1. Magnetic Behavior of LHC Correctors: Issues for Machine Operation W. Venturini Delsolaro AT-MTM; Inputs from A. Lombardi, M. Giovannozzi, S. Fartoukh, J.P. Koutchouk, V. Remondino, R.Wolf LHC workshop “Chamonix XIV” January 18-21, 2005

2. Outline Magnetic measurements available today Issues on the magnetic behavior Transfer functions: required accuracy, hysteresis and reproducibility of machine settings Field quality panorama Cross talks Plan for the remaining (cold) measurements Conclusions

3. Corrector Zoo

4. Where we are: summary of cold measurements and c/w campaigns (FQWG 16/11/04) Corrector typePre seriesSeriesCold/warm MCS10+10nonegood MCDO10+10nonepoor MO3 assembliesnone1 mod., fair MQT/S3 assemblies8 modulespoor, improving MCB1 assembly2 ass. + 4 mod.good MS1 assembly1 ass. + 3 mod.1 mod., fair MCBC1 assembly1 module1 mod., fair MCBYnone - MQTL2 modules-- MCBX+MCBXA217/25fair MQSX+MCSOX18/9to check

5. Tolerable uncertainties on the settings of main components (1) Orbit Correctors in the Arcs (MCB, individually powered): Closed orbit perturbation from N randomly distributed kicks: For any given, the tolerable ΔBl rms is found, as a function of Bρ, and of correction scenario taking rms =2 mm, N=200, the tolerable ΔBl rms at 7 TeV is about 4 10 -2 Tm, that is 2% of the maximum value (same at injection  to get a circulating pilot beam?) Becomes 1‰, if we take = 0.1 mm (for efficiency of collimation)  1.28 10 -4 Tm absolute rms error at injection   0.3% of rms excitation of arc correctors

6. Tolerable uncertainties on the settings of main components (2): Tuning Quadrupoles (MQT) From the operational tolerance on tune shifts (±3 10 -3 ) At injection, it corresponds to a total integrated MQT field (in Tm at 17 mm) of 5.3 10 -3 Tm 6.7 10 -4 Tm accuracy for one single magnet Figures 10 times lower if we take 10% of the operational tolerance From which one gets  Q/  B 2 l=0.56/Tm at 17 mm at injection

7. Tolerable uncertainties (3)… MCS: 1.5 10 -4 Tm absolute accuracy at injection to assure reproducibility of Q’ within 10 units MS: 7 10 -4 Tm absolute accuracy at injection  10 unit of Q’ MO to be determined, not critical: 5% should be OK IR correctors  to be determined, potentially critical

8. Sample sizes for cold tests From σ of cold measurements (when available), and required uncertainty u, for a 100(1- α)% confidence interval  Deduce n(u, α) from the usual formula for the estimated standard error of a sample of n units u= σ t(α, n-1)√(1/n-1/N) Where t is the Student distr. and N the population number  Different u, σ and N for each corrector type

9. The problem of hysteresis Magnetic hysteresis from the superconducting filaments and from the iron affects all the sc correctors “Likely” settings at injection for some correctors (orbit, tuning, b3 spool pieces) are at very low current Trims might be numerous and require reversing of current ramps (for example orbit corrections) As a consequence, hysteresis on the corrector transfer functions results in a “randomization” of the corrector magnetic state (position on the hysteresis loops: upper or lower branch) Consequences on reproducibility of settings, notably between runs  compare the resulting “uncertainty” to operational optics tolerances

10. Table of Hysteresis at 0A for some corrector types (Mainly from pre series measurements)

11. Hysteresis of orbit corrections Compare kick at injection due to hysteresis to some tolerance on CO displacement….  10 -3 Tm at injection randomly distributed amongst 200 MCB  782 μm rms on CO 1) Reproducibility at 100 μm level not to be obtained if hysteresis is ignored 2) May have an influence on the convergence of correction algorithms

12. Hysteresis of tune corrections Taking ΔQ/ΔB 2 l=0.56/Tm at injection, the hysteresis width of a single MQT corresponds to ΔQ=1.1 10 -4 For one circuit of 8 MQT  9 10 -4, Remember the tolerance on ΔQ=±3 10 -3 Considering 8 circuits  7 ·10 -3 (!)

13. Consequence on tune corrections at injection From cold measurement of MQT-MA-003 ΔI to cross the loop is related to re-penetration of filaments plus iron hysteresis: H p =30 mT (1 A for the MQT)  7 10 -3

14. Corresponds to a jump in Q’ of 3.8 units Excitation curve of a pre series MCS

15. Hysteresis of Lattice Sextupoles Corresponds to more than 10 units of Q’

16. Field quality panorama

17. Warm measurements: the emerging spikes b3=-40 units in MCBC b6=-10 units and b10=-15 units in MQT, and… MQTL!

18. Field quality at warm and at 1.9 K of the first 2 MQTL modules (pre series) Likely field quality of Q6 in IR3 and IR7, done with 6 MQTL

19. Series MCBC module measured at warm and at 1.9 K

20. Cross talks Between apertures at high field (MSCB, MQTL) Checked for 2 MSCB variants and found to be negligible (order of 10 -4 Tm between the MCB) Effects foreseen for the MQTL assemblies In nested magnets (MCDO, Inner Triplet correctors) Very few measurements, to be completed with extended programs on the spare units

21. Cross talk effects in nested magnets (MCBX)

22. Proposal for minimal cold measurements plan Corrector typeTFHysteresis measurement setting up cycle MCS10+10 (1%)yes MCDO10+10 (1%)? MO9no MQT/S9yes MSCB12yes MCBC9yes MCBY9yes MQTL4yes MCBX+MCBXA-yes MQSX+MCSOX-yes

23. Conclusions The knowledge of the transfer functions with  10 -3 accuracy would be needed to set some corrections. Transfer functions are not linear. Very few measurements so far. Sample sizes not defined The hysteresis of main components is an issue. Set up cycles will have to be defined, in particular for nested magnets. Refined measurements and models may be needed for operation Field quality of MQTL and MCBC is at the limit of tolerance Plan for the cold series measurements must provide sufficient experimental data for modeling work

24. Thanks to L. Bottura, A. Lombardi, S. Fartoukh, M. Giovannozzi, J. P. Koutchouk, V. Remondino, L. Walckiers R. Wolf