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LOCO for LHC Kajetan Fuchsberger OMCM Workshop, CERN 2011-06-21

LOCO for LHC Kajetan Fuchsberger OMCM Workshop, CERN 2011-06-21. Many thanks to: J. Wenninger, T. Baer, V. Kain, G. Mueller. Contents. Contents. The LOCO principle. SVD. Set of parameters. Difference vector:. Set of observables. Sensitivity Matrix: ( Jacobian ). Orbit response.

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LOCO for LHC Kajetan Fuchsberger OMCM Workshop, CERN 2011-06-21

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  1. LOCO for LHC • Kajetan Fuchsberger • OMCM Workshop, CERN 2011-06-21 • Many thanks to: • J. Wenninger, T. Baer, V. Kain, G. Mueller

  2. Contents

  3. Contents

  4. The LOCO principle SVD Set of parameters Differencevector: Set of observables Sensitivity Matrix: (Jacobian)

  5. Orbit response Orbit response matrix: • Possible parameters: • Corrector gains, tilts … • Monitor gains, tilts … • Arbitrary model parameters.

  6. Contents

  7. Challenges @ LHC • # Monitors/beam (2 planes): • # Correctors/beam (2 planes): • Different problems/challenges for different applications: • Size of Sensitivity Matrix: • Memory consumption • SVD inversion time • Calculation time for Sensitivity matrix: • # twiss runs • Measurement time. ~ Shifts

  8. Memory Consumption • Size of Sensitivity Matrix: • #rows • #columns #parameters. • E.g. Monitor- & Corrector Gains only: • 1 beam, 2 planes: • GB2 beams, 2 planes: GB

  9. SVD inversion time … #rows; … #cols • Inversion time Est. on Intel Desktop PC (3.17 GHz):

  10. Monitor/COD Gain fits 8 GB, 12 h 1088 530  Possible, but tedious…

  11. Optics parameter fits Dominated by twiss time; SVD inversion negligible.

  12. Contents

  13. Ex. I • Monitor Gains in Transfer lines and LHC Average gain of 1.13:  Resulting from uncorrected electronics (Correction was later on applied in frontends) • Fits done with corrector gains fixed • At least 2 additional parameters (quad chains) to take care of phase advance

  14. Ex. II – a • Phase advance error in Transfer line TI 8 MCIAV.81304 Growing Phase Error • Suspicion: Higher order field components in the main bends: • , : quadrupolar and sextupolar field error, respectively.

  15. Ex. II - b • Off-momentum Kick response Combined sensitivity matrix: Momentum offset: 7 measurements with different values for (-2 … +2 permill) Trimmed value Unknown offset • 4 correctors / measurement / plane • Fits with 4 parameters: , , and

  16. Ex. II - c • Measured Chromaticity (TI 8) Nominal model Fitted model about doubled, vanishes.

  17. Ex. III - a • TI8-LHC dispersion matching Initial situation: Mismatch Beam TI 8 LHC

  18. Ex. III - b • MD: Letting MICADO select 2 most effective out of 10 individually powered quads. • Later: SVD together with additional constraints to ensure phase advance at collimators (3 per plane) Combined sensitivity matrix: Kick response Dispersion Additional Constraints

  19. Ex. III - c After correction: Almost perfect! TI 8 LHC Constrained by Kick-Response!

  20. Ex. IV Systematic in LHC arcs • Fit: • Circulating beam • 60 correctors (distribute) • All BPMS • No monitor/corrector gains fitted • 9 Parameters: • 1 Systematic per sector • Systematic detuning of quads Result: Model prediction (WISE) well reproduced.

  21. Other Observations • Fitting corr+monitor gains  mostly doubtable result (Errors distributed between corr and monitor gains). Works well, if one is fixed. • Check ofCOD polarity was done ‚visually ‘. • LHC BPMs can have many different problems: • Polarity flip • Plane flip • Beam flip • Wrong rotation (e.g. BPMS, rotated by 45 deg) • + Any combination of these.  Not easily covered by automatic fit.

  22. Contents

  23. LOCO @ LHC • Aloha - “Another Linear Optics Helper Application” • Input Data: Kick-Response, Dispersion, Beta-Beat (from TBT) • Algorithms: SVD, MICADO • Works for every accelerator with existing MadX model • Plug-In system: Easy to add e.g. new input formats, algorithms….

  24. JMad • Tight coupling to model  All MadX parameters can be used •  JMad: Java API for MadX

  25. General Remark • Optics analysis is an interactive process. • It is not sufficient to have good algorithms, we also need good tools (preferable online): • Well integrated • Interactive and Intuitive • Good Software GUIs well designed, tested, documented, reusable…

  26. Contents

  27. Conclusions & Outlook • LOCO for LHC? Yes, we can!(And we did!) • LOCO principle was intensively used during LHC commissioning, especially for single-pass applications (Transfer lines, injection tests). • Full BPM+COD gain fit for ring should be possible but is problematic (8GB ram, 12 h). The effort is questionable. • Optics fit in ring works fine, but better covered by multiturn measurements. (faster, no influence of gains) • It would be useful to join efforts to better integrate/merge different optics measurement methods/tools  e.g. „Optics Analysis Workbench“? (Aloha could serve as starting point; Plug-In System)

  28. The end • Thankyouforyourattention!

  29. Additional Material

  30. Ex. II September 2008, first injection B2 to point 7: Example: MCBH.14R7.B2 Blue bars: measured, red dots: model.  Clear result: Inversion of Q6.L7.B2

  31. Influence on response matrix

  32. Full Sensitivity matrix

  33. Column factors

  34. LOCO principle

  35. Kick-Response

  36. The LOCO principle , Observables Parameters Difference vector by solving Fit minimizes Sensitivity matrix : SVD

  37. Kick response COD kicks , Positions , Response matrix , • Possible parameters: • Corrector Gains • Monitor Gains • Arbitrary model parameters

  38. SVD inversion time … #rows; … #cols • Inversion time Estimation on Intel Desktop PC (3.17 GHz):

  39. Monitor/COD Gain fits II

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