1. The SuperB Accelerator Lattice M. E
The SuperB Accelerator Lattice M. E. Biagini, LNF-INFN for the SuperB Accelerator Team 2nd IRC Meeting Rome, April 29th 2008

2. Outline Evolution of lattice SuperB transparency conditions
Beam-beam simulations
Layout of rings and Final Focus
Dynamic aperture
Conclusions

3. SuperB Accelerator Contributors
M. E. Biagini, M. Boscolo, A. Drago, T. Demma, S. Guiducci, M. Preger,
P. Raimondi, S. Tomassini, C. Vaccarezza, M. Zobov (INFN/LNF, Italy)
Y. Cai, A. Fisher, S. Heifets, A. Novokhatski, M.T. Pivi, J. Seeman, M. Sullivan, U. Wienands, W. Wittmer (SLAC, US)
T. Agoh, K. Ohmi, Y. Ohnishi (KEK, Japan)
I. Koop, S. Nikitin, E. Levichev, P. Piminov, D. Shatilov (BINP, Russia)
Wolski (Liverpool University, UK)
M. Venturini (LBNL, US)
S. Bettoni (CERN, Switzerland)
A. Variola (LAL/Orsay, France)
E. Paoloni, G. Marchiori (Pisa University, Italy)

4. Evolution of lattice (1)
Several accelerator issues have been addressed after completion of the CDR. In particular:
Power consumption
Costs
Site requirements
Beam parameters
Crab waist compensation
Optimization of ring cell and Final Focus
QD0 quadrupole design
Touschek backgrounds (see Uli’s talk)
Polarization schemes (see Uli’s talk)
The evolution of the lattice design is a consequence of the effort in minimizing costs and power consumption
Arcs design was further optimized in order to:
improve chromatic properties
increase dynamic aperture
decrease intrinsic emittance

5. Evolution of lattice (2)
Natural emittance decreases further by increasing the arc cell mx, 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
Reduced ring length and symmetry to:
4 “arcs”, 14 cells/arc
Only 2 wiggler straights, 40 m long, empty in Phase I (no wigglers needed)
One Final Focus section
One long straight for RF, injection (beams will be vertically separated here)
Two spin rotator sections (matching in progress)

6. SuperB transparency condition
To have equal tune shifts with asymmetric energies in PEP-II and KEKB the “design” beam currents ratio was:
I+/I- ~ E-/E+
Due to SuperB large crossing angle, new conditions are possible: LER and HER beams can have different emittances and b* and equal currents 
Present B-factories design
SuperB

7. New transparency condition
We want 
LER sees a shorter interaction region, (4/7 of the HER one)
LER has a smaller by*, easier to acheive in the Final Focus
LER has larger emittance, 2.8 nm, better for Tousheck effect and tolerance to instabilities e+ e-
LER
HER

8. New transparency condition (2)
Both beam lifetimes are increased (larger emittances), injection rates reduced
Beam-eam simulations show good results, no blow up is seen for HER, 1-3% for LER, but some more optimization is possible: tunes, crabbing (L=1036 is still predicted)
Upgrade parameters can be implemented in any order:
- decrease the emittances first, or...
- increase the bunch charge, or...
- increase the number of bunches, or...
- decrease the bunch length
Less RF Voltage is needed

9. SuperB New Parameters
Beam-beam
transparency
conditions in red

10. Example of beam-beam tune scans for different schemes
D. Shatilov
Lifetrack code
Blue: bad
Red: good
y=0.07
y=0.07
Head-on, Lmax = 2.45· Ordinary crossing, Lmax = 2.05·1034
y=0.17
SuperB
Large , CW = 0, Lmax = 1.6· Crab Waist, Lmax = 1.05·1036

11. Beam tails and Luminosity vs Crab sextupole strength
CDR parameteres here
y= 0.183
s= 16 msec
y= 0.212
s= 12 msec
Ax = (0 : 20)sx Ay = (0 : 50)sy
D. Shatilov, M. Zobov, IV SuperB Workshop

12. Luminosity and blow-up vs damping time and Np
Nominal damping: 10msec/3Km rings
2.5 times longer
5 times longer
CDR parameteres here
Np = 2.5 x 1010
Ax x Ay = 15 sx x 20 sy
Np = 5.0 x 1010
Ax x Ay = 25 sx x 80 sy
D. Shatilov, M. Zobov,
IV SuperB Workshop

13. Beam-beam blow-up L=1036 cm-2 s-1 D. Shatilov, 2007
New parameteres here
LER
Crab=0.9Geom_Crab
HER
Crab=0.8Geom_Crab
No blow up is seen for HER,
1-3% for LER, but some more optimization is still possible: tunes, crabbing...
L=1036 cm-2 s-1

14. The Rings
Same length and similar lattice, low emittance lattice inspired by ILC Damping Rings
HER, 7 GeV, ex = 1.6 nm, ts = 19.8 msec
LER, 4 GeV, 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 design NLC-like, with 18 HER-type bends
Rings cross in one Interaction Point with a 48 mrad horizontal crossing angle
Two regions allocated to spin rotators
Circumference scaled down to shortest possible
Rings lattice based on recycling PEP-II hardware (save a lot of money !)
Total power: 17 MW, lower than PEP-II

15. New layout Alternating sequence of two different arc cells:
mx = p cell, that provides the best dynamic aperture,
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.
chromatic function Wx < 20 everywhere
b and a variation with particle momentum are close to zero
larger dynamic aperture
Cell #2
Cell #1
LER
HER

16. Final Focus SuperB FF requirements different from the ILC-FF
needs geometric aberrations small, sextupoles should be uninterleaved
bends not needed to be weak (smaller synchrotron radiation)
bends should all have the same sign, to avoid chicanes (to keep the geometry simple) and help to reduce the arc length
FF design complies all the requirements in terms of high order aberrations correction
Needs to be slightly modified for LER to take care of energy asymmetry
NLC-like solution was chosen, since has better bandwidth and smaller FF emittance growth

17. Final Focus
Crab sextupoles included in the design, give about 30% reduction in Dynamic Aperture
Two additional sextupoles at the IP phase cancel the 3rd order chromaticity providing an excