1. E. Todesco THE LHC MAGNETIC MODEL AT 6.5 TEV E. Todesco CERN, Geneva Switzerland With contributions from N. Aquilina, L. Bottura, R. De Maria, L. Deniau, S. Fartoukh, P. Ferracin, L. Fiscarelli, P. Hagen, M. Giovannozzi, M. Lamont, E. Maclean, N. Sammut, M. Schaumann, F. Schmidt, M. Solfaroli Camillocci, M. Streczylk, R. Tomas Garcia, W. Venturini Delsolaro, J. Wenninger http://www.cern.ch/fidel CERN, 17 th March 2016 Accelerator Sector Seminar

2. E. Todesco The LHC magnetic model at 6.5 TeV - 2 CONTENTS Field model of the LHC Tune and gradients in the quadrupoles Chromaticity and b 3 in the dipoles Nonlinear terms An outlook for Future Circular Collider FiDeL also includes precycle prescriptions – not given here

3. E. Todesco HOW TO EXPRESS A GOOD FIELD A main magnet for particle accelerators provides the main component (dipole or quadrupole) Field imperfections within 2/3 of the aperture should be smaller than 0.1% of the main component Usually this is expressed through a multipolar expansion Where B N is the main component Where R ref is 2/3 of the magnet aperutre Where the multipoles b n, a n are expressed in « units » The beam dynamics requirements impose multipoles smaller than 1 to 10 units This implies a precision in cable positioning of ~0.1 mm, plus some requirements on the superconductor The LHC magnetic model at 6.5 TeV - 3 Dipole ( B 1 ) Quadrupole ( B 2 )

4. E. Todesco THE FIELD MODEL FOR THE LHC We start with the main component B 1 (dipole) or B 2 (quad) Since we are dealing with electromagnets, we divide it by the current to have the « transfer function T N » (how much field for 1 A) Dependence of T N and multipoles on the current is complex There is a term independent of the current (the geometric) related to Biot-Savart But then there are a few nonlinear effects, so there is a sum of components, each one with a different physical source Model of b 3 in the main LHC dipoles versus current (left) and time (right) [N. Sammut, L. Bottura, et al Phys. Rev. STABs] The LHC magnetic model at 6.5 TeV - 4

5. E. Todesco THE FIELD MODEL FOR THE LHC The saturation It is due to the saturation of the iron – it is important at high fields Modelled through a arctan like term, ie smth that makes a step between two values Model of b 3 in the main LHC dipoles versus current (left) and time (right) [N. Sammut, L. Bottura, et al Phys. Rev. STABs] The LHC magnetic model at 6.5 TeV - 5 An arctan function to fit saturation

6. E. Todesco THE FIELD MODEL FOR THE LHC The magnetization (or persistent current) It is due to the magnetization of the superconductor filaments - it is important at low fields, negligible at high fields Modelled through a hyperbolic-like term A/I  plus other Model of b 3 in the main LHC dipoles versus current (left) and time (right) [N. Sammut, L. Bottura, et al Phys. Rev. STABs] The LHC magnetic model at 6.5 TeV - 6 An hyperbolic function to fit persistent current

7. E. Todesco THE FIELD MODEL FOR THE LHC The decay At injection, a part of the magnetization decays Modelled through a double exponential in time Saturation times are of the order of hours Model of b 3 in the main LHC dipoles versus current (left) and time (right) [N. Sammut, L. Bottura, et al Phys. Rev. STABs] The LHC magnetic model at 6.5 TeV - 7

8. E. Todesco THE FIELD MODEL FOR THE LHC The snapback At the beginning of the ramp the whole part of magnetization that decayed disappears rapidly (snaps back) Modelled through a exponential in current – takes place over 10 A Model of b 3 in the main LHC dipoles versus current (left) and time (right) [N. Sammut, L. Bottura, et al Phys. Rev. STABs] The LHC magnetic model at 6.5 TeV - 8

9. E. Todesco THE FIELD MODEL FOR THE LHC The field model (FiDeL) is made of The equations given in the previous slides The values of the coefficients are obtained by fit of magnetic measurements on the whole magnet production Some components (geometric) measured for all magnets Other components measured for a sample of magnets Project started many many years ago by an idea of L. Bottura Several thousands of coefficients ! Only for the geometric of the main dipoles, we have 1200 (magnets) * 2 (apertures) * 22 (multipoles) = 50 000 coefficients! Precision of measurements Main dipole component: 10 units absolute, 2-5 relative Main quadrupole components: 20 units absolute Lower order multipoles: within 0.1 units High order multipoles: towards 0.01 units and lower The LHC magnetic model at 6.5 TeV - 9

10. E. Todesco THE FIELD MODEL FOR THE LHC Implementation in LSA LSA provides the currents to the LHC magnet – contains the FiDeL parametrization (M. Lamont, et al.) Individual models of magnets are averaged for the circuits Correctors are set to compensate measured field errors Implementation in WISE In 2005, the project was launched by an idea of J. P. Koutchouk WISE provides the best estimate of the field errors to be used by tracking codes for simulation (P. Hagen, with ABP support) To be able to have the best models of the LHC to compare and understand measurements, and to test new hypothesis etc. The LHC magnetic model at 6.5 TeV - 10

11. E. Todesco The LHC magnetic model at 6.5 TeV - 11 CONTENTS Field model of the LHC Tune and gradients in the quadrupoles Chromaticity and b 3 in the dipoles Nonlinear terms An outlook for Future Circular Collider

12. E. Todesco TUNE AND QUADRUPOLE GRADIENTS The tune is the number of oscillations in the transverse plane Nominal value is 64.280 and 59.310 (at injection) Need to control at 0.001, so 16 ppm This is extremely challenging! With the tune you see very small effects Tune is always measured during operation Precision of measurement is of the order of 0.001 A feedback system to lock it on the nominal values is available It is used during the ramp The LHC magnetic model at 6.5 TeV - 12

13. E. Todesco TUNE AND QUADRUPOLE GRADIENTS Tune is given by the quadrupoles, five types in the LHC MQ (main) Two IPQ: MQM, MQY (matching sections) Two triplet magnets: MQXA, MQXB In the table we give the impact of a variation of quadrupole gradient of 0.1% For the main quads, this gives 0.65, it is 600 times the tolerance! Then, second order effects Sextupole crossed with an offset give tune Note: the main problem is the main component The LHC magnetic model at 6.5 TeV - 13

14. E. Todesco TUNE AND QUADRUPOLE GRADIENTS Example: measure of decay of main component in main quadrupoles The LHC magnetic model at 6.5 TeV - 14 Decay of b 2 in main quadrupoles at injection [L.Deniau]

15. E. Todesco TUNE AND QUADRUPOLE GRADIENTS Tune measurements give the precision of quadrupole model Here we show the tune during ramp, removed all the corrections applied If the model were perfect we would just see the cross at 64.28, 59.31 (integer part not shown in the plot) Injection: we are 0.12 far from 64, so 0.12/64=0.002  0.2% High field: 0.1% This is in line with expected from the absolute precision of magnetic measurements Amazing check of the whole chain! Bare tune during ramp (blue: beam1 red:beam2) [M. Juchno] The LHC magnetic model at 6.5 TeV - 15 0.1% 0.2%

16. E. Todesco TUNE DECAY Tune decay is visible and has to be corrected: 0.02 So it is 20 times larger than control requirement: needs correction Amplitude in agreement with expected from magnetic measurements, dependence on powering history About 50% larger in the H plane (not all from quads) Time constant of 1000 s, slower than in individual magnets Fit problem: first minutes cannot be measured, so amplitude is extrapolated Bare H tune during ramp (blue: beam1 red:beam2) [M. Juchno] The LHC magnetic model at 6.5 TeV - 16

17. E. Todesco TUNE SNAPBACK Tune snapback takes places in the first 20-30 A (35-40 s) In horizontal plane agrees with FiDeL exponential In vertical different behaviour – to be investigated Tune snapback during ramp (full dot: H emtpy dot: vertical) [M. Schaumann] The LHC magnetic model at 6.5 TeV - 17

18. E. Todesco The LHC magnetic model at 6.5 TeV - 18 CONTENTS Field model of the LHC Tune and gradients in the quadrupoles Chromaticity and b 3 in the dipoles Nonlinear terms An outlook for Future Circular Collider

19. E. Todesco CHROMATICITY AND b 3 Chromaticity is the variation of tune with the energy of the beam 1 unit of chromaticity means that 0.1% variation of beam energy gives a variation of 0.001 of tune Chromaticity is usually set in the range 2-15 Negative chromaticity gives instability, but low values are usually preferred So we have walk on the edge of a canyon OP and ABP would like to control chroma within 1 unit Far from being trivial … To measure chromaticity we need to excite the beam So usually chromaticity is not known in standard operation (we are blind) It is measured in few special cases to make some feed-forward The LHC magnetic model at 6.5 TeV - 19

20. E. Todesco CHROMATICITY AND b 3 Chromaticity is proportional to the following compoennts The quadrupoles give a natural chromaticity, that is not far from the tune of the machine (60 in our case) The b 3 in the dipoles gives chromaticity, it is -43/35 units in H/V per unit of b 3 If you remember that during ramp the persistent current component is 7 units of b 3, this gives about 300 units of chromaticity change during the ramp Controlling chromaticity during ramp within 1 units means correction with a 0.3% error Second order: an octupole (as the Landau octupole) with a beam misalignment gives a sextupole, ie, chromaticity The LHC magnetic model at 6.5 TeV - 20

21. E. Todesco CHROMATICITY AND b 3 Chroma control is done through different defense lines Two magnet families: The lattice sextupoles MSF, MSD (two parameters F and D, in reality four families are used) to correct natural chroma and to trim chroma The spool pieces MCS (one parameter, in reality one per octant) to correct the b 3 in the dipoles (ie the 300 units of swing) First correction done through FiDeL in the spool pieces Typically, FiDeL correction has a 5% error in the static part and 20% in the dynamic part, so this is not enough Then a measurement is done and a feed-forward is applied to the lattice sextupoles With this you manage to flatten within a band of ~10 to 20 units width during ramp The LHC magnetic model at 6.5 TeV - 21

22. E. Todesco CHROMATICITY AND b3 IN THE DIPOLES In LHC chromaticity changes 300 by units due to the 7 units change of b 3 persistent current in the dipoles 1 b 3 in the dipole is 43/-35 units of chroma in H/V Target for control is ~1 chroma unit, today achieved 10 units b 3 in the main LHC dipoles, and injection energy at 450 GeV [L. Deniau, P. Ferracin] The LHC magnetic model at 6.5 TeV - 22

23. E. Todesco CHROMATICITY AND b3 IN THE DIPOLES Chromaticity measurable only for small intensity beams Few data, but show good reproducibility Above 2 kA, chroma stable within 5 units, out of 300 swing  correction within 1-2% Below 2 kA, we have a missing ~1 b 3 unit – to be investigated Chromaticity change during ramp (red: H black: V) [M. Solfaroli Camillocci] The LHC magnetic model at 6.5 TeV - 23

24. E. Todesco CHROMATICITY AND b3 IN THE DIPOLES Chromaticity measurable only for small intensity beams Few data, but show good reproducibility Above 2 kA, chroma stable within 5 units, out of 300 swing  correction within 1-2% Below 2 kA, we have a missing ~1 b 3 unit – to be investigated Chromaticity transformed in missing b 3 in the main LHC dipoles: measurements (black and red) and 1 units of persistent (green) The LHC magnetic model at 6.5 TeV - 24

25. E. Todesco CHROMATICITY SNAPBACK Decay and snapback visible, about 1 unit of b 3, 40 units of chroma Take place in ~30 A, with time constant in agreement with magnetic measurements We find g 3 sb ~0.2 units/A versus a value of 0.18 units/A through magnetic measurements b 3 in the main LHC dipoles, and injection energy at 450 GeV The LHC magnetic model at 6.5 TeV - 25

26. E. Todesco The LHC magnetic model at 6.5 TeV - 26 CONTENTS Field model of the LHC Tune and gradients in the quadrupoles Chromaticity and b 3 in the dipoles Nonlinear terms An outlook for Future Circular Collider

27. E. Todesco NONLINEAR TERMS In general we have no observables on the high order terms, with the exception of Q’’ (second order chroma) is proportional to b 4 Q’’’ (third order chroma) is proportional to b 5 Amplitude dependent tune dQ/dx is proportional to b 4 Both b 4 and b 5 and correctoed with spool pieces The correction is set to locally correct the b 4, b 5 of the dipoles, but it also gives the same correction to cancel Q’’ and Q’’’ Main results at injection [E. Maclean] Q’’ understood, when fine effects are taken into account The Q’’ correction also cancels the amplitude dependent detuning, so b4 correction is local For Q’’’, we need to reduce the MCD powering to set it to zero This is an enigma, MCD settings lead to overcorrection Having same analysis at 6.5 TeV would help a lot the understanding The LHC magnetic model at 6.5 TeV - 27

28. E. Todesco NONLINEAR TERMS The other quantity we can access is the dynamic aperture Ie the place where you start having significant losses This can be measured with the beam and computed with the model In HERA the agreement was within a factor two In the LHC we manage to have a agreement within a few sigma This is a significant improvement in the ability of modeling The LHC magnetic model at 6.5 TeV - 28 Agreement between simulations and measured dynamic aperture in two different cases [E. Maclean]

29. E. Todesco The LHC magnetic model at 6.5 TeV - 29 CONTENTS Field model of the LHC Tune and gradients in the quadrupoles Chromaticity and b 3 in the dipoles Nonlinear terms An outlook for Future Circular Collider

30. E. Todesco OUTLOOK FOR FCC What happens for the Future Circular Collider? Are there bottlnecks or showstoppers with the expected size and optics? Can we work out reasonable targets for magnets? First considerations on tune The control requirement of 0.001 does not change If tune is larger, control gets more difficult! If we keep the same cell length as in the LHC, four times larger machine, four times larger tune But the cell length in FCC is doubled from 100 to 200 m, so we just double the tune [D. Schulte] Control of 0.001 out of 120 means 8 ppm level reproducibility on gradients – challenging, but just two times more difficult than LHC All steps reducing the tune are welcome Going to 60° phase advance would help The LHC magnetic model at 6.5 TeV - 30

31. E. Todesco OUTLOOK FOR FCC Sensitivities of chroma on b 3 in the dipoles is also doubled 1 units of b 3 will give 80 chromaticity units (R. Tomas Garcia) I would place a maximum target for persistent current component on the 16 T dipoles at <10 units Note that field quality in a 15-16 T dipole is much easier than in a 11 T dipole – present 15-16 T design fits within the 10 units This would give a 1000 chroma swing, 3 times larger then the LHC already challenging, above these values I think we enter a new regime Target for b 3 snapback: 1 unit This would give 50% larger chroma snapback than in the LHC The LHC magnetic model at 6.5 TeV - 31

32. E. Todesco OUTLOOK FOR FCC An MD in the LHC with 225 GeV injection could confirm the possibility of steering 3 times larger chroma swings From 7 units of persistent to 20 units And 3 times lager snapback Proposal under study [M. Solfaroli, B. Goddard, J. Wenninger, M. Lamont, et many others] Measurements done on 4001 dipole [L. Fiscarelli] The LHC magnetic model at 6.5 TeV - 32 225 GeV injection 450 GeV injection

33. E. Todesco CONCLUSIONS Quadrupole gradients precise to 0.1-0.2%, as expected Decay and snapback of main component of quadrupole give tune decay and snapback To be corrected Snapback shape is exp in H plane, but not in V Large chromaticity swing induced by b 3 persistent current in the main dipoles (300 chroma units) 1 unit missing b 3 out of 7 expected Decay and snapback in line with expectations Time constant of snapback longer than in magnetic measurement Disentangling the effect is a complex operation – work in progress and will follow during runII Feedback to design of future machines is relevant The LHC magnetic model at 6.5 TeV - 33

34. E. Todesco REFERENCES The mytical paper with the decay and snapback discovery … D. A. Finely, et al., “Time-dependent chromaticity changes in Tevatron” Particle Accelerator Conference, 1987, 151-3. and Luca paper with correlation between decay and snapback L. Bottura, et al., “A scaling law for the snapback in superconducting accelerator magnets” IEEE Trans. Appl. Supercond., vol. 15, 2005, pp. 1217-20. The PRSTAB papers on the construction of the model N. Sammut, L. Bottura, J. Micallef, “Formulation to predict the harmonics of the superconducting Large Hadron Collider magnets,” Phys. Rev. STAB., vol. 9, 2006, Art. ID. 012402. N. Sammut, L. Bottura, P. Bauer, G. Velev, T. Pieloni, J. Micallef, “Formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Dynamic field changes and scaling laws” Phys. Rev. STAB., vol. 10, 2007, Art. ID. 082802. N. Sammut, L. Bottura, G. Deferne, W. Venturini Delsolaro, “Formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Precycle ramp rate effects and magnet characterization” Phys. Rev. STAB., vol. 10, 2007, Art. ID. 082802. Works about the RunI results N. Aquilina, et al., “Tune variations in the Large Hadron Colllider” Nucl. Instrum. Meth., vol. 778, 2015, pp. 6-13. N. Aquilina, M. Lamont, M. Strzeclzyk, E. Todesco, N. Sammut, “Chromaticity decay due to superconducting dipoles on the injection plateau of the LHC” Phys. Rev. STAB., vol. 15, 2012, Art. ID. 032401 Works about the RunII results E. Todesco, L. Bottura, M. Giovannozzi, P. Hagen, M. Juchno, M. Lamont, E. Maclean, R. Tomas Garcia, M. Schaumann, F. Schmidt, M. Solfaroli Camillocci, J. Wenninger, “The magnetic model of the LHC at 6.5 TeV” IEEE Trans. Appl. Supercond., 2016, in press The LHC magnetic model at 6.5 TeV - 34