1. M. E. Biagini, LNF-INFN SuperB IRC Meeting Frascati, Nov. 12-13, 2007
SuperB Rings lattice
M. E. Biagini, LNF-INFN
SuperB IRC Meeting
Frascati, Nov , 2007

2. Overview
The SuperB lattice as described in the Conceptual Design Report is the result of a vast international collaboration between experts from BINP, Cockroft Institute, INFN, KEKB, LAL/Orsay, SLAC.
This collaboration is very important for the completion of the Technical Design Report
The design is flexible but challenging and the synergy with the ILC Damping Rings, which helped in focusing key issues, will be important for addressing some of the topics

3. Motivations for update
Several accelerator issues have been addressed after completion of the CDR. In particular:
Power consumption
Costs
Site requirements
Crab waist compensation
Optimization of ring cell and Final Focus (lattice, emittance, dynamic aperture)
QD0 quadrupole design
Touschek backgrounds (see IR & Detector talks)
Polarization schemes (see Polarization talk)
The evolution of the lattice design is a consequence of the effort in minimizing costs and power consumption.

4. The Rings HER, 7 GeV same length and similar lattice LER, 4 GeV
Rings cross in one Interaction Point
Ultra low emittance lattice: inspired by ILC Damping Rings
Circumference scaled down to shortest possible
Rings design based on PEP-II hardware

5. SuperB Parameters (Nov. 2007)
(In red the CDR values)

6. Main differences from CDR
Shorter ring (25%)
Longer Tousheck lifetime in LER (x2.3)
Lower vertical tune shift (13%)
No wigglers in Phase I, less wigglers in Phase II and III
More relaxed LER parameters
Lower currents (20%)
Longer damping times (20%)

7. Lattice optimization (1)
Emittance of rings should be of the order of 3-1 nm, damping times <25 msec. Three steps in design:
First lattice used TME cell (ILC-DR):
x-phase advance/cell mx = 0.375
y-phase advance/cell my = 0.18
p-cell with lower emittance (CDR):
x-phase advance/cell mx = 0.5
y-phase advance/cell my = 0.2
2 new cells with larger phase advance:
x-phase advance/cell mx = 0.5 and 0.72
y-phase advance/cell my = 0.2 and 0.27

8. Lattice optimization (2)
Natural emittance decreases further by increasing the arc cell x-phase advance, and nominal values can be obtained even without inserting wigglers
Dynamic aperture shrinks with larger mx, but is still large enough (Final Focus is the dominant factor)
x-emittance vs x-phase advance/cell

9. New layout (1) Reduced lenght and symmetry to: 4 “arcs”, 14 cells/arc
Only 2 wiggler straights, 40 m long, empty in Phase I
Final Focus
One long straight for RF, injection (beams will be vertically separated here)
2 sections will be devoted to polarization scheme
Arcs further optimized in order to:
- improve chromatic properties
- increase dynamic aperture
- decrease intrinsic emittance

10. QF/2-QD-B-B-QF-B-B-QD-QF/2
New layout (2)
Alternating sequence of two different arc cells: a mx = p cell, that provides the best dynamic aperture, and a mx = 0.72 cell with much smaller intrinsic emittance which provides phase slippage for sextupoles pairs, so that one arc corrects all phases of chromaticity. Then:
- chromatic function Wx < 20 everywhere
- b and a variation with particle momentum are close to zero
- larger dynamic aperture
Cell #1: L=20 m, mx = 0.72, my = 0.27
Cell #2: L=21 m, mx = 0.5, my = 0.2
New cell layout (double-cell wrt CDR lattice):
QF/2-QD-B-B-QF-B-B-QD-QF/2

11. New layout (3) HER: ex = 1.6 nm, ts = 19.8 msec
LER: ex = 2.8 nm, ts = 19.5 msec
HER cells host 2 x 5.4 m long PEP-II dipoles
LER cells host 4 x 0.45 m long PEP-II dipoles
Final Focus sections have 18 HER-type bends (16 in CDR)
2 straights between cells can host wigglers if needed
2 new sections, about 200 m long, will be added for the polarization scheme (not included in present lattice)
Total length ~ 1800 m

12. Arc cells layout
LER
HER
Cell #1
Cell #1
Cell #2
Cell #2

13. Final Focus Optimization
Increased crossing angle to 2*25 mrad (was 2*17 mrad)
Increased L*=0.4 m (was 0.3 m)
Horizontal beam separation at QD0: 2 cm, about 180 sx
Increased QF1 length to 0.7m in order to decrease its synchrotron radiation. If necessary it could be lenghtened further
Radiative Bhabhas hitting the IR beam pipes are a lot
Sychrotron radiation power is large
A possible solution with a septum QD0 is being studied:
- Super Conducting array of wires placed in the middle of QD0 to shift the magnetic center, opposite for the 2 beams, to get no net steering from QD0 (Bettoni, Paoloni design). Overall thickness ~ 8mm, leaving about 60 sx of beam stay-clear
- PM solution for QD0: array could be with normal conducting wires

14. New layout (4) Total length ~1800 m Length 20 m Length 280 m
Courtesy E.Paoloni, G. Marchiori

15. Example of QD0 design
S. Bettoni, E. Paoloni
Work in progress

16. Final Focus optical functions
Crab
sextupoles
LER: bx* = 35 mm, by* = 220 m
HER: bx* = 20 mm, by* = 390 m

17. Rings optical functions
LER
HER

18. Chromatic functions FF

19. Dynamic Aperture With crab sextupoles DA represents stability area
x-plane
xmax = 60 sx no coupling
DA represents stability area
of particles over many turns
Lifetimes depend on it
y-plane
ymax = 30 sy full coupling
Crab sextupoles
reduce DA by 30%

20. Work in progress
Polarization scheme matching in lattice (BINP, SLAC, LNF)
New QD0 design, will allow to decrease IR background problems (LNF, Pisa)
IR optimization with new QD0 (SLAC)
Dynamic aperture optimization with crab sextupoles (BINP, LNF)
Beam-beam studies with non linearities (BINP, LNF)
Beam-beam and polarization interaction (BINP)

21. Conclusions New cell layout more flexible in terms of emittance
New rings are shorter and cheaper
Possible to run Phase #1 without wigglers
Upgrade parameters possible with wiggler installation
More work is in progress both for lattice and beam dynamics issues