Dynamic Aperture and Alignment for FCChh D Boutin

Dynamic Aperture and Alignment for FCC-hh D. Boutin, B. Dalena

Motivation • Design linear and non-linear correction scheme for alignment errors and magnets field quality of the arcs • Provide tolerances for the alignments and for the main multipoles components of arc magnets • Key issues: – Reserve space for correctors in the arc cells – Get an order of magnitude for the correctors strengths to identify possible R&D needed – Define tolerances on magnets alignment errors and main magnetic fields – Define tolerances on the main multipoles components to ensure DA > 12 at injection 13/04/2017 B. Dalena, FCC-hh design meeting 2

Status of Alignment • First specifications for the alignment and main field errors: Element Dipole Quad BPM • Error Descr. Units FCC LHC Comments σ(x), σ(y) mm 0. 5 no effect on observables studied σ(θ), δ(φ) transv. rot. mrad 0. 07 ? est. from dipole geometry and σ(x/y) σ(ψ) roll angle mrad 0. 5 n/a effect on vertical plane σ(δB/B) random b 1 % 0. 1 0. 08 LHC value includes σ(ψ) σ(x), σ(y) mm 0. 2 0. 36 σ(θ), δ(φ) transv. rot. mrad 0. 06 ? est. from quad geometry and σ(x/y) σ(ψ) roll angle mrad 1 0. 5 σ(δB/B) random b 2 % 0. 1 0. 3 σ(x), σ(y) mm 0. 35 0. 24 LHC value relative to quad (0. 43 absolute) σ(read) mm 0. 2 0. 5 For baseline 99. 97 km the table values give: – orbit corrector max strength = 4 T. m (Nb-Ti limit) – residual orbit, beta-beating, dispersion-beating below LHC limits (at 90% C. L. ) and compatible with beam screen design 13/04/2017 B. Dalena, FCC-hh design meeting 3

Alignment perspectives • For Berlin – Analyze new layout (weakness: higher beta-beating…) – Random b 2 and a 2 components of the main dipoles added – First evaluation of coupling (a 2) correctors and b 2 correctors • For CDR – Integration with insertions corrections (high luminosity IR, other ? ) – Effect of non-fully random assignment of linear errors – Correlation between errors • Future (after CDR) – Push the orbit correctors maximum field above 4 T 13/04/2017 B. Dalena, FCC-hh design meeting 4

Status of dynamic aperture Systematic • • • Rref = 0. 017 m First evaluation of DA due to main dipole field quality at injection (3. 3 Te. V) and at collision for baseline 99. 97 km First tolerances on systematic components b 3 (3 units at collision) and b 5 (2 units at injection) B 3 correctors (MCS) specs G = 4430 T/m 2, L=0. 11 m, one corrector for each dipole model x = random number with Gaussian distribution cut at 1. 5 (U) and 3 (R) 13/04/2017 (E. Todesco FCC-hh design meeting 28/05/2015) B. Dalena, FCC-hh design meeting 5

Dynamic aperture perspectives • For Berlin – DA of new layout (minimum DA at injection unchanged) – First evaluation of effect of linear imperfections (Alignment) on DA – First evaluation of new dipole field quality table (beam-magnet coordination meeting of 28/04/2017) • For CDR – Points presented at Berlin more studied and digested – Tolerances on random multipole components – Tune scan • Future (after CDR) – Follow up Magnet R&D and multipole harmonics measurements of Nb 3 Sn magnets – Magnet field quality at very low energy (injection option at 1. 3 -1. 5 Te. V ) – Impact of longitudinal dependence of multipole harmonics 13/04/2017 B. Dalena, FCC-hh design meeting 6