Considerations for Nonlinear Beam Dynamics in NSLS-II lattice design Weiming Guo 05/26/08

1. Considerations for Nonlinear Beam Dynamics in NSLS-II lattice designWeiming Guo 05/26/08 Acknowledgement: J. Bengtsson S. Kramer S. Krinsky B. Nash

2. Outline 1. Introduction to the linear lattice 2. Nonlinear requirements: injection and Toschek scattering 3. Minimum needed sextupole families 4. Required physical aperture 5. Effects of the multipole field errors Subjects will not be covered: On-going optimization of the nonlinear lattice; Misalignment errors; choice of the working point; and effects of the damping wigglers and IDs Method: Simulation using Elegant

3. Main Design Parameters Beam Energy 3 GeV Circumference 792 m Circulating current 500 mA Total number of buckets 1320 Lifetime 3 hours Electron beam stability 10% beam size Top-off injection current stability <1% ID straights for undulators >21 Straight length 9.3/6.6 m

4. Magnets and lattice Natural emittance with 0, 1, 2, 3, 5 and 8 DWs added Courtesy of S. Kramer Quad. Family: 8, 10 magnets per cell Sext. Family: 9, 10 magnets per cell Chromaticity per cell: -3.4/-1.4

5. Linear Lattice design approaches • Large bending radius enhances the effect of the damping wigglers • Strict double-bend-acromat • Two reasons NSLS-II is sensitive to the residual dispersion: • 1nm emittance. For βx =2 m, ηx=4.5 cm, βxεx~(ηxσδ)2 • Damping wiggler has quantumn excitation effect

6. Nonlinear Design Goal Bumped stored beam Injected beam (σx=0.39 mm, σ´x=77 μrad) Septum (σx=0.15 mm) 1+1.2 mm 3+1 mm 3.5 mm δ Minimum required dynamic aperture Courtesy of I. Pinayev 2. Sufficient dynamic aperture to keep Touschek scattered particles with δ= ±2.5% Off momentum particle 1. Sufficient dynamic aperture (>11mm) for injection On momentum particle

7. Source of the nonlinearity Frist order chromatic terms (5) Frist order geometric terms (5) Amplitude tune dependence Second order chromaticity

8. Number of chromatic sextupole families Conclusion: Because the betatron phase advance in the dispersive region is small (x: ~ 10o, y~ 20o), the five chromatic terms have only two degree of freedom.  7~8 sextupole families

9. Stay-clear aperture 38x12.5 mm

10. Dynamic Aperture with Multipole Error The Feb.-08 multipole components at 25 mm DA collapse at negative momentum

11. Effects of Multipoles Conclusion: introducing systematic multipole errors doesn’t add resonance lines.

12. Amplitude Tune Dependence Conclusion: Multipole terms changes the tunes at large amplitude dramatically, and makes the stable area smaller.

13. Why Negative Momentum?

14. Minimizing 2nd Order Dispersion

15. Tune Scan Delta = -3.0% Delta = -3.0% Area of DA Delta = 0.0% Delta = 3.0% Conclusion: moving the tune doesn’t solve this problem.

16. Squeeze the Tune Excursion The re-tuned lattice Tunes moved, sextupoles reoptimized CDR lattice with multipole errors Red: Jan4th lattice Black: re-tuned lattice

17. New Specifications Multipole components of high precision magnets (25 mm)

18. Summary • Nonlinear design goal to provide sufficient dynamic aperture for injection and Touschek scattered particles up to δ=2.5% • There are 8 sextupole families in the lattice, one more might be added. • The physical aperture is conservatively retained. • The reduction of the dynamic aperture due to multipole errors is show to be the momentum related tune shift with amplitude. • Identified the multipole errors in the high dispersion region, and required increasing the pole radius. • Further optimization of the dynamic aperture is proceeding.