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

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 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 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 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 >

5 LHC magnets and hysteresis

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 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 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 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 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 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 RQ10.L1B2 1.9K)

13 RQ10.L2B2 1.9K)

14 RQ10.L4B2 1.9K) 1.8

15 RQ4.L1B2 4.5K) 0.0

16 RQ4.L2B1 4.5K) ~ worst case DCMAG amplitude for MQY

17 RQ7.L4B2 1.9K) 1.8

18 RQ7.L8B2 1.9K)

19 RQ7.R2B1 1.9K)

20 RQ8.R2B1 1.9K) ~ worst case DCMAG amplitude for MQM

21 RQ9.L5B2 1.9K)

22

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