1. SuperB Lattice Studies M. Biagini LNF-INFN ILCDR07 Workshop, LNF-Frascati Mar. 5-7, 2007

2. Overview The lattice for SuperB rings needs to comply with several issues: –small emittances –asymmetric energies –insertion of a Final Focus (similar to ILC), with very small  * –dynamic aperture & lifetimes Fortunately enough the new large crossing angle & small collision parameters scheme with crab-waist has relaxed the requests on the bunch lengths and beam currents Main objective was to design a lattice that could deliver at least 1x10 36 luminosity while keeping wall power requirements as low as possible !

3. History of lattice studies First lattice studied was ILC-DR OCS, with the TME (Theoretical Minimum Emittance) cell, circumference 6 Km: –Energies were changed from 5x5 to 4x7 –Same RF frequency –4 GeV: same wiggler field, same bend length –7 GeV: same wiggler field, double bend length, less wiggler sections

4. OCS ILC 4 GeV ring ILCDR-like Wiggler cell 7 GeV ring ILCDR-like Arc cell

5. History of lattice studies (cont.) Second step was to shorten the circumference, still keeping the TME cell: –3.2 Km, 2.4 Km were studied –an ILC-like Final Focus was inserted in the lattice –lower wiggler field used, possibility to use PM magnets, saving on operation power

6. 2.4 Km with FF

7. Comparison of parameters for different circumferences 4 GeV7 GeV C (m)6114.3251.2392.6114.3251.2392. B w (T)1.61.4 1.61.4 L bend (m)5.6 6.7211.210.66.72 N. bends96 10096 100 B bend (T)0.0780.1550.1250.1360.1440.218 Uo (MeV/turn)5.74.43.510.76.47. N. wigg. cells888444  x (ms) 28.819.818.226.24.15.8  s (ms) 14.410.9.11312.7.9  x (nm) 0.50.380.370.50.5650.64 EE 1.1x10 -3 1.x10 -3 1.3x10 -3 1.32x10 -3 1.35x10 -3 I beam (A)2.5 1.4 P beam (MW)14.11.8.815.9.9.8

8. History of lattice studies (cont.) Third step was to design lattices compatible with the PEP-II magnets: –Still using TME cell –PEP-II magnets all used, need more –Used a 6-fold symmetry, PEP-II like –Optimized Final Focus (FFTB-likeis now similar in length to an arc –PEP-II RF system First results: –HER can use all PEP-II present magnets and get required emittance and damping time –LER needs new, 4 times longer, dipoles to get required emittance and damping time –Changing energy asymmetry does not help

9. Cells with PEP-II HER magnets,  x =0.375,  y =0.125 (TME) 2 HER dipoles Side by side 4 LER dipoles side by side

10. 7 GeV HER with PEP-II magnets  x = 0.84 nm  s = 19.6 msec U o = 4. MeV/turn C =3.111 Km B w = 1.4 T 2 wiggler section

11. 4 GeV LER with PEP-II magnets  x = 0.58 nm  s = 18 msec U o =2.3 MeV/turn C =3.111 Km B w = 1.5 T 4 wiggler sections

12. History of lattice studies (cont.) Fourth step: lattice optimization –shorten the arcs by using less cells with smaller intrinsic emittance: TME:  x =0.375,  y =0.14  New cell ( ,0.4  :  x =0.5,  y =0.2 –smaller natural chromaticity: Q x ’ from -80 to -55 Q y ’ unchanged –optimized phase advance between arcs (periodic on 3 arcs) to get best performances –fewer elements: 6 arcs with 10 cells, HER ring has 120 5.4m long bends + 16 5.4m long bends for the FF –arcs are 250 m long –overall ring lenght 1.975 Km

13. Schematic layout of 6-fold ring

14. Arc cell LER-type,  x =0.5,  y =0.2 Arc cell HER-type,  x =0.5,  y =0.2 LER HER

15. HER, 7 GeV Uses 120 PEP-II HER dipoles, 5.4 m long + 16 Final Focus 5.4 m long PEP-II HER dipoles  x =1 nm (was 0.8nm)  z = 5.3 mm (was 7mm)  s = 10.3 msec B wig = 1.05 T 2 dipoles/cell, ( ,0.4  phase advance Reduced number of sextupole families (2) w.r.t. TME Optimized phase advance between arcs (  /3) to get best performances LER, 4 GeV Same lattice design as HER 240 PEP-II LER dipoles (only 192 are available!), 0.45 m long, + 16 Final Focus 5.4 m long PEP-II HER dipoles  x =1.73 nm  z = 6 mm  s = 10.3 msec B wig = 1.05 T We can use leftover dipoles from HER, but the ring loses its symmetry, the matching sections are not “optically beautiful”

16. Ring Parameters Energy (GeV)47 C (m)1975.5 B w (T)1.191.05 L bend (m) (Arc/FF)0.9/5.4/5.410.8/5.4 N. Bends (Arc/FF)160/40/16120/16 Uo (MeV/turn)2.34.5 Wiggler sections: N, L tot (m)4, 100  z (mm) 6.5.4  s (ms) 10.3  x (nm) 1.21. Emittance ratio0.25% EE 1.x10 -3 Momentum compaction2.7x10 -4 4.1x10 -4 s 0.0140.022 Vrf (MV), N cav 6, 818, 24 N part (x10 10 )3.311.89 I beam (A)2.51.44 P beam (MW)5.76.5 Frf (MHz)476 N bunches 3000 Gap5% P wall (MW) (50% eff) 2 rings24.4 xx 20mm xx 4m4m x’x’200  rad yy 200  m yy 20nm y’y’100  rad zz 7mm 2*  30mrad IP Parameters

