1. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Lattice studies for low momentum compaction in LER M.E. Biagini LNF-INFN, Frascati

2. Super B-Factory Workshop, Hawaii, April 20-22, 2005 SBF Parameters (J. Seeman) L (cm -2 s -1 ) 7x10 35 10 36 E (GeV) 83.58  x (cm) 15  y (mm) 1.5  x /  y (nm) 28/0.3 40/0.4  l (mm) 1.8 NbNb 6900 I 6.815.51023  (mrad) ±15 xx.105.108 yy.107.105 HERLERHERLER

3. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Present LER Lattice C = 2200 m 6 sextants, 90° FODO lattice + dispersion suppressor One IR Dipoles 0.45 m Momentum compaction +0.0012

4. Super B-Factory Workshop, Hawaii, April 20-22, 2005 New SBF lattice Guideline: use the existing tunnel and magnets Different layout using present LER dipoles & quads Several lattices considered: –“KEKB-like” 2.5  (H. Koiso, K. Oide) –“KEKB-like” 3.5  –“KEKB-like” 7.5  –“SSC-booster-like” 3.5  (U. Wienands)

5. Super B-Factory Workshop, Hawaii, April 20-22, 2005 New SBF lattice For flexibility, easy chromaticity correction, and  c tunability the “KEK-B like” 2.5  lattice was suitable to our needs Preliminary lattice with no IR insertion Two lattices were studied: –Low negative  c (-1.6x10 -4 ) –Low positive  c (+7x10 -4 )

6. Super B-Factory Workshop, Hawaii, April 20-22, 2005 “KEK-B like” 2.5  Ring is 2200 m long and has 6 sextants and 6 long straight sections with no dispersion Each sextant houses two 2.5  cells and two dispersion suppressors One cell has 4 bending units, each one has 3 LER dipoles, and 6 independently powered LER quadrupoles (16 families in one sextant) Phase advance/cell is 2.5  Each straight section has 4 FODO cells

7. Super B-Factory Workshop, Hawaii, April 20-22, 2005 “KEK-B like” 2.5  Lattice allows for chromaticity correction by non-interleaved sextupoles connected by a –I pseudo-transformer QF2 QF6QF4 QF2 QD1QD3QD5 QD3 QD5 QD1

8. Super B-Factory Workshop, Hawaii, April 20-22, 2005 “KEK-B like” 2.5  Total number of independently powered quadupoles is 16 so far Preliminary design has 2 sextupoles families to correct arc chromaticity “Local” chromaticity correction to be implemented once IR is inserted

9. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Negative  c lattice (-1.6x10 -4 ) Arc + Dispersion suppressor

10. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Negative  c lattice One sextant

11. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Negative  c lattice Whole ring

12. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Beam Dynamics with  c < 0 Bunch is shorter with a more regular shape Longitudinal beam-beam effects are less dangerous Microwave instability threshold is higher Sextupoles can be relaxed since head-tail disappears

13. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Bunch lengthening The rms length  l of the equilibrium charge distribution in the bunch, neglecting the lengthening process coming from the short-range wakefields, is: However the bunch has to remain short up to the design current. The Boussard criterion can be used to estimate the µ-wave threshold: For current values beyond the threshold, assuming purely inductive ring impedance,  l is:

14. Super B-Factory Workshop, Hawaii, April 20-22, 2005 DA  NE A negative momentum compaction lattice (-0.017 for e -, -0.019 for e + ) was designed and implemented last year to study bunch length In both e + and e - rings a bunch shortening was observed and  -wave threshold was increased (higher for e + ring that has lower impedance) Not used in collision since a vertical blow-up observed in the e - beam (larger impedance due to clearing electrodes)

15. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Measured DA  NE bunch length alfa < 0 alfa > 0 e+e+ Bunch length vs bunch current for V RF = 110 kV and 120 kV  -wave Bunch length vs bunch current for V RF = 165 kV e-e- Potential well  -wave Potential well

16. Super B-Factory Workshop, Hawaii, April 20-22, 2005 SBF Due to HOM losses and beam loading at high current (from 15.5 to 23 A), very high RF voltage will be needed (from 33 to 55 MV) With such a high voltage to have desired bunch length the |  c | value must be larger than that achieved (1.6x10 -4 ) Microwave instability threshold is very low (less than 0.5 mA) for the case studied, a bunch shortening is however observed in preliminary simulations (A. Novokhatski) A positive low  c = +7x10 -4 lattice was then designed   l = 1.8 mm, I th ~ 3 mA A larger negative momentum compaction lattice is under study

17. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Preliminary bunch length simulations (A. Novokhatski)  c < 0  l = 1.75 mm I th < 0.5 mA  c > 0  l = 1.8 mm I th > 3 mA

18. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Positive  c lattice (  c = +7x10 -4,  x = 40 nm ) Arc + Dispersion suppressor

19. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Positive  c lattice One sextant

20. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Positive  c lattice Whole ring

21. Super B-Factory Workshop, Hawaii, April 20-22, 2005 IR design IR design has to cope with: –low-  * –crossing angle –local chromaticity correction –radiation background issues (M. Sullivan) –shared QD1 quadrupole in LER & HER –vertical chicane to bring LER beam to collide with HER beam First QD at 0.35 m from IP, shared by both beams (constraint)

22. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Preliminary LER IR  x * = 25 cm  y * = 3 mm  x * = 15 cm  y * = 1.5 mm Possible improvements: adjust phase advance between last arc bend and QF to optimize Touscheck lifetime QD-QF doublet

23. Super B-Factory Workshop, Hawaii, April 20-22, 2005 Preliminary HER IR  x * = 25 cm  y * = 3 mm  x * = 15 cm  y * = 1.5 mm Decreased distance between QD Doublet, to decrease peak  y Second QD necessary to keep HER beam focused