Transfer Function of the Quadrupoles And Expected b -Beating at injection.

1. Transfer Function of the QuadrupolesAnd Expected b-Beating at injection. S. Sanfilippo and P. Hagen, J.-P. Koutchouk, M. Giovannozzi, T. Risselada Acknowledgments: S. Fartoukh, A. Lombardi, Y. Papaphilippou Workshop Chamonix XV 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

2. Special thanks to : • L.Bottura, N. Smirnov, M. Buzio, M.Calvi, N.Sammut, G.Deferne, M.Gateau, W. Venturini-Delsolaro & his team, O.Dunkel, J.Garcia.Perez & his team, D.Cornuet and his team (AT-MTM), E.Todesco (AT-MAS) for calibration measurements and analysis, follow-up, general information and feed-back. • R. Ostojic & his team, N. Catalan-Lasheras, S. Ramberger (AT-MEL), J.Di-Marco (FNAL) for the follow-up of the measurement results and feed-back on the instrument performance. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

3. Outline • Motivations. • Sources of gradient errors. • Study of the gradient errors coming from the measurements: • Uncertainty of the measurement systems. • Cross-calibration results and estimate of the absolute accuracy. • Analytical estimate of the impact of the gradient errors on the b-beating (static case): • Arc quadrupole. • Stand alone magnets- impact of the magnetic history. • MAD Computation of the b-beating. • b-beating results versus targets. • Conclusions. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

4. Motivations • Target: the aperture budget being tight, try as much as possible to minimize the gradient uncertainties. • Budget:(S.Fartoukh, O.Brüning, LPR 501) • Overall budget of (Db/b)peak=21% (i.e. 10% of r.m.s beam size) • Off momentum b-beating (~7% for H and 5% for V) • Gradient errors: (Dbx/bx)peak<14%, (Dby/by)peak<16% • Method: analytical estimate and numerical computations (MAD-X) Example for MQs C (L,N,K,bx,y) Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

5. Sources of gradient errors • “Static” error sources : • Knowledge of the transfer function (uncertainty, random) of the quadrupoles (MQ, MQM, MQY, MQX, MQW, MQTL). • Systematic and random of b2 in dipoles (MB). • Precision of the power converters. • Transfer function dependence on the magnetic field history. • Mismatch of the MQT’s when performing a tune shift DQ~ ± 0.1. • Feed-downs from lattice and spool-piece sextupoles. • “Dynamic” error sources : • Variation of MQ’s transfer functions during the decay, snap-back. • PC tracking errors on B2(MQ)/B1(MB). • Chromaticity correction during the decay/snap-back. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

6. Break-down of uncertainties in the transfer function (static) • Quadrupoles measured at cold. • Precision of the measurement system (resolution, reproducibility, calibration uncertainty). • Uncertainty on the cold magnet state (history dependence). • Quadrupoles measured at warm (or partially at cold). • Precision of the measurement system (resolution, reproducibility, calibration uncertainty). • Uncertainty on the magnet state (history dependence). • Precision of the warm-to-cold correlation and uncertainty on the extrapolation. • Quadrupoles powered in series: • Spread of the transfer function due to manufacturing tolerances. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

7. Break-down of the errors coming from the measurement systems • Resolution:Smallest variation that the system can measure. • For all the systems used resolution is better that 1 unit. ( not discussed in the following) • Reproducibility:Random coming from 10 consecutive measurements under the same conditions. • Uncertainty:Absolute accuracy of the system. • Errors coming from the calibration of the systems. • The systematic part is removed using cross-calibration between systems. All measurement errors are supposed to be normally distributed. The uncertainty and the reproducibility will be given at 1 s. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

8. Measurement systems of transfer function at cold (SM18) • Long rotating coils(7 pairs for MB, 2 - for SSS) • Uncertainty (Gdl)~ 10-15 units, reproducibility <1 unit. • Automated scanner(2 heads) • Used for SSS & special SSSs of variable lengths • One 600/700mm-long rotating coil, longitudinal scanning over magnet length. • Uncertainty (Gdl)~ 10 units, reproducibility~0.2 unit. Superconducting dipole on the cold test bench in SM18 equipped with rotating coil system • Single Stretched Wire (SSW)(3 systems) • 1 wire loop over any total magnet length. • Integrated strength of quadrupoles and dipoles.Uncertainty (Gdl): ~5 units, reproducibility~1 units at high field but ~10 units low field (for quads). SSW for special SSS measurement Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

9. QIMM Measurements at cold (block 4) and industry (warm) 4)Rotating coils in vertical facility(2 pairs) • Used for MQMC, MQM, MQY • Test in a vertical cryostat with no anti-cryostat: higher uncertainty on absolute value of Gdl (but relative value between two currents is reliable). • Uncertainty (Gdl):~40 units, reproducibility ~ 1 unit. Vertical test facility. 5) Industry moles (300 K) :QIMM(2 pairs) • Used for MQ, MQMC, MQM, MQY,MQW and dipoles. • Uncertainty (Gdl) ~ 20 units • Reproducibility ~ 0.2-3 units depending on the mole. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

10. Uncertainty and reproducibility for cold measurements systems • Reproducibility for all systems is excellent (<1 unit) except the SSW at low current (1 kA). • Uncertainty on the quadrupole of 5 (SSW) to 30 units (coils) has a large variability from system to system: • Calibration errors: Rotation radius reproducible only to 5-30 mm • Mechanics: Uncertainty on the coil rotation axis position during real measurement. reproducibility low field Courtesy L.Bottura • Improvement of the calibration procedure (scanner, long shaft) already started. • A plan of cross calibration between systems is on going to reduce the uncertainty. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

