1. BROOKHAVEN SCIENCE ASSOCIATES Abstract Magnetic Specifications and Tolerances Weiming Guo, NSLS-II Project In this presentation I briefly introduced the physics considerations that lead to the current cell configuration, the number, type and separation of the magnets in the lattice, and the specifications on the magnet tuning range and field quality. The statistical results were then shown for the received magnets. By examining the strength uniformness, magnet saturation, and the harmonic values, we conclude that the magnets are of good quality and meet our requirements. A comparison with SOLEIL magnets was made and we found the lower order harmonic terms of NSLS-II magnets are much smaller, which will improve the accelerator performance. *Work performed under auspices of the United States Department of Energy, under contract DE-AC02-98CH10886 0

2. BROOKHAVEN SCIENCE ASSOCIATES 1 Requirements and Specifications Weiming Guo NSLS-II BNL, April, 2012

3. BROOKHAVEN SCIENCE ASSOCIATES 2 Outline Physics considerations leading to the magnet specifications Overview of the quality of the received NSLS-II magnets Comparison with SOLEIL magnets Retrospect and remarks

4. BROOKHAVEN SCIENCE ASSOCIATES 3 Specifications Concerning Magnets 1. Type and number of magnets, aperture, magnetic separation 2. Quadrupoles and sextupoles: strength, tuning range, stability, and field quality 3. Dipole: strength, homogeneity, and stability 4. Current, voltage

5. BROOKHAVEN SCIENCE ASSOCIATES 4 Deterministic or Nondeterministic  Some basic parameters determined early by administrative decision: Magnet aperture, number and strength of the dipoles  Parameters determined through optimization ( Deterministic ) Number and type of multipole magnets, polarity, and power connection pattern Magnet strength and tuning range Sextupole uniformity  Parameters determined through interaction with engineering groups ( interactive and iterative ): Power supply tolerances: Physics requirements ←→ mitigation approaches ←→ commercial availability Field quality (harmonics): general guidelines from physics ←→ Initiated from magnet design and prototyping ←→ approved by beam dynamics ←→ adjustments based on fabrication feedback Alignment tolerance ←→ field quality, implementation approaches Magnet measurement quality must be sufficient to check physics requirements on field, however limited by cost and schedule

6. BROOKHAVEN SCIENCE ASSOCIATES 5 Cell Configuration and Evolution 10 quadrupole magnets per cell, independent power supplies (initially 4 quads in the matching section) 9 sextupole families, 3 chromatic and 6 geometric. (initially 12 sextupole families) 2 slow correctors and 2 BPMs per girder to allow girder by girder orbit correction 2 additional high stability BPMs in each straight section to improve stability 3 fast correctors per cell for fast orbit correction most of the magnet to magnet separation is standardized to 17.5 cm. (straights increased from 5/8 to 6.6/9.3) 3-pole wiggler was added to the lattice to provide dipole radiation F F F C C C C C C F 3-pole wiggler

7. BROOKHAVEN SCIENCE ASSOCIATES 6 Magnet Tuning Range Magnet Length Min.Max. Design QH1 0.275 0.361.62 2 QH2 0.448 1.321.79 1.96 QH3 0.275 1.281.76 2 QL1 0.275 0.682.00 2 QL2 0.448 1.621.83 1.96 QL3 0.275 1.11.60 2 QM1 0.25 0.731.09 1.1 QM2 0.283 1.21.3 1.34 Quadrupole tuning range (K 1 1/m 2 ) Methodology to the Quadrupole Magnet Tuning Range 1)Searched an assemble of solutions with working point evenly distributed in the tune window (ν x ±1, ν y ±1); 2)Lattices with smaller beta functions in the straights; and 3)low momentum compaction lattice The table is the statistical results of all the above lattice solutions. Sextupole strength limit: (400 T/m 2 ) 1)It is 30% more than the typical settings for chromaticity correction for chromatic sextupoles 2)Geometric sextupoles have the same limits as the chromatic sextupoles 3)An assemble of lattice solution have been optimized, and dynamic aperture is not limited by the maximum strength

8. BROOKHAVEN SCIENCE ASSOCIATES 7 Higher Order Multipole Specification Quad Multipole Specification (r=25mm) Sext Multipole Specification (r=25mm) Amplitude-tune dependence At δ=-2.5% Dynamic aperture at δ=-2.5% when the multipoles are multiplied by the indicated factors The higher order multipoles generates nonlinear detuning, which limits the dynamic aperture. The off-momentum particles are more susceptible due to the large orbit excursion, which is the reason for large aperture at the peak dispersion. The dynamic aperture is acceptable when the multipoles are multiplied by a factor of 2.