17. History of lattice studies (cont.) Fifth step: further optimize the lattice to save on RF power: –longer circumference (2.250 Km) –same emittances in both rings –12 cells in each arc –less wiggler sections –relaxed requirements on damping times (from bb simulations) –changed crossing angle to 17 mrad (IR design constraint)

18. Upgrade path C(m)  s (ms)  x (nm)  z (nm) Power 10 Cells arc 4 wig 197010.51.05.323.2 12 Cells arc 4 wig 224012.50.65.021.0 12 Cells arc 2 wig 224015.80.84.717.0 12 Cells arc No wig 224021.51.054.211.5

19. 12 cells arcs Two more cells have been added to each arc in order to have similar emittances in both rings This complies with the choice to have a larger circumference This allows to have a completely symmetric lattice for LER, adding “new” 0.75 m long bends The rings have now exactly the same emittances and damping times Four wiggler sections are needed for LER, just 2 for HER

20. LER 12 cells

21. Chromatic functions No FF With FF

22. HER 12 cells

23. Chromatic functions No FF With FF

24. “12 cells” Ring Parameters Energy (GeV)47 C (m)2250 B w (T)1.0.83 L bend (m) (Arc/FF)0.45/0.75/5.45.4/5.4 N. Bends (Arc/FF)120/120/16120/16 Uo (MeV/turn)1.93.3 Wiggler sections: N, L tot (m)4, 1002, 100  z (mm) 4.75.  s (ms) 16.  x (nm) 0.8 Emittance ratio0.25% EE 1.x10 -3 Momentum compaction1.8x10 -4 3.x10 -4 s 0.0110.02 Vrf (MV), N cav 6, 818, 24 N part (x10 10 )6.163.52 I beam (A)2.31.3 P beam (MW)4.44.3 Frf (MHz)476 N bunches 1733 Gap5% P wall (MW) (50% eff) 2 rings17 xx 20mm xx 4m4m x’x’200  rad yy 200  m yy 20nm y’y’100  rad zz 7mm 2*  30mrad IP Parameters

25. Studied an FFTB/OLD-NLC stile solution: two sextupoles pairs (x and y) at -I Non local chromatic correction limits the bandwidth: strong 3rd order chromaticity (V12666 and V34666 in transport notation, T126 (X=T126*X’*dE/E) and T346 is the “natural” chromaticity) Two additional sextupoles at the IP phase cancel these aberration providing an excellent bandwidth. Since they are placed at a minimum betas location, they do not reduce the dynamic aperture Two additional weak (about 10% of the main x sexts) x-sextupoles interleaved with the main y-sexts, do restore the –I between the y-sexts for off-momentum particles, thus improving the ring energy acceptance Final Focus (FFTB-like)

26. FFTB-stile Final Focus IP phase sexts Sf Sd Sf Ring+FF Bandwidth Sf -I restoring “weak” sextupoles

27. FF with IP-phase sexts Minimum betay at the IP phase becomes a maximum for off momenta

28. HER ring with FF lattice Chromaticity through the ring

29. IBS in LER (A. Wolski) Blu: betatron coupling makes a 10 % contribution to the vertical emittance, with vertical dispersion contributing 50% Red: betatron coupling and vertical dispersion make equal contribution to the vertical emittance xx EE yy zz If betatron coupling dominates: increase in  y will be equal to increase in  x. If betatron coupling and vertical dispersion give roughly equal contributions to  y : relative increase in  y (50%) is half relative increase in  x (100%)

30. IBS in HER (A. Wolski) Blu: betatron coupling makes a 10 % contribution to the vertical emittance, with vertical dispersion contributing 50% Red: betatron coupling and vertical dispersion make equal contribution to the vertical emittance xx yy zz EE Lower bunch charge, higher E: better results

31. Dynamic aperture (Y. Cai) Two sextupole families used to save on number of sextupoles Chromaticity corrected to zero Tune set close to half integer LEGO used for first evaluation Due to the very strong sextupoles in the FF dynamic aperture needs to be computed including high order terms in the Hamiltonian

32. No errors: 70  x (1 nm-rad) and 200  y (0.5 nm-rad) With errors (5 seeds), no degradation Dynamic aperture of HER lattice without FF

33. Dynamic aperture of HER lattice with FF Paraxial approximation is not accurate enough for the quadrupole magnets in the Final Focus Better than the paraxial approximation: fourth order momentum terms included 23  y full coupling 21  x no coupling 42  x no coupling

34. Dynamic aperture of HER lattice with errors Errors in regular arcs only: no significant reduction Errors in regular arcs and FF: significant reduction Amplitude dependent terms, like crossing terms between the horizontal and vertical planes, are rather large. These result from the interference among the non-interlaced sextupoles and may be the reason of small dynamic aperture.

35. Dynamic aperture of LER lattice with FF and multipole errors

36. Conclusions on DA Dynamic aperture is basically limited by the final focus system Dynamic aperture is small but more than adequate for the stored beam which has extremely small size The acceptance for a large injected beam remains to be studied

37. Conclusions We have studied the feasibility of small emittance rings using all the PEP-II magnets, modifying the ILC DR design The rings have circumference flexibility The FF design complies all the requirements in term of high order aberrations correction All PEP-II magnets are used, dimensions and fields are in range. Few new dipoles in LER, and some quadrupoles and sextupoles are needed RF requirements are met by the present PEP-II RF system