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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

Main studies: MQM and MQY - I 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. 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

Main studies: MQM and MQY - III DA reduction at large angle Systematic value of b10 for MQY Scan over MQY multipoles 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

Main studies: MQM and MQY - IV DA reduction at small angle Scan over MQY multipoles 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting Main studies: MQX Impact of measured field quality of triplet quadrupoles at injection. Impact on DA at small angles 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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. 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting Summary of results - II Loss of DA visible also on average DA. 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting Analysis of the performance of the DA protocol: realisation dependence - I 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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. 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting

M. Giovannozzi - XIX LHC MAC Meeting 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 16/06/2006 M. Giovannozzi - XIX LHC MAC Meeting