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Impact of Errors and Damping Wigglers on the Lattice W. Guo 02/26/2009 NSLS-II ASAC Meeting

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. Outline.

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Impact of Errors and Damping Wigglers on the Lattice W. Guo 02/26/2009 NSLS-II ASAC Meeting

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  1. 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. 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. 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. Quadrupole Tuning Range ◊=Stable solution found by the Elegant optimizer 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 Vary the tunes by ±0.5 units Variation of quad strength (T/m) Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*J Index = I*10 + J

  5. Variation of Beta Functions in the Straights Lower βx in short straight βx =1.1 m βy =1.9 m Lower βx in long straight

  6. 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 EL2-B EL1-A EL3-A EL4-B EL5-B EL6-B X EL1-D EL2-D X EL3-D • 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. Separated Function Configuration of Correctors

  7. Higher Stability for Quadrupole Power Suppliers Dynamic b beat due to Limited PS stability Formal Changed Processed, cost impact 160k$ Need actively cooled ADC (RMS 2s cut-off) Nota Bene: PS Engineer: 100 ppm is full range @ ~4s Accelerator Physicist: Dk/k @ 2.5·10-5

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

  9. 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 ( αx =0), symmetry in y ( αy =0) and phase advance in x (μx) 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. A Test Solution • Chromatic sextupoles have the same strength in all 5 super-periods: 3 knobs • Geometric sextupoles are different in the DW super-period: 14 knobs • Beta function

  11. Tune Excursion due to Momentum Variation

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

  13. Higher Order Multipole Specification • Quadrupole Multipole Specification • Sextupole multipole specification

  14. 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 • σquad = 19 μm • σsext = 17 μm 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. • σquad = 12 μm • σsext = 14 μm

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

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

  19. 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 absorbers • Radiation damping and RF cavity are added. • Vrf = 3.2 MV, rf bucket height is 3.1%. • Touschek lifetime is 5 hours.

  20. 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. Backup slides

  22. Sextupole Tuning Range K2 from nonlinear optimization 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 Variation of K2 (1/m3) Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*J Index = I*10 + J SL2,SM1,SM2: K2<40 The rest: K2<30

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

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