1. Field quality update and recent tracking results
Massimo Giovannozzi
CERN
Y. Cai, Y. Nosochkov, M.-H. Wang (SLAC)
R. de Maria, E. McIntosh (CERN)
Acknowledgements: G. Arduini, S. Fartoukh, E. Todesco

2. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

3. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

4. Introduction What is new since last HiLumi workshop:
Layout used for DA simulations:
HLLHCV1.0
Updated expected error tables:
Nb-Ti 105 mm D2 separation dipoles
Nb3Sn 150 mm aperture IT quadrupoles
Nb-Ti 90 mm Q4 quadrupoles
Complete analysis of injection and collision
Field quality data: classification as “specification” and “expected” tables.
Not the latest layout, but the results are considered to be realistic also for HLLHCV1.2
28/10/15
HiLumi Workshop MG

5. Simulations set-up HLLHCV1.0 lattice layout:
Collision:
round optics with b*= 15 cm at IP1, IP5; latest operational set-up with ±2 mm half separation and ±295 mrad half crossing angle at IP1, IP5 at 7 TeV
flat optics with b*= 7.5/30 cm at IP1, IP5;
Injection: nominal optics with b*= 6 m at IP1, IP5 at 450 GeV
Linear chromaticity x = +3
Landau damping octupoles turned off
SixTrack simulation set-up:
105 turns, 60 error seeds, 30 particle pairs per amplitude step (2s), 11 x-y angles
Initial Dp/p: 2.7×10-4 (7 TeV), 7.5×10-4 (450 GeV)
Tune: 62.31, (7 TeV), 62.28, (450 GeV)
Normalized emittance = 3.75 mm-rad
Arc errors and corrections included
IT correctors are turned on in IR1, IR5 (7 TeV) and turned off in IR2, IR8
Field Quality error tables for D1, D2, Q4, Q5 magnets:
D1_errortable_v1_spec, D2_errortable_v5_spec (b2=0), Q4_errortable_v2_spec, Q5_errortable_v0_spec
Thanks to S. Fartoukh for providing the original SixTrack mask files
28/10/15
HiLumi Workshop MG

6. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

7. DA optimization at injection energy
It has been noted previously that the DA of HiLumi LHC at injection is ~1 s smaller as compared to the present LHC DA
One way to improve the DA is to optimize phase advance between IP1 and IP5 (S. Fartoukh) as this may improve compensation of the effects of IT non-linear field errors
mx,y
nx,y - mx,y
Procedure of IP1-IP5 phase adjustment has been implemented (R. De Maria)
Presently:
mx = [2p]
my = [2p]
nx - mx = [2p]
ny - my = [2p]
28/10/15
Field Quality error table for IT magnets:
IT_errortable_v66_5 (b2=0)
HiLumi Workshop MG

8. Sensitivity to IP1-IP5 vertical phase advance at injection
DA sensitivity to IP1-IP5 vertical phase advance is relatively weak (±0.1 s)
28/10/15
HiLumi Workshop MG

9. Sensitivity to IP1-IP5 horizontal phase advance at injection
Strong DA sensitivity to IP1-IP5 horizontal phase advance
The DA is increased by ~0.5s near mx = nx/2 = [2p]. To some degree, this phase may be equivalent to periodicity of 2 (IP1-to-IP5 in x-plane) which may help to better suppressing the effects of IT systematic field errors.
It appears that DA may oscillate with the mx, so there may be another optimum phase advance further away from the current value
28/10/15
HiLumi Workshop MG

10. DA versus IP1-IP5 phase advance at injection in 3D
The minimum DA exhibits fluctuation from point to point as it is dominated by one worst seed
The average DA shows a smooth behavior as it is determined by all 60 seeds
The DA is clearly dependent on x-phase advance while it is only weakly dependent on y-phase advance
28/10/15
HiLumi Workshop MG

11. Improvement of DA at injection
Optimizing the IP1-IP5 x-phase advance increases the horizontal DA which determines the minimum DA at injection (see points in the ellipse at small angles)
Both the minimum and average DA improve by ~0.5 s by setting the x-phase advance near to [2p]
Original: DAmin = 9.73 s, DAave = s
mx = , my = [2p]
New: DAmin = s, DAave = s
mx = 31.14, my = [2p]
28/10/15
Study in progress!
HiLumi Workshop MG

12. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

13. DA sensitivity to IT non-linear field corrector strengths at collision
In reality, the way the non-linear correctors are set up will be different from the standard approach based on MAD-X/SixTrack. Moreover, the unavoidable limited knowledge of the IT field quality and correctors’ transfer function will impact on the final quality of the corrections.
It is therefore important to evaluate the impact of such strength deviation on the DA at collision energy
In this study, the IT corrector strengths were varied in the following way:
Only the corrector strengths of one order (n = 3 to 6) were varied at a time, while the other correctors were set at the nominal strengths
Strengths of all correctors of the same order in IP1 and IP5 were scaled with the same factor (from 0.7 to 1.3) relative to their nominal strengths
At this time, the completed results include the b3, a3, b4, a4 correctors. The study of other correctors is in progress.
28/10/15
Field Quality error table for IT magnets:
IT_errortable_v66_5 (b2=0)
HiLumi Workshop MG