9. BROOKHAVEN SCIENCE ASSOCIATES 8 Sextupole Linearity and Uniformity Sextupole strength uniformity Required 0.5%rms, measured: <0.3%rms 9816 + Sextupole transfer function: linear region

10. BROOKHAVEN SCIENCE ASSOCIATES 9 Quadrupole Linearity and Uniformity Quadrupole saturation: <5% Magnet typeStandard deviation (%) 9801/20.11 9804/70.13 9809,98120.16 98150.07 Quadrupole strength uniformity At half of the full excitation current

11. BROOKHAVEN SCIENCE ASSOCIATES 10 Quadrupole 1 st Systematic Harmonic B6 started to grow when magnet saturates; However the growth is small and the field quality is in-spec.

12. BROOKHAVEN SCIENCE ASSOCIATES 11 Typical Lower Order Terms Lower order terms have apparent current dependence Small current: pole move? Large current: saturation.

13. BROOKHAVEN SCIENCE ASSOCIATES 12 Typical Higher Order Terms Higher order terms: small, in-spec, and current-independent.

14. BROOKHAVEN SCIENCE ASSOCIATES 13 Statistics of Sextupoles

15. BROOKHAVEN SCIENCE ASSOCIATES 14 Statistics of Quadrupoles

16. BROOKHAVEN SCIENCE ASSOCIATES 15 Summary on Magnet Field Quality 1. Uniformity: <0.3% rms for quadrupole and sextupoles, meets requirement (0.5%) 2. Saturation: sextupole linear, quadrupole <5% saturation, field quality meets spec. 3. Lower order harmonics have a small current dependence, and higher order terms are current-independent. 4. Due to assembly errors, a fraction of sextupoles have lower order terms slightly exceeding the specifications, for example, octupole and decapole terms. 5. The higher order terms are mostly small and in-spec. Conclusion: the magnet field quality is very good.

17. BROOKHAVEN SCIENCE ASSOCIATES 16 Comparison with SOLEIL BNLSOLEIL Aperture (mm) 66, 9066 Magnetic length (m) 0.25,0.275, 0.28,0.45 0.32, 0.46 Maximum gradient (T/m) 14/21/2119.7, 23 Harmonics Radius, current 25mm,100A25mm,200A B32 ( 66mm) 3 (90mm) -1.3±1.6, 2.4±1.3 B42222 -2.4±2.6, -6±1.2 B63 0.5 1.1±0.2, 0.3±0.2 B103 0.5 0.16±0.02, 0.44±0.02 B143 0.1 0.1±0.01, 0.1±0.01 BNLSOLEIL Aperture (mm)6873 Magnetic length (m) 0.20.16 Max. G. (T/m 2 )400320 Harmonics Radius, Current 25mm,80A25mm,Max. I B130-16±29 B513.3±2.9 B711.2±0.8 B92-1.1±0.7 B151-0.5±0.04 B21-0.25±0.006 Quadrupole (Prd Danfysik, Mesrd SOLEIL) Sextupole (Prd and Mesrd SIGMAPHI)

18. BROOKHAVEN SCIENCE ASSOCIATES 17 Retrospect and Remarks Which terms are important? Answer: lower order terms, a4, b4, a5, b5, a6, b6. Smaller values will definitely improve the accelerator performance. What is the required approach? 1) 1~2x10 -4 leads to ~10 μm pole precision, which requires EDM process and 2) Individual shimming to eliminate the assembly errors. Should the quadrupole systematic terms be tighter? Answer: Yes, even though the current specs satisfy our requirement. Should we have specified the whole tuning range rather than a single point? Answer: yes. Meeting the spec at 100% strength is still questionable. Could the magnet types be reduced? Answer: 9801 quad could be replaced by 9809 quad at the price of 1.5m space totally. Should have set tolerances for all specified quantities. Skew quadrupole magnetic length and field quality were not specified in the beginning Reproducibility requirement was not specified on the field quality