First evaluation of Dynamic Aperture at injection for FCC- hh

1. First evaluation of Dynamic Aperture at injection for FCC-hh B. Dalena Thanks to: D. Boutin, A. Chancé, R. Martin, J. Payet, K. N. Sjobaek

2. Outline • Arcs design • Dipole’s field errors and Dynamic Aperture • First tolerances on b3S and correctors integrated strength • First consideration on b5s B. Dalena, FCC week 2016

3. Arcs design • MD and b3 correctors have same length as LHC • 2 focusing and 2 defocusing sextupole families • No octupole and decapole correctors are integrated so far • No skew quadrupoles and skew sextupoles • Each quad is equipped with a trim • Relative position of the BPM and the orbit corrector are different from LHC • see D. Boutin talk • Given a minimum beam screen radius 0.132 m  25 r.m.s. beam size at injection B. Dalena, FCC week 2016

4. Dipoles errors table Systematic First table for dipoles multipole errors provided (E. Todesco FCC-hh design meeting 28/05/2015) • = random number with Gaussian distribution cut at 1.5 (U) and 3 (R) • In the following we use • the same seed for U for all dipoles of the same arc • different seed for R for each dipole • random and uncertainty b2 and a2 not considered (skew correctors not inserted in the lattice yet) • magnet misalignments not considered Fractional part of tunes: Qx = .28, Qy = .31 injection Qx = .31, Qy = .32 collision Rref = 0.017 m B. Dalena, FCC week 2016

5. DA with errors: injection • Inputs long-term DA study: • 60 seeds • 30 particle pairs • Emit norm 2.2e-6 m.rad • E0 = 3.3 TeV • Q’ = 2 • dp/p = 0.00075 (LHC) • dp/p max = 0.002 •  step = 2,   [2-40] explored • 5 angles  [0,90o] without dipoles errors DA > 80  with nominal dipoles errors: “systematic” b3 uncorrected (chromaticity due to b3 corrected)  no need to correct b3S =-5 units • b3S = 15 units intolerable without correction • effect of different straight sections: up to 3 of average DA (at 15°) B. Dalena, FCC week 2016

6. DA with errors: collision • Inputs long-term DA study: • 60 seeds • 30 particle pairs • Emit norm 2.2e-6 m.rad • E0 = 3.3 TeV • Q’ = 2 • dp/p = 0.00075 (LHC) • dp/p max = 0.002 •  step = 2,   [2-40] explored • 5 angles  [0,90o] without dipoles errors minimum DA > 54  “systematic” b3 uncorrected (chromaticity due to b3 corrected) with nominal dipoles errors: • b3S=20 units intolerable without correction (minimum DA 8  and sextupoles strength more than 3 times the *=0.3 m optics) • need to correct b3S(with b3S = 0 units, minimum DA  28 ) • effect of different straight sections: smaller than at injection (different multipoles play a role) B. Dalena, FCC week 2016

7. b3 and MCS strength: collision Based on LHC project report 501 MCS integrated strength for B= 0.471 T, LMCS =0.11 m Integrated strength to correct one unit of b3S  = 1/Ndipole LHC MCS correct @ LHC |b3S| < 3 [10-4] equal to 70% of MCS max integrated strength @ FCC |b3S| < 1.57 [10-4] equal to 70% of MCS max integrated strength  FCC |b3S| < 3 [10-4] equal to 70% of 2 x MCS integrated strength of LHC (to have same tolerance of LHC at FCC) B. Dalena, FCC week 2016

8. b3 correctors: collision Average b3S for each of the 8 arcs is corrected with spool pieces MCS, one at every dipole (same scheme of HL-LHC). • b3S=20 reduce DA in collision to < 10 σ • 81% of the maximum MCS strength in collision fully correct b3S=3 units (minimum DA 28 σ) B. Dalena, FCC week 2016

9. b3 correctors: injection Average b3S for each of the 8 arcs is corrected with spool pieces MCS, one at every dipole (as in collision). • 23% of the maximum MCS strength at fully correct b3S =15 units (minimum DA > 12 σ) B. Dalena, FCC week 2016

10. b3 at injection (possible limit) Based on LHC project report 501 At injection the MCS strength can correct up to 34 b3 units (67 in LHC), nevertheless a tolerance on b3S can come from feed-down effects.  LHC = closed orbit = 0.4 mm at injection in LHC = random component of main dipole  which is limited by induced beta-beating < 0. 7 units (corresponding to 14% peak allowed beta beating = 10% beam size growth) at injection in LHC  for the moment we can assume the same values for FCC B. Dalena, FCC week 2016

11. b5 at injection • Inputs long-term DA study: • 60 seeds • 30 particle pairs • Emit norm 2.2e-6 m.rad • E0 = 3.3 TeV • Q’ = 2 • dp/p = 0.00075 (LHC) • dp/p max = 0.002 •  step = 2,   [2-40] explored • 5 angles  [0,90o]  with b3 correctors DA is above 12 σ at injection, do we really need the b5 correctors ? • b5S = 1 units reduce average DA of 3 σ at 15° • similar effect is produced by different straight sections (different phase advance in the long arcs) B. Dalena, FCC week 2016

12. Conclusion • Present dipole’s errors table gives good DA at injection • No need to correct 5 units of b3s at injection • b3S =15 uncorrected units gives already DA < 10  • 23% of the maximum MCS strength at injection fully correct b3S=15 units (minimum DA > 12 σ) • Present dipole’s errors table gives DA < 10  in collision • 81% of the maximum MCS strength at collision fully correct b3S=3 units (minimum DA of 28 σ) • With b3 correctors DA is above 12 σ at injection, do we really need the b5 correctors ? Outlook • Effect of the higher order multipoles • Tolerances on the systematic and random components • Effect of different optics (straight section, arc’s phase advances) • Misalignment and feed-down B. Dalena, FCC week 2016