14. DA sensitivity to strengths of b3, a3, b4, a4 IT correctors at collision
The b3 corrector strongly reduces the DA at the lower-than-nominal strength; its impact is weak at the higher-than-nominal strength. Linear chromaticity is always maintained at +3.
The impact of a3 corrector setting is minor in the studied range
The b4 corrector has a minor effect on the minimum DA, but moderately reduces the average DA at the lower-than-nominal strength
The a4 corrector moderately reduces minimum DA at the lower-than-nominal strength as well as the average DA at the higher-than-nominal strength
28/10/15
Study in progress!
HiLumi Workshop MG

15. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

16. IT field quality status and simulation results
Numerical simulations are performed to assess the compatibility of FQ estimates with beam dynamics.
So far, proposed reduction of random components and systematic to provide a DA value not too small.
Below: expected error table for collision energy. Figures in blue are estimates of multipoles; figures in red are upper bounds determined with beam dynamics
numerical simulations.
28/10/15
HiLumi Workshop MG

17. IT field quality status and simulation results
With the latest layout HLLHCV1.2 and the triplet review, a new version of the field quality for the new triplet quadrupoles has been released. The effect of fringe fields is included (see talk by E. Todesco).
Integrated ends multipoles
Multipoles corresponding to the integral of body+ends
Multipoles corresponding to magnet body
28/10/15
HiLumi Workshop MG

18. IT field quality status and simulation results
The latest field quality estimate is based on the new triplets’ length. The value has been adapted to the layout under study, HLLHCV1.0.
In these preliminary studies, the model for the fringe field is simplified: a single kick represented the integrated effect.
Several configurations tested:
Injection/Collision -> Round/Flat
Body and ends/Integral errors -> Expected error table/Reviewed error table with reduced random/uncertainty components
28/10/15
Injection
(systematic FQ component)
Collision
(systematic FQ component)
HiLumi Workshop MG

19. IT field quality status and simulation results: injection
Impact of different error tables (integral magnetic model)
Impact of different error models (expected error tables)
28/10/15
Error bars represent the 60 seeds used in numerical simulations
HiLumi Workshop MG
At injection
No meaningful differences are found for DAave
Small differences are found for DAmin
as a function of
Error tables: expected or with reduced random/uncertainty component
Magnet models: integral or body + ends

20. IT field quality status and simulation results: collision - round
Impact of different error tables (integral magnetic model)
Impact of different error models (expected error tables)
28/10/15
Error bars represent the 60 seeds used in numerical simulations
At collision (round optics) as a function of
Error tables: expected or with reduced random/uncertainty component
Small differences are found for DAave
Sizeable differences are found for Damin
Magnet models: integral or body + ends
Small differences are found for Damin
HiLumi Workshop MG

21. IT field quality status and simulation results: collision - flat
Impact of different error tables (integral magnetic model)
Impact of different error models (expected error tables)
28/10/15
Error bars represent the 60 seeds used in numerical simulations
At collision (flat optics) as a function of
Error tables: expected or with reduced random/uncertainty component
Sizeable differences are found for DAave
Sizeable differences are found for Damin
Magnet models: integral or body + ends
Small differences are found for DAave
HiLumi Workshop MG

22. Outline
Introduction
Dependence of dynamic aperture on IP1-5 phase advance at injection
Sensitivity of dynamic aperture on quality of non-linear corrections in IR1/5
IT field quality status and simulation results
Summary and outlook
28/10/15
HiLumi Workshop MG

23. Summary and outlook - I
Dynamic aperture at injection energy can be increased by ~0.5 s by optimizing the phase advance (mostly in the horizontal plane) between IP1 and IP5. The optimal phase advance will be determined after completing the full scan (work in progress).
The next step will be to check the situation at top energy (for both round and flat optics).
Study of DA versus IT non-linear field corrector strengths for the round optics at collision energy showed that
The DA is reduced when the b3 and b4 corrector strengths are below nominal (with the b3 having the strongest effect).
The DA is moderately reduced by the non-ideal a4 corrector strength.
The DA is fairly insensitive to a3 corrector strength in the studied range (0.7 to 1.3) and to the strengths of b3, b4 correctors above their nominal strengths.
The study for the other IT correctors is in progress.
28/10/15
HiLumi Workshop MG

24. Summary and outlook - II
Concerning the new IT field quality including end effects
At injection energy, no/small differences are found on DA as a function of error table (expected or reduced random/uncertainty); magnet model (integral or body+ends).
At collision energy, differences are found on DA as a function of error table (expected or reduced random/uncertainty); magnet model (integral or body+ends). The differences are larger for flat rather than round optics.
Next steps:
Consider the longitudinal variation of the field in the IT ends: this requires developing a symplectic integrator
Consider end effects also for D1 and D2.
Globally, DAmin is even more (with respect to the situation reported at the 4th HiLumi meeting) dangerously approaching the value of 8 s (for round optics)!
For flat it is already smaller…
28/10/15
HiLumi Workshop MG

25. Thank you for your attention
28/10/15
HiLumi Workshop MG