1. Optimization of dynamic aperture for the ESRF upgrade Andrea Franchi on behalf of the ASD Beam Dynamics Group Workshop on Accelerator R&D for Ultimate Storage Rings October 30-November 1, 2012 Huairou, Beijing

2. Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade 2 Outlines The Hybrid Multi-Bend (HMB) lattice Nonlinear optics: existing ESR SR Vs HMB lattice Optimizing dynamic aperture

3. 3 Outlines The Hybrid Multi-Bend (HMB) lattice Nonlinear optics: existing ESR SR Vs HMB lattice Optimizing dynamic aperture Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

4. 4 The Hybrid Multi-Bend (HMB) lattice Double-Bend Achromat (DBA) Many 3 rd gen. SR sources Local dispersion bump (originally closed) for chromaticity correction Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

5. 5 The Hybrid Multi-Bend (HMB) lattice Multi-Bend Achromat (MBA) MAX IV and other USRs No dispersion bump, its value is a trade-off between emittance and sextupoles (DA) Double-Bend Achromat (DBA) Many 3 rd gen. SR sources Local dispersion bump (originally closed) for chromaticity correction Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

6. 6 The Hybrid Multi-Bend (HMB) lattice multi-bend for lower emittance Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

7. 7 The Hybrid Multi-Bend (HMB) lattice multi-bend for lower emittance dispersion bump for efficient chromaticity correction => “weak” sextupoles (<0.6kT/m) Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

8. 8 The Hybrid Multi-Bend (HMB) lattice multi-bend for lower emittance dispersion bump for efficient chromaticity correction => “weak” sextupoles (<0.6kT/m) no need of “large” dispersion on the three inner dipoles => small Hx and Ex Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

9. 9 The Hybrid Multi-Bend (HMB) lattice ESRF existing (DBA) cell Ex = 4 nm  rad tunes (36.44,13.39) nat. chromaticity (-130, -58) Proposed HMB cell Ex = 160 pm  rad tunes (75.60, 27.60) nat. chromaticity (-97, -79) Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

10. 10 Outlines The Hybrid Multi-Bend (HMB) lattice Nonlinear optics: existing ESR SR Vs HMB lattice Optimizing dynamic aperture Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

11. 11 Nonlinear optics: the HMB lattice Δφ x =(2n+1)π to minimize at the cell ends the Resonance Driving Terms from x 3 ( f 3000 and f 1200 ≈ 0) => elliptical horizontal phase space Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade phase advance between pairs of (chrom.) sextupoles: HMB lattice V107 Δφ x =(2n+1)π Δφ y =nπ

12. 12 Nonlinear optics: the HMB lattice Δφ x =(2n+1)π to minimize at the cell ends the Resonance Driving Terms from x 3 ( f 3000 and f 1200 ≈ 0) => elliptical horizontal phase space + Δφ y =nπ minimize those from xy 2 ( f 1 020 and f 0120 ≈ 0) rendering vertical phase space elliptical too [ f 0111 ≈ 0 from Δφ x =π] … Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade phase advance between pairs of (chrom.) sextupoles: HMB lattice V107 Δφ x =(2n+1)π Δφ y =nπ

13. 13 Nonlinear optics: the HMB lattice Δφ x =(2n+1)π to minimize at the cell ends the Resonance Driving Terms from x 3 ( f 3000 and f 1200 ≈ 0) => elliptical horizontal phase space + Δφ y =nπ minimize those from xy 2 ( f 1 020 and f 0120 ≈ 0) rendering vertical phase space elliptical too [ f 0111 ≈ 0 from Δφ x =π] … … provided that second-order (octupolar-like) RDTs are kept low Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade phase advance between pairs of (chrom.) sextupoles: HMB lattice V107 no harmonic sextupoles Δφ x =(2n+1)π Δφ y =nπ

14. no harmonic sextupoles 14 Nonlinear optics: the HMB lattice Δφ x =(2n+1)π to minimize at the cell ends the Resonance Driving Terms from x 3 ( f 3000 and f 1200 ≈ 0) => elliptical horizontal phase space Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade Δφ x >3πΔφ x =3πΔφ x <3π HMB lattice V107 phase advance between pairs of (chrom.) sextupoles: Δφ x =(2n+1)π Δφ y =nπ

15. 15 Nonlinear optics: the HMB lattice This constraint does not help minimize amplitude-dependent detuning generated by second-order cross-products of sextupolar terms within the cell [  cos(Δφ x ), sin(3Δφ y ), … ] and across other cells. Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V107 phase advance between pairs of (chrom.) sextupoles: Δφ x =(2n+1)π Δφ y =nπ no harmonic sextupoles