11. Measurement and cross-calibration test plan • The original idea (100% of cold tests) had to be adapted as we went along and: • ~15% of the MBs, MQs, will be tested at cold: we will rely on warm data and established the warm to cold correlation. • Cross-calibration with 3 systems: rotating coils/SSW/scanner for stand-alone magnets. • Special tests are planned have started in block 4 to study the impact of the magnetic history. Courtesy L.Bottura Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

12. Gdl measurements at cold with two systems for arc MQs. SSW system (1.9 K) / scanner (1.9 K). Before calibration of the scanner. After new calibration procedure . • Significant improvement : values from the two systems within 5 units (rms). Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

13. Quadrupoles (B2) cross-calibrationSSW/rotating coil SSW system (1.9 K) / rotating coil measurements (1.9 K). Courtesy M.Calvi Calibration has to be improved. All the shafts have to be calibrated. • Goal: To guarantee a maximal uncertainty of the transfer function measured • with any system (including the vertical facility) of Umeas. syst ~10 units (rms). Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

14. Dipole (B1) cross-calibration SSW system (1.9 K) / 15-m long rotating coil (1.9 K). Courtesy M.Buzio • Uncertainty for MB transfer function measurement at cold Umeas. syst~ 3 units (rms). Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

15. units Comments Uncertainty s 13 85% of MQ measured production s p reduction by ~30% after (2n+1) pairing 9 (Y.Papaphilippou) effective s in units 4 20 MQs measured (warm/cold) (rms) U 5 SSW used for the W/C meas system s due to the impact of magnetic history 2 s b 11 quadratic sum 2 K x/ Ky 0.76 0.78 FQWG March 2005 9 9 (Db/b) /(Db/b) [%] (3s) (Db/b) s peak x,y [%] peak= C . b x y x,y 2 Impact of the b2 errors on the b- beating: Arc quadrupoles Courtesy E.Todesco Courtesy Y. Papaphilippou after sorting Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

16. Impact of the random b2for stand alone magnets • Magnets measured fully at cold (MQY, MQX) or fully at warm (MQW): Uncertainty coming from the measurement system. • MQM(C,L), MQTL measured partially at cold: uncertainty from the warm to cold correlation to be added. • Contribution of the magnetic history significant (working current between 100-300 A) to be added for all. Analytical estimate of Db/b [%] peak for stand alone quadrupoles. • This class of magnets gives total contribution of about 13 % (peak at 3s). Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

17. Influence of the magnetic history on the b2 knowledge • First experiment on MQY: • Measurements with different minimum current of pre-cycle. • Change of TF values up to 60 units at injection current ~100 A! ref. cycle • 25 special tests foreseen in Block 4 on MQM(C), MQY in 2006. Courtesy W.Venturini. • Magnetic modeling will follow. Rough estimate of the uncertainty coming from the modeling ~ 10 units (rms). Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

18. Simulation model of the b-beating Configurable options: (class of magnets, random sampling… Installation database Layout + MEB slot allocation Database of warm magnetic measurements Generator of magnetic imperfections Database of cold magnetic measurements MAD-X LHC machine calculations Nominal LHC sequence and optics definitions. NB: Simulation carried out with nominal optics V6.5 at injection energy. Correctors and MQT for tune shift are set to 0. β-beat calculations Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

19. Simulation model: details and assumptions • Measurements at cold are used for cryo-magnets whenever available. • Magnets not yet built are drawn from a Gaussian distribution matching observed production spread in warm measurements. • Cryo-magnets with warm measurements are then extrapolated to cold by a warm-cold correlation (systematic and Gaussian random). • Allocation of magnets to slots not yet defined by MEB are drawn randomly. • The simulations assume that the power supplies are re-calibrated to provide the nominal average gradient when there is a chain of magnets. • For the power supplies the reproducibility chosen is that for one day and originate from the values of the design report. • The statistics are based on 30 seeds. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

20. Db/b-distributions Distribution of the Db/bsampling in the machine circumference for MQs (1 seed). • Distributions are not Gaussian (Kolmogorov-Smirnov test). • The ratio (Db/b)peak/(Db/b)rms is found to be about 2.2. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

21. b-beating targets/simulations Estimations from the FQWG (March 2005) Not re-computed with MAD but initial targets re-scaled. Re-computed with MAD Not re-computed with MAD, identical targets. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

22. Conclusions and issues (1) • Good agreement between the targets/analytical estimates and the results obtained from a model based on actual magnetic errors and slot allocation. Checks are going on for the case of stand alone magnets. • At injection the static b-beating budget will be respected however: • The error on the b2 knowledge due to the magnetic history dependence is assumed to be at level of 10 units (r.m.s). • The special magnetic measurement program planned in block 4 for 2006 (25 tests)+ modeling have to be carried out. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains

23. Conclusions and issues (2) • Next issue : The knowledge of the transfer function in dynamic state (snap back/squeeze). • A dedicated magnetic measurement program with the appropriate cycles has to be performed. • Additional numerical simulations using the MAD-X model will be carried out to: • Investigate the b-beating values during snap/back and squeeze. • Evaluate the feed-down effects from sextupoles using the information from the geometry database and cross-check with targets/analytical calculations. Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains