1. MQM and MQY harmonics in Fidel Walter Venturini Delsolaro FIDEL meeting, 28 April 2009

2. Outline Models for MQM and MQY harmonics Warm-Cold correlations (with and without µ-corrections) Generic models for b 6 and b 10 REFPARM files

3. Measurement data and REFPARM All magnets were measured at warm during series production with rotating coils (TF + first 10 multipoles) 50 MQM apertures and 26 MQY apertures measured at cold in Block 4 Agreement for REFPARM: – for each magnet we give the value of the first 10 multipoles extrapolated at cold from the w/c correlations, i.e. adding the average C-W shift –plus a model of b 6 and of b 10 (first two allowed harmonics).

4. Summary MQM harmonics at warm

5. Warm – cold correlations: MQM b3 b3 cold units b3 warm units

6. Warm – cold correlations: MQM a3 a3 cold units a3 warm units

7. Warm – cold correlations: MQM b4 b4 cold units b4 warm units

8. Warm – cold correlations: MQM a4 a4 cold units a4 warm units

9. Warm – cold correlations: MQM b6 b6 cold units b6 warm units

10. Warm – cold correlations: MQM b10 b10 cold units b10 warm units

11. Allowed harmonics at cold: b 6

12. Not allowed harmonics at cold, example: b 3

13. MQM, b 6 hysteresis loops

14. MQM, b 10 hysteresis loops

15. b 6 model for MQM Active components: GEOMETRIC DC magnetization RES magnetization I GEOM = 2000 A µ = -10 p = 0.55 q = 1 ρ = 0.2 τ = 10.5

16. b 10 model for MQM Active components: GEOMETRIC DC magnetization RES magnetization I GEOM = 2000 A µ = 0.5 p = 0.6 q = 1.5 ρ = 0.048 τ = 4.18

17. Summary MQY harmonics at warm

18. Warm – cold correlations: MQY b3 b3 cold units b3 warm units

19. Warm – cold correlations: MQY a3 a3 cold units a3 warm units

20. Warm – cold correlations: MQY b4 b4 cold units b4 warm units

21. Warm – cold correlations: MQY a4 a4 cold units a4 warm units

22. Warm – cold correlations: MQY b6 b6 cold units b6 warm units

23. Warm – cold correlations: MQY b6, after correction for permeability by P. Hagen b6 cold units b6 warm units

24. Warm – cold correlations: MQY b10 b10 cold units b10 warm units

25. Warm – cold correlations: MQY b10, after correction for permeability by P. Hagen b10 cold units b10 warm units

26. W-C offsets for MQM and MQY MQM MQY

27. Influence of pre-cycles on b 6

28. b 6 model for MQY Active components: GEOMETRIC DC magnetization RES magnetization I GEOM = 1500 A µ = -4.5 p = 0.5 q = 1 ρ = 0.2 τ = 6.3

29. b 10 model for MQY Active components: GEOMETRIC DC magnetization RES magnetization I GEOM = 1500 A µ = 0.14 p = 0.4 q = 1.5 ρ = 0.0025 τ = 7

30. REFPAR files

31. Conclusions MQM and MQY static models are defined Cold Warm correlations are improved by corrections for permeability REFPARM files are filled with final GEOM values for ALL magnets b6 and b10 models are available as generic, OK for the current range above I _low For I< I _low the strategy (as for the TF) is to modify the RES MAG component. However this is delicate, very sensitive to the exponent in the power law Therefore, final values of the RES MAG parameters will be given also taking into account of the results of the complementary measurements (ongoing for MQY).