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UPDATE ON DYNAMIC APERTURE SIMULATIONS

UPDATE ON DYNAMIC APERTURE SIMULATIONS. M. Giovannozzi For the AB/ABP-LHC Optics and Commissioning Section Protocol of DA computation and target Main studies: MQM and MQY MQX MQTL Analysis of the performance of the DA protocol Outlook Acknowledgements: S. Fartoukh.

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UPDATE ON DYNAMIC APERTURE SIMULATIONS

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  1. UPDATE ON DYNAMIC APERTURE SIMULATIONS M. Giovannozzi For the AB/ABP-LHC Optics and Commissioning Section Protocol of DA computation and target Main studies: MQM and MQY MQX MQTL Analysis of the performance of the DA protocol Outlook Acknowledgements: S. Fartoukh M. Giovannozzi - XIX LHC MAC Meeting

  2. Protocol of DA computation and target - I • Massive tracking of initial conditions for sufficient number of turns to determine stability of initial condition. • Conditions: • 105 turns • Initial conditions distributed along 5 directions in the (x, y) phase space • 15 initial conditions (couples for Lyapounov exponent evaluation)/beam sigma • Scan from 8-20 sigma • Momentum offset set to 0.75×10-3 -> ¾ of bucket height • 60 realisations of the LHC lattice for random magnetic errors M. Giovannozzi - XIX LHC MAC Meeting

  3. Protocol of DA computation and target - II • Machine model: • Optics version: V6.4 with nonlinear package correctors in Q3 moved -> effectively V6.5 optics • Magnetic errors: • Only nonlinear imperfections • Magnetic errors are derived from: magnetic models and/or measurement • Machine status: mainly injection M. Giovannozzi - XIX LHC MAC Meeting

  4. Protocol of DA computation and target - III • Recap of targets for DA value: • Injection: 12 sigma • Margin from simulations at injection to reality: factor of 2 • Break down of contributions to DA uncertainty • Extrapolation to 107 turns 7 % • Finite mesh size in tracking 5 % • Amplitude ratio 5 % • Linear imperfections 5 % • Time-dependent effects 10 % • Ripple 10 % • Safety margin 20 % CPU-time M. Giovannozzi - XIX LHC MAC Meeting

  5. Aim of the studies • Define target values of the field quality of the magnets. • Magnet production/installation is in full swing, hence: • DA is used to provide feedback on the field quality of the magnets with impact on the hardware, e.g. change of cross section -> main dipoles and quadrupoles • DA is used to assess impact of field quality of magnet classes whenever this deviates from beam dynamic targets M. Giovannozzi - XIX LHC MAC Meeting

  6. Main studies: MQM and MQY - I • MQM: • Three types (MQM, MQMC, MQML) depending on length. • Used in the dispersion suppressor and matching sections • MQY • Large aperture quadrupoles used in the matching sections • Issues: • Wide range of powering values at injection -> hysteresis effects cannot be neglected • Sometimes located in regions with high beta-values, e.g. IR4/6. • Approach: • Scan each multipole around the measured value of a given mutipole to determine acceptable ranges. M. Giovannozzi - XIX LHC MAC Meeting

  7. Main studies: MQM and MQY - II Typical values for the optical functions for MQY quadrupoles Values comparable with max beta-functions for MQM-like quadrupoles M. Giovannozzi - XIX LHC MAC Meeting

  8. Main studies: MQM and MQY - III DA reduction at large angle Systematic value of b10 for MQY Scan over MQY multipoles M. Giovannozzi - XIX LHC MAC Meeting

  9. Main studies: MQM and MQY - IV DA reduction at small angle Scan over MQY multipoles M. Giovannozzi - XIX LHC MAC Meeting

  10. Main studies: MQX Impact of measured field quality of triplet quadrupoles at injection. Impact on DA at small angles M. Giovannozzi - XIX LHC MAC Meeting

  11. Main studies: MQTL - I • Long trim quadrupoles used: • As correctors (i.e. combined with an MQ) in all Q11 and Q10, Q9, Q8, Q7 in IR3/7 • Main quadrupoles in Q6 assembly in IR3/7 • Field quality feature a large systematic b10 of about 15 units. • Feed down effects due to vertical closed orbit, generating a9 (see impact on DA for MQY) were checked. M. Giovannozzi - XIX LHC MAC Meeting

  12. Main studies: MQTL - II Magnetic errors computed as feed-down from the measured field quality of random orbit (4 mm) are used. No dramatic impact on DA M. Giovannozzi - XIX LHC MAC Meeting

  13. Summary of results - I Minimum DA (over angles) decreased from 11.2 -> 10.4 All magnets, but MBs and MQs, reduce DA by 1 sigma M. Giovannozzi - XIX LHC MAC Meeting

  14. Summary of results - II Loss of DA visible also on average DA. M. Giovannozzi - XIX LHC MAC Meeting

  15. Analysis of the performance of the DA protocol - I • Detailed analysis of dependence of the DA estimate on: • Number of angles -> pushed up to 103 (for 60 realisations) • Number of realisations -> pushed up to 600 (for 5 angles) • The model used is LHC, optics V6.4 (injection) with errors in • Main dipoles • Main quadrupoles • Cold separation dipoles M. Giovannozzi - XIX LHC MAC Meeting

  16. Analysis of the performance of the DA protocol: angle dependence Minimum DA (over realisations and angles) vs. # angles qNangles, i = 90° i /(Nangles +1), 1 < i < Nangles This indicates that about 20-50 angles should be used ~ 5% -> corresponding to the allocated budget M. Giovannozzi - XIX LHC MAC Meeting

  17. Analysis of the performance of the DA protocol: realisation dependence - I M. Giovannozzi - XIX LHC MAC Meeting

  18. Analysis of the performance of the DA protocol: realisation dependence - II This indicates that about 300 realisations should be used -> not feasible This spread is much reduced for the most realistic LHC model -> this might mitigate the need for more realisations M. Giovannozzi - XIX LHC MAC Meeting

  19. Outlook - I • Present status of DA studies: • Minimum (over realisations and angles) DA is 10.4 sigma • The model used is the most complete possible -> magnetic errors from simulations gradually replaced by those results from magnetic measurements and all classes of magnets are included • Improvement of the model: • Move to the latest optics version V6.500 • Improvement of the protocol for DA computation • Increase number of angles and realisations M. Giovannozzi - XIX LHC MAC Meeting

  20. Outlook - II • Next step • Take into account slot assignment activity from Magnet Evaluation Board • Take into account pre-assignment of magnets, e.g. all SSS are already pre-assigned • Assign actual measured errors • General comment: • The field quality of each individual is taken into account in the slot allocation process, e.g.: • b2 for quadrupoles (beta-beating) • b1, a2, b3 for dipoles (corrector strength, coupling, 3rd order driving term) • The impact on DA is yet to be evaluated. M. Giovannozzi - XIX LHC MAC Meeting

  21. Outlook - III • Tools • Software tool developed by Colleagues in AT/MAS-MA to gather information from databases (magnetic and slot allocation) • New routines to assign measured errors in MAD-X developed inside AB/ABP-LOC • First result: beta-beating correction based on the best estimate of the distribution of b2 errors in the machine as-installed M. Giovannozzi - XIX LHC MAC Meeting

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