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.
Linear matrix elements
Second order matrix elements
Violation of the symplectic condition !
Dragt-Finn factorization :
[A. Dragt et al., Ann. Rev. Nucl. Part. Sci. 38 (1988) 455]
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…
Importance of the benchmarking of codes
[T. Asaka and J. Resta Lopez, CLIC-Note-637]
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
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
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 !
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.
Luminosity versus vertical offset
Analytic calculation considering a rigid gaussian beam:
Simulations with Guinea-Pig: it includes beam-beam effects
Dy= 3.5 (CLIC)
Nominal: L=2x1034 cm-2s-1
85 % of the nominal