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

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 2015 - MG

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 2015 - MG

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 2015 - MG

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, 60.32 (7 TeV), 62.28, 60.31 (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 2015 - MG

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 2015 - MG

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 = 31.1954 [2p] my = 30.3679 [2p] nx - mx = 31.0846 [2p] ny - my = 29.9421 [2p] 28/10/15 Field Quality error table for IT magnets: IT_errortable_v66_5 (b2=0) HiLumi Workshop 2015 - MG

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 2015 - MG

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 = 31.14 [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 2015 - MG

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 2015 - MG

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 31.14 [2p] Original: DAmin = 9.73 s, DAave = 10.36 s mx = 31.1954, my = 30.3679 [2p] New: DAmin = 10.20 s, DAave = 10.86 s mx = 31.14, my = 30.26 [2p] 28/10/15 Study in progress! HiLumi Workshop 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - 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

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

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 2015 - MG

Thank you for your attention 28/10/15 HiLumi Workshop 2015 - MG