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
16/06/2006
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
16/06/2006
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
16/06/2006
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 %
Safety margin %
CPU-time
16/06/2006
M. Giovannozzi - XIX LHC MAC Meeting

5. 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

6. 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

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

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

10. 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

11. 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

12. 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

13. M. Giovannozzi - XIX LHC MAC Meeting
Summary of results - I
Minimum DA (over angles) decreased from > 10.4
All magnets, but MBs and MQs, reduce DA by 1 sigma
16/06/2006
M. Giovannozzi - XIX LHC MAC Meeting

14. 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

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
16/06/2006
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 angles should be used
~ 5% -> corresponding to the allocated budget
16/06/2006
M. Giovannozzi - XIX LHC MAC Meeting

17. 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

18. 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

19. 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

20. 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

21. 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