1. 1 BROOKHAVEN SCIENCE ASSOCIATES Impact of Errors and Damping Wigglers on the Lattice W. Guo 02/26/2009 NSLS-II ASAC Meeting Acknowledgement: M. Borland J. Bengtsson S. Kramer S. Krinsky Y. Li B. Nash D. Hseuh O. Singh Mechanical Group

2. 2 BROOKHAVEN SCIENCE ASSOCIATES Outline Tunability of the linear lattice and magnet strength New configuration of the correctors Nonlinear lattice: Introduction of a third chromatic sextupole knob Integration of the damping wigglers Tolerances on magnetic field and misalignment errors Characterization of nonlinear dynamics

3. 3 BROOKHAVEN SCIENCE ASSOCIATES Lattice and Magnet Type Standard Quadrupole (66 mm): Type A: Single coil, short,11 T/m Type B: single coil, wide, 11 T/m Type C: Double Coil, long, 22 T/m Type D: Doulbe Coil, short, 22 T/m Type E: Double Coil, Wide, 22 T/m Large Aperture: 90 mm, 15 T/m Normal Sextupole : Type A: Symmetric, 68mm Type B: Wide, 68 mm Large Aperture: 76 mm All sextupoles have maximum strength of 400 T/m2

4. 4 BROOKHAVEN SCIENCE ASSOCIATES Quadrupole Tuning Range Variation of quad strength (T/m) Quad Len. min max ave Nominal -------------------------------------------- QH1 0.25 5.229 17.802 -6.996 -6.887 QH2 0.4 15.651 20.059 16.55 16.562 QH3 0.25 14.077 19.106 -18.486 -18.75 QL1 0.25 15.336 20.981 -18.123 -17.841 QL2 0.4 19.736 20.379 20.126 20.13 QL3 0.25 12.251 16.504 -15.282 -15.586 QM1 0.25 7.787 10.849 -8.497 -8.251 QM2 0.25 13.737 14.67 13.961 13.885 Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*J Index = I*10 + J ◊ =Stable solution found by the Elegant optimizer Vary the tunes by ±0.5 units

5. 5 BROOKHAVEN SCIENCE ASSOCIATES Variation of Beta Functions in the Straights Lower β x in long straight Lower β x in short straight β x =1.1 m β y =1.9 m

6. 6 BROOKHAVEN SCIENCE ASSOCIATES Separated Function Configuration of Correctors  A & B – Slow corrector; FS DC strength = 800 microrad  A -100 mm Aperture (qty=8);  B – 156 mm Aperture (qty=4); mounted over bellows  D – Air core fast correctors; qty=6  Mounted Over SS chamber  FS DC Strength = 10-15 microrad  Combined DC/AC function EL1-A EL2-B EL3-A EL4-B EL1-D X X EL2-D EL3-D EL5-B EL6-B It has been shown that 3 fast correctors per cell are adequate for fast orbit correction. The closed orbit can be corrected to satisfactory level with the new configuration of the slow correctors.

7. 7 BROOKHAVEN SCIENCE ASSOCIATES Higher Stability for Quadrupole Power Suppliers Beta beat x (%)Beta beat y (%)Sigma nuxSigma nuy 100 ppm0.70.31.1×10 -3 6×10 -4 50 ppm0.350.167×10 -4 4×10 -4 X c.o. Long St.X c.o..Dispersion L.S.Dispersion S.S. 100 ppm0.15 µm0.04 µm1 mm0.35 mm 50 ppm0.06 µm0.02 µm0.5 mm0.18 mm Nota Bene: PS Engineer: 100 ppm is full range @ ~4  Accelerator Physicist:  k/k  ·10 -5 (RMS 2  cut-off) Formal Changed Processed, cost impact 160k$ Need actively cooled ADC Dynamic  beat due to Limited PS stability

8. 8 BROOKHAVEN SCIENCE ASSOCIATES Methods of Introducing a Third Chromatic Sextupole QM1 QM2 QM2 QM1 SM1 SM2 SM1 0.2 QM1 QM2 QM2 QM1 SM1 SM2 SM1 0.59 0.28 Present Layout: After the move: Magnet layout of a super-period (two cells) Beam direction

9. 9 BROOKHAVEN SCIENCE ASSOCIATES Integration of the Damping Wigglers Damping wigglers are modeled using kickmaps. Radiation integrals are derived from the simplified sinusoidal field model. The linear lattice is corrected using the three quadrupole families in the long straight. Symmetriy in x ( α x =0), symmetry in y ( α y =0) and phase advance in x (μ x ) are restored. Phase advance in y is not restored due to lack of knobs but resulting deviation is tolerable. Quadrupole strength changes by ~ 1%, and linear chromaticity also changes slightly. The geometric sextupoles are powered independently in the DW supercell. One-third of the ring is used for nonlinear optimization.

10. 10 BROOKHAVEN SCIENCE ASSOCIATES A Test Solution Beta function Long St.Short St.DW LS Betax20.41.820.3 Betay3.31.12.5 Chromatic sextupoles have the same strength in all 5 super-periods: 3 knobs Geometric sextupoles are different in the DW super-period: 14 knobs

11. 11 BROOKHAVEN SCIENCE ASSOCIATES Tune Excursion due to Momentum Variation

12. 12 BROOKHAVEN SCIENCE ASSOCIATES Amplitude Tune Dependence and Frequency Map (Without Errors) 3 DWs and 3 IVUs added, but with no errors.

13. 13 BROOKHAVEN SCIENCE ASSOCIATES Higher Order Multipole Specification systematicNormal [x 10 -4 ] @ 25 mm High precision [x10 -4 ] @ 25 mm B611.0 B104.50.5 B144.00.1 non-systematic B11.0 B33.0 B41.0 B50.1 B7-B90.1 B11-B13,B15-B200.1 Skew terms A1,A311 A4 and above0.1 Quadrupole Multipole Specification systematicNormal [x 10 -4 ] @ 25 mm High precision [x10 -4 ] @ 25 mm B910.5 B1510.5 B2140.5 non-systematic B1102 B212 B410.5 B5-B70.5 B80.1 B10-b140.2 B16-b200.10.2 Skew terms A15.0 A41.01 A5 and above0.1 Sextupole multipole specification

14. 14 BROOKHAVEN SCIENCE ASSOCIATES Misalignment Error and Closed Orbit Correction Misalignment Specification: Girder to girder : 100 um Magnet on girder: 30 um Girder roll: 0.5 mr Magnet roll: 0.2 mr Move along the beam direction: 0.5 mm Simulation Method and Correction: Each Girder is modeled by two independent ends with offsets and roll errors; Each Magnet has its own offsets and roll; The total error is the summation. The closed orbit is corrected using a Beam-based Alignment like algorithm. Each cell has 6 correctors and 6 BPMs. Beam is centered at the BPMs. σ quad = 19 μm σ sext = 17 μm σ quad = 12 μm σ sext = 14 μm

15. 15 BROOKHAVEN SCIENCE ASSOCIATES Beta Beat Correction All quadrupoles are powered independently. Beta functions are measured and corrected at the BPMs. The residual beta beat is 0.4% rms in both planes.

16. 16 BROOKHAVEN SCIENCE ASSOCIATES Frequency Map in (x,p) (With Errors, 3 DWs) Misalignment errors and higher order multipole Errors are included. Closed orbit and beta beat are corrected. 3 DWs and 3 IVUs are added. Kick maps limit the vertical aperture.

17. 17 BROOKHAVEN SCIENCE ASSOCIATES Frequency Map in (x,y) (On-momentum, With Errors, 3 DWs) On Momentum: x > 11 mm for injectin δ Dynamic aperture required to keep particles with momentum offset

18. 18 BROOKHAVEN SCIENCE ASSOCIATES Frequency Map in (x,y) (Off-momentum,With Errors, 3 DWs) Delta = -2.5% Delta = 2.5%

19. 19 BROOKHAVEN SCIENCE ASSOCIATES Momentum Aperture The horizontal physical aperture is limited by the photon absorbers. The photon absorbers are placed such that particles with δ=±3% are not blocked. Vacumm chamber absorber s Radiation damping and RF cavity are added. Vrf = 3.2 MV, rf bucket height is 3.1%. Touschek lifetime is 5 hours.

20. 20 BROOKHAVEN SCIENCE ASSOCIATES Conclusion The magnets have adequate strength for needed tune and beta function variations. To provide a third independent chromatic sextupole knob, we propose to move the Downstream SM1 sextupole toward higher dispersion, maintaining 15-fold translation invariance. This can be done with minimum impact on the mechanical design. A lattice configuration with integrated damping wigglers is presented. The test solution exhibits satisfactory behavior in the presence of magnet field error and misalignment error. It meets the requirement on the dynamic aperture for injection and provides >3 hours’ Touschek lifetime.

21. 21 BROOKHAVEN SCIENCE ASSOCIATES Backup slides

22. 22 BROOKHAVEN SCIENCE ASSOCIATES Sextupole Tuning Range Variation of K2 (1/m 3 ) Sext min max ave ---------------------------------------(%)-- SH1 -2.22 15.04 4.05 212.99 SH2 12.93 24.36 18.75 30.49 SH3 -33.93 -23.51 -26.79 -19.45 SH4 -1.01 6.28 3.47 105.11 SL1 -17.64 2.74 -14.71 -69.26 SL2 33.62 40.00 39.12 8.16 SL3 -29.23 -24.19 -26.95 -9.34 SM1 -19.43 -14.67 -17.11 -13.90 SM2 17.64 21.85 19.94 10.55 Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*J Index = I*10 + J K2 from nonlinear optimization SL2,SM1,SM2: K2<40 The rest: K2<30

23. 23 BROOKHAVEN SCIENCE ASSOCIATES Increasing the Sensitivity of 2 nd Order Chromaticity The location is optimized for both 2 nd order and 3 rd order chromaticity An extra knob for higher order chromaticity. y x Long Straight SM1