Importance of the benchmarking of codes Guinea-Pig Multiparticle tracking Optics lattice Beam-beam interaction transport performance MAD Placet SAD … Lie [T. Asaka and J. Resta Lopez, CLIC-Note-637]

  4. Nanometer-Size Beams in CLIC Nominal: σx=40.12 nm; σy=0.55 nm Simulations: σx≈47.3 nm; σy≈0.65 nm Beam profile at the IP: Some problems: Residual horizontal dispersion at the IP

  5. Nanometer-Size Beams in CLIC Phase space at the IP: Particles with lower energy than the nominal one (1500 GeV) contribute strongly to the tails of the transversal phase space

  6. Chromatic effects in phase space Chromatic aberrations study by means of tracking from matched initial ellipses at 1σ for the transversal plane X Red line: center ellipse movement in phase space up to third order !

  7. Chromatic effects in phase space Chromatic aberrations study by means of tracking from matched initial ellipses at 1σ (figure on the left)and 3σ (figure on the right) for the transversal plane Y The particles at high position amplitude of several sigmas contribute to the population of the long tails. For the case of the ellipses at 3σ in the vertical phase space, it is possible to observe a strong deformation of the shape caused by the sextupoles located in the FFS.

  8. Limits of the Luminosity L/L0Placet Without SR With SR • Tolerable bandwidth up to 1 % energy spread • The synchrotron radiation is a very important limitation factor for the • luminosity

  9. Collimation issues in CLIC

  10. Beam-beam effects Luminosity versus vertical offset Analytic calculation considering a rigid gaussian beam: Simulations with Guinea-Pig: it includes beam-beam effects Disruption parameters: Dy= 3.5 (CLIC) Dy=19.4 (ILC)

  11. ILC integrated simulations Input LINAC BDS Beam-Beam Output Updated simulations: Placet Guinea-Pig FB Simulink G. White version (2005): Input LINAC BDS Beam-Beam Output Placet Matmerlin Guinea-Pig FB Simulink

  12. Ground motion and FB system Nominal: L=2x1034 cm-2s-1 85 % of the nominal luminosity

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