1. 1 BROOKHAVEN SCIENCE ASSOCIATES 1 NSLS-II Lattice Design 1.TBA-24 Lattice Design - Advantages and shortcomings Low emittance -> high chromaticity -> small DA from nonlinear dynam. TBA dispersion region major limitation for reducing sextupole strength 2.DBA-32 Lattice Design - Damping Wigglers for Emittance Control Linear design with working point for non-linear DA optimization ID’s eXtra long (15m) and standard Length (6m) Dipole designed for damping wigglers DA and frequency map for bare lattice with 11 sextupole families DA with alignment tolerances 3.Summary of Lattice Parameters for DBA-32(8) S. Kramer, J. Bengtsson, S. Krinsky, T. Shaftan, D. Wang, L. Yun, I. Pinayev May 11,2006

2. 2 BROOKHAVEN SCIENCE ASSOCIATES 2 TBA-24 Lattice Design TBA-24 Lattice Design worked on for ~2 years Reached 1.5 nm emittance in 630m but DA small,  2.2nm 758m

3. 3 BROOKHAVEN SCIENCE ASSOCIATES 3 TBA-24 Lattice Features TBA-24 Lattice very flexible Lower emittance per period than DBA, 24 period ε x >0.38 nm Tune variable over big range for constant emittance α 1 variable without breaking symmetry of lattice, i.e. isochronous tune TBA-24 Lattice has small dispersion like DBA-48 Even with low chromaticity (~2.2/period) sextupoles strong DA low and challenging to expand without giving up on low emittance Minimum number of ID’s for users

4. 4 BROOKHAVEN SCIENCE ASSOCIATES 4 Reconsider DBA Lattice Option Higher emittance/period  more periods, more ID’s Use extra ID’s for emittance control with damping wigglers Wigglers have potentially less DA impact and counter users changes Optimize emittance damping with low field dipoles Dispersion region has freedom to increase dispersion, reducing chromatic sextupole strength Lesson from TBA-24 study of ID Quadruplet for phase and beta functions matching for undulators

5. 5 BROOKHAVEN SCIENCE ASSOCIATES 5 Basic DBA-32 Cell 6m ID Q x = 1.09 (1.13), ξ x = -3.38 (-3.6) ε x =1.66 (1.74)nm (ESRF@3GeV) Q y = 0.72 (0.35), ξ y = -1.25 (-1.01) C= 868 (845)m +35.2m in dipoles

6. 6 BROOKHAVEN SCIENCE ASSOCIATES 6 Two Types of ID with SP=8 ID’s = 15m +3* 6m C=929.8m ε x =1.66 nm ξ x,y = -3.26,-1.13/per

7. 7 BROOKHAVEN SCIENCE ASSOCIATES 7 Emittance vs Damping Wiggler B-field Energy Spread vs Wiggler Field Lw = 54m ρw = 1.4*Bρ/Bw Bdipole=0.33T   Bdipole=0.66T Bdipole=0.66T   Bdipole=0.33T Emittance change vs Wiggler Field

8. 8 BROOKHAVEN SCIENCE ASSOCIATES 8 Damping Wigglers in 4-15m ID Power radiated could exceed 125KW in one 15 ID, canting will reduce threat to front end components and yield 3 or more user beams

9. 9 BROOKHAVEN SCIENCE ASSOCIATES 9 DBA32 Working Point SP=8 Tune selected from DA scan and optimized for reduced Closed Orbit Amplification

10. 10 BROOKHAVEN SCIENCE ASSOCIATES 10 BROOKHAVEN SCIENCE ASSOCIATES Closed Orbit Amplification Factors Quadrupole alignment tolerance reduced by small Beta functions and tune

11. 11 BROOKHAVEN SCIENCE ASSOCIATES 11 BROOKHAVEN SCIENCE ASSOCIATES DBA32 Tune Scan for Cell At each tune value: driving terms were optimized to 3 rd order and DA area calculated yields peak near (4.29,2.615)

12. 12 BROOKHAVEN SCIENCE ASSOCIATES 12 BROOKHAVEN SCIENCE ASSOCIATES DA for Tune and 11 Sext. Families Frequency map shows diffusion at high order resonances and tune shifts

13. 13 BROOKHAVEN SCIENCE ASSOCIATES 13 BROOKHAVEN SCIENCE ASSOCIATES Alignment tolerances on Quads and Sextupoles <100μm corrected DA and momentum aperture for constant momentum error adequate for injection Asymmetry in momentum aperture from high order chromaticity and dispersion Tolerances on BPM to sextupole centering okay for < 30μm 7 BPM and 7 Corrector magnets / period

14. 14 BROOKHAVEN SCIENCE ASSOCIATES 14 BROOKHAVEN SCIENCE ASSOCIATES Adding Synchrotron Oscillations DA maintains reasonable values but momentum aperture more symmetric For random alignment tolerances < 100 μm with correction injection okay

15. 15 BROOKHAVEN SCIENCE ASSOCIATES 15 BROOKHAVEN SCIENCE ASSOCIATES NSLS-II Lattice Parameters Energy33.6GeV I o (Total Current)0.5000.241Amps Circumference929.805 meters f o (revolution freq) 0.3224 MHz Harmonic No.15602*3*4*5*13 α 1, α 2, α 1 / α 2 3.32*10 -4 -1.82*10 -4 -1.81 U o (Dipole)234.5486.2KeV U o (Dip.+1.8T)1231.21921.8KeV ε crit 1.963.287KeV ε x (bare) 1.662.39nm ε x (54m 1.8T) 0.470.687nm δ e bare (+1.8T) 0.046 (0.10)0.0558 (0.12)% L b (bare, 3%RF) 2.7 (9)3.11 (10.34)mm (psec)  x,  y,  e ( bare) 79.5,79.4, 39.746, 45.9, 23msec (Q x, Q x ) = (34.38, 20.68) (ξ x, ξ x ) = (-104.4, -36.2) β x, β y (6m ID) = 6.2, 1.42 β x, β y (15m ID) = 15.1, 16.2

16. 16 BROOKHAVEN SCIENCE ASSOCIATES 16 BROOKHAVEN SCIENCE ASSOCIATES NSLS-II Lattice Summary DBA-32 lattice has advantage of dispersion region optimized to reduce sextupole strengths and nonlinear driving terms Extra ID’s used for damping wigglers to lower emittance and control user changes of the emittance from changing gaps Damping wigglers provide high flux, brilliance beams for users missing from dipoles, dipole beam great VUV sources Dynamic aperture with tolerances, first look appears achievable Quadruplet in ID’s essential for control of linear optics from undulators