1. The implementation of hysteresis in the FIDEL model and implications for the LHC operation P. Hagen November 2010

2. 2 Hysteresis in the FiDeL model o The FiDeL description of the magnets assume / require that a specific pre-cycle has been followed o The reason being that the hysteresis depend upon the magnet history o There are 3 components in the FiDeL model which contribute to hysteresis: o PEN - current penetration in the cable filaments o DCMAG - persistent currents in SC magnets o RESMAG – residual magnetisation of materials o PEN is only used in MQM and MQY to model exponential behavior @ low B o DCMAG depends upon the sign of the dI/dt (ramp up or down). We do not know the exact conditions (Δt, ΔI) causing a switch of branch o RESMAG depends upon the history (previous cycle)

3. 3 Example of TF with RESMAG hysteresis o The curves a, b, c, d correspond to different pre-cycles (Imin and Imax) o The person implementing FiDeL for a magnet must decide upon which curve (or something in-between) based upon how the magnet is used o Example MQWA, pre-cycle constrained by power supply + magnet only ramp-up (dI/dt > 0) so we only use that specific branch

4. 4 Extending the FiDeL model to 4 quadrants! o In FiDeL we basically model one quadrant (1 or 4) o The sign of the current is not given by FiDeL but by the powering scheme o The width of the hysteresis depends on the previous Imin and Imax I > 0I < 0 Imin < 0 I < 0 I > 0 Imin > 0 12 34

5. 5 LHC magnets and hysteresis

6. 6 Cat A – no operational issues o Magnets which operate in a current range with little hysteresis o and.. or … o Magnets which only ramp-up with beam present, well-defined pre-cycle and relevant hysteresis components are included in the FiDeL model o Most main magnets belong to this category Il buono (the good)

7. 7 Cat B – minor operational issues o Magnets which operate in a current range with hysteresis and relevant hysteresis components are NOT included in the FiDeL model o … but it is assumed that they do not cause operational problems o We pretend they behave linearly in the low-current region o Most corrector magnets belong to this category… o The neglect of hysteresis in orbit, tune and coupling correctors is compensated by real-time measurements and adjustments o Correctors without well-defined operational cycles are probably impossible to model wrt hysteresis o Nevertheless, we believe there are corrector magnets which have known cycles and where model could be improved if justified by operation: MCD, MCO, MQTLI, MSS ? Il buono? (the good?)

8. 8 Cat C – assumed operational issue il brutto (the bad) o Magnets which operate in a current range with hysteresis and relevant hysteresis components are NOT included in the FiDeL model o … and it is assumed that they do cause operational problems o We have so far only put the corrector MCS into this category o The current crosses 0 during LHC ramp-up so there will be an error in TF of several %

9. 9 Cat D – known operational issue il cattivo (the ugly) o Magnets which change ramp direction during operation (dI/dt) and which include a FiDeL DCMAG component o This happens to the final focus and insertion quads during the squeeze: MQXA, MQXB, MQM/C/L, MQY o This causes the TF to jump, if we literally follow the FiDeL model o LSA adds smoothing in order to keep power supplies happy o They require continuous I function with well-defined constraints on dI/dt, d 2 I/dt 2 o But … trims of these magnets become unpredictable as it may cause the DCMAG component to change sign, so it gives an upper limit on the smallest possible trim

10. 10 http://www.youtube.com/watch?v=1hYV-JSjpyU The question is, to branch or not to branch? Ignorance (pretend it does not happen) Or … Complexity when trimming A persistent answer is needed for 2011 run Keep in mind the effect will ~ disappear with 7 TeV

11. 11 MQXA1.L2 (1.9K) In following slides, red numbers give DCMAG in units of GEOmetric component. This is ½ width of hysteresis 0.7

12. 12 RQ10.L1B2 (MQML @ 1.9K) 1.9 1.6

13. 13 RQ10.L2B2 (MQML @ 1.9K) 1.8 1.7

14. 14 RQ10.L4B2 (MQML @ 1.9K) 1.8

15. 15 RQ4.L1B2 (MQY @ 4.5K) 0.0

16. 16 RQ4.L2B1 (MQY @ 4.5K) 0.0 0.2 ~ worst case DCMAG amplitude for MQY

17. 17 RQ7.L4B2 (MQM @ 1.9K) 1.8

18. 18 RQ7.L8B2 (MQM @ 1.9K) 2.3 2.6

19. 19 RQ7.R2B1 (MQM @ 1.9K) 2.6 2.7 2.5 2.8 2.7 2.8

20. 20 RQ8.R2B1 (MQML @ 1.9K) 2.7 3.1 4.2 ~ worst case DCMAG amplitude for MQM

21. 21 RQ9.L5B2 (MQMC @ 1.9K) 2.1 2.2 2.1

22. 22

23. 23 RQ10.R5B2 (MQML @ 1.9K) 1.8 ΔI DCMAG = 2 * 1.8 / 10000 * 2334 A = 0.84 A The trim discrepancy of 5 A seems not justified!