1. BROOKHAVEN SCIENCE ASSOCIATES CD2 LATTICE IMPROVEMENTS Accelerator Systems Advisory Committee April 23-24, 2007 Stephen Kramer for the NSLS-II Design Team Rev C

2. BROOKHAVEN SCIENCE ASSOCIATES CD2 LATTICE CHANGES Reduction in Number of Elements Quadruplets in ID straight sections replaced by Triplets: -2 Quads per cell For tune and beta function matching +1Quad in dispersion region +1Sext. Symm. Short Straight Section -1Sext for reduced Beta-X Net per cell:11-Quads (9families), 13-Sext (10families) CDR:12-Q(10), 13-S(11) Add Length to ID straight sections Vacuum Group better defined transition section to undulators/wigglers Short ID drift length 5  6.6m and Long ID 8  8.6m, allow IDs 5 and 7m Add Three Pole Wigglers in dispersion region TPW active length 20cm with 2mradian central bend > 1T plus 20cm free space Impact on emittance  x ~ 0.18 to 0.2nm for 15- TPWs 15* (8.6m LIDs + 6.6m SIDs + 4 *0.40m(0.20m) TPWs )= 252m 32.2% Circumference=783.3m (25% CDR 780.3m)

3. BROOKHAVEN SCIENCE ASSOCIATES Other Considerations Variable bend radius dipoles “ Theoretical ” improvement from iso-magnetic field case < of 3X reduction, but already DBA 2X MEDBA DW yields clear and controllable factor of 4 to 5X Higher power radiated from dipole reduces DW affect High field at low dispersion end of dipole makes overlap of dipole radiation with ID more troublesome i.e. “ Decker distortions ” maybe needed for XBPMs

4. 4 BROOKHAVEN SCIENCE ASSOCIATES CD2 Lattice Functions one Cell Quadrupole Triplets in ID Straight sections, Trim quad. in center of dispersion region, TPW Circumference =783.3m ( 780.3m CDR)

5. 5 BROOKHAVEN SCIENCE ASSOCIATES CDR Lattice Functions Quadruplets allow greater flexibility for beta functions in IDs and tune scan range for constant emittance and length Johan showed 4-Qs not needed for wiggler/ID affect cancellation

6. 6 BROOKHAVEN SCIENCE ASSOCIATES Impact of Triplets in IDs Requirements in ID: For given β x,y,, α x,y =0, need to match β x & α x at entrance to dipole for emittance 2-Qs needed also match β y & α y to same values from SSS and LSS: 1-Q maybe, 2-Qs better Dispersion region 1-Q needed for achromatic condition 2-Q for peak η x, β x Symmetry requires α x,y =0 and β x,y at sextupoles Trim Quad allows this matching and tune scan with less length variations S [meters]

7. 7 BROOKHAVEN SCIENCE ASSOCIATES CDR Quad Closed Orbit Amplif. Factor Misalignment of quadrupole centers, drive large Closed Orbit Distortion Closed Orbit Amplification Factors (COAF) defined as RMS(cod)/ RMS(error) ~50X in both planes or 100 µ m RMS Quad. misalignment  5mm offset of COD in lattice

8. 8 BROOKHAVEN SCIENCE ASSOCIATES CD2 QUADRUPOLE COAFs Stronger Quadrupole Focusing and Higher Beta functions yields COAFs (52,56)  (59,64) Increased in SID Y 12  19

9. 9 BROOKHAVEN SCIENCE ASSOCIATES CD2 Magnet Alignment Tolerances Quadrupole and Sextupoles have centers measured to a resolution of 10 and 15 µ m with vibrating wire technique Allow 2X for resolution, alignment Tolerance <30 µ m on girder Girder alignment Tolerance in tunnel <100 µ m (as achieved elsewhere ) girder amplification factors (3.8,3.1) in ID are ~3 to 5X less than COAF Std(COD) for 315 seeds with girder alignment dX,dY=10 µ m random at both ends

10. 10 BROOKHAVEN SCIENCE ASSOCIATES DA and Diffusion Map CD2 Using 8/10 sextupole families β x = 17 m β y = 2.3m

11. 11 BROOKHAVEN SCIENCE ASSOCIATES DA and Diffusion Map CDR Using 11/11 sextupole families βx = 18.2 m βy = 3.1m

12. 12 BROOKHAVEN SCIENCE ASSOCIATES DA for Corrected Alignment Errors Alignment Tolers. Girders & Dipoles = 100 µ m Quads & Sexts. = 30 µ m BBA BPMs acc. 10 µ m

13. 13 BROOKHAVEN SCIENCE ASSOCIATES Tune shift controlled for Jx,y & dP/P ~ 3% δ= dp/p Fractional Tune vs Momentum Offset

14. 14 BROOKHAVEN SCIENCE ASSOCIATES Changes in Source Parameters Length Long ID [m] Long ID β x,, β y Length Short ID [m] Short ID β x,, β y TPW(0.2m) β x,, β y, η x CD28.616.9,2.36.62.08,1.54.1, 21.8, 0.168 CDR818.1, 3.152.7, 0.95 NA  x = 0.5nm  y = 8pm Long ID  x,,  x’ [um, urad] Long ID  y,  y’ [um, urad] Short ID  x,  x’ [um, urad] Short ID  y,  y’ [um, urad] TPW  x,  y [um, um] CD291.9,5.434.3,1.8732.25,15.53.47,2.3174,13.2 CDR95.3,5.254.97,1.636.9,13.62.75,2.9NA

15. 15 BROOKHAVEN SCIENCE ASSOCIATES CD2 Lattice Parameters Circumference [m]783.3Number of cells/SP30 / 15 Energy [GeV]3 (3.6)RF Frequency [MHz]500 Uo [KeV] (8- 7m DW) 286.39 (1320) Dipole Bend radius [m]25.02  x [nm] (8- 7m DW) 2.006 (0.501) Energy Spread [%] (8- 7m DW) 0.051 (0.01)  y [pm] 8Bunch length [ps]10-20 Tunes Qx,Qy 33.35, 16.28 Synchrotron frequency [KHz]3.1 β x,, β y LID/SID [m]16.9,2.3 2.08,1.5 ID length total (active) [m]8.6 (7) 6.6 (5)

16. 16 BROOKHAVEN SCIENCE ASSOCIATES Summary and Additional Work Reduction of quadrupoles in ID straight sections Increased ID length for vacuum transitions and components Added possibility for 30+ TPWs to provide sources for NSLS beam line migration (15 Planned) Trim quad added to settle length and allow tune scanning Need improved sextupole and nonlinear tuning Need further study of field tolerances Need to calculate non- linear impact of TPWs