16. 16 Nonlinear optics: existing ESR SR Vs HMB lattice ESR (DBA) Storage Ring 3 chromatic and 4 harmonic sextupoles dQx/dJx = -15x10 3 d 2 Qx/dJx 2 = 0.3x10 9 dQy/dJx = -11x10 3 d 2 Qy/dJx 2 = 0.2x10 9 dQy/dJy = 12x10 3 d 2 Qy/dJy 2 = 0.2x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade  x=37m @ injection ! septum blade @ -5mm (20σ) with inj bump 3σ contour inj. beam

17. 17 Nonlinear optics: existing ESR SR Vs HMB lattice HMB lattice (V107) 2+4 chromatic sextupoles, no harmonic sextupoles dQx/dJx = 100x10 3 d 2 Qx/dJx 2 = 5.9x10 9 dQy/dJx = -80x10 3 d 2 Qy/dJx 2 =29.3x10 9 dQy/dJy = 40x10 3 d 2 Qy/dJy 2 = 0.9x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade  x=14.4m @ injection septum blade @ -2mm (40σ) with inj bump 3σ contour inj. beam

18. 18 Nonlinear optics: existing ESR SR Vs HMB lattice HMB lattice (V107) 2+4 chromatic sextupoles, no harmonic sextupoles dQx/dJx = 100x10 3 d 2 Qx/dJx 2 = 5.9x10 9 dQy/dJx = -80x10 3 d 2 Qy/dJx 2 =29.3x10 9 dQy/dJy = 40x10 3 d 2 Qy/dJy 2 = 0.9x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade  x=14.4m @ injection septum blade @ -20mm

19. 19 Nonlinear optics: existing ESR SR Vs HMB lattice HMB lattice (V107) 2+4 chromatic sextupoles, no harmonic sextupoles dQx/dJx = 100x10 3 d 2 Qx/dJx 2 = 5.9x10 9 dQy/dJx = -80x10 3 d 2 Qy/dJx 2 =29.3x10 9 dQy/dJy = 40x10 3 d 2 Qy/dJy 2 = 0.9x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade  x=14.4m @ injection septum blade @ -20mm How can we reduce amplitude-dependent detuning? HMB lattice V107

20. 20 Outlines The Hybrid Multi-Bend (HMB) lattice Nonlinear optics: existing ESR SR Vs HMB lattice Optimizing dynamic aperture Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

21. 21 Outlines The Hybrid Multi-Bend (HMB) lattice Nonlinear optics: existing ESR SR Vs HMB lattice Optimizing dynamic aperture very preliminary, focused on horizontal DA only, not yet optimized in vertical plane and energy deviation. Lattice errors: focusing errors from H & V (6μm RMS) displacement of sextupoles generating ~2% peak beta-beating & 5% coupling, no sext. field errors, orbit corrected. Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

22. 22 Optimizing dynamic aperture dQx/dJx = 100x10 3 d 2 Qx/dJx 2 = 5.9x10 9 dQy/dJx = -80x10 3 d 2 Qy/dJx 2 =29.3x10 9 dQy/dJy = 40x10 3 d 2 Qy/dJy 2 = 0.9x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V107 Δφ x =3π HMB lattice (V107)

23. 23 Optimizing dynamic aperture dQx/dJx = -2x10 3 d 2 Qx/dJx 2 = 2.7x10 9 dQy/dJx = -82x10 3 d 2 Qy/dJx 2 =30.6x10 9 dQy/dJy = -1x10 3 d 2 Qy/dJy 2 = 0.6x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V139 HMB lattice (V139) shorter bends for equipment lower hor. and ver. detuning cross-term detuning still too large Δφ x >3π

24. 24 Optimizing dynamic aperture dQx/dJx = -11x10 3 d 2 Qx/dJx 2 = 0.6x10 9 dQy/dJx = -15x10 3 d 2 Qy/dJx 2 =19.3x10 9 dQy/dJy = -9x10 3 d 2 Qy/dJy 2 = 4.1x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V140-T3 HMB lattice (V140-T3) swapped centre quad sext. added thin octu- and dodeca-pole lower cross-term detuning Δφ x >3π

25. 25 Optimizing dynamic aperture dQx/dJx = -5x10 3 d 2 Qx/dJx 2 = 0.6x10 9 dQy/dJx = -3x10 3 d 2 Qy/dJx 2 =17.7x10 9 dQy/dJy = -6x10 3 d 2 Qy/dJy 2 = 3.8x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V140-1 HMB lattice (V140-1) octupole component in QF0 added dodecapole removed lower cross-term detuning Δφ x =3π

26. 26 Optimizing dynamic aperture dQx/dJx = -4x10 3 d 2 Qx/dJx 2 = 0.5x10 9 dQy/dJx = -3x10 3 d 2 Qy/dJx 2 = 0.1x10 9 dQy/dJy = -5x10 3 d 2 Qy/dJy 2 = 1.0x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V172-F HMB lattice (V172-F) octupole component in QD0 added long. gradient in dipoles lower cross-term detuning Δφ x <3π

27. 27 Optimizing dynamic aperture dQx/dJx = -4x10 3 d 2 Qx/dJx 2 = 0.5x10 9 dQy/dJx = -3x10 3 d 2 Qy/dJx 2 = 0.1x10 9 dQy/dJy = -5x10 3 d 2 Qy/dJy 2 = 1.0x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V172-F Δφ x < π HMB lattice (V172-F) octupole component in QD0 added long. gradient in dipoles lower cross-term detuning

28. 28 Optimizing dynamic aperture dQx/dJx = -4x10 3 d 2 Qx/dJx 2 = 0.5x10 9 dQy/dJx = -3x10 3 d 2 Qy/dJx 2 = 0.1x10 9 dQy/dJy = -5x10 3 d 2 Qy/dJy 2 = 1.0x10 9 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade HMB lattice V172-F Δφ x < π HMB lattice (V172-F) octupole component in QD0 added long. gradient in dipoles lower cross-term detuning good for Touschek lifetime good for injection efficiency

29. 29 Conclusion lattice design in advanced status of development (standard) magnet requirements within reach of existing technology (100 T/m for quads, 2kT/m 2 for sexts) dynamic properties already compatible with present injection system good energy acceptance lattice still evolving to further improve its performances and to match hardware constraints (diagnostic, vacuum, front ends, etc…) Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

30. 30 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade

31. 31 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade # NAMELANGLER0B0G1G2G3LBETXBETYDX #[m][mrad][m][T][T/m][T/m^2] [m] [mm] "QFMA"0.2593.714.167.21 4.3 "QDMA"0.20-87.772.3311.39 2.9 "BPI1E"0.359.8935.380.571.5212.67 3.4 "BPI1D"0.356.8950.760.401.1613.73 7.2 "BPI1C"0.355.4064.860.311.0314.85 13.1 "BPI1B"0.354.2083.400.241.1516.03 20.6 "BPI1A"0.353.6097.300.211.5017.27 29.6 "QDID"0.20-38.352.1317.04 39.1 "SD1A"0.30-18083.8413.44 55.4 "SF1A"0.18 1885 10.056.87 92.9 "QF0"0.1555.2911.595.86 100.0 "OCF0"0.00-1321511.595.86 100.0 "QF0"0.1555.2910.856.16 97.0 "SF1A"0.18 1885 8.437.50 85.7 "OCF"0.10-116464.3010.92 61.5 "SD1B"0.30 -1808 2.1713.99 43.1 "QD0"0.20-57.821.3914.52 33.0 "BPI1A"0.353.6097.300.211.1110.58 24.5 "BPI1B"0.354.2083.400.241.167.98 19.4 "BPI1C"0.355.4064.860.311.425.76 15.9 "BPI1D"0.356.8950.760.401.913.94 14.7 "BPI1E"0.359.8935.380.572.612.52 16.3 "QF1"0.32102.682.242.33 15.8 "BPI2E1"0.3512.7427.470.73-44.040.364.68 7.4 "BPI2E2"0.3512.7427.470.73-44.040.743.40 10.9 "QF2"0.4596.522.061.75 16.7 "BPI2E1"0.3512.7427.470.73-44.040.684.02 7.5 HMB lattice

32. 32 Andrea Franchi Optimization of dynamic aperture for the ESRF upgrade # NAMELANGLER0B0G1G2BETXBETYDX #[m][mrad][m][T][T/m][T/m^2][m] [mm] SBEND2.4598.0024.960.861.7732.1679.40 g1.qf20.947.8626.4816.34111.60 g1.qd30.53-12.147.8133.3459.54 g1.qd40.42-12.1010.8728.24219.10 g1.qf50.5214.7826.8115.17344.30 g1.qd60.52-16.4720.5341.279.45 g1.qf70.9213.7152.419.0830.79 g2.s040.40124.3138.008.16134.30 g2.s060.40-165.1518.8522.2093.90 g2.s130.40-88.0215.3923.32260.90 g2.s190.40443.3226.5315.61342.30 g2.s200.40-419.4314.3727.19250.60 g2.s220.40-95.8130.4730.1615.43 g2.s240.40132.3344.478.1530.80 ESRF SR

33. Beam response after horizontal kick …

34. … and its spectrum (FFT) measured

35. … and its spectrum (FFT) simulated

36. … and its spectrum (FFT) measured

37. its normal sextupolar RDTs measured

38. … and its spectrum (FFT) measured

39. its skew sextupolar RDTs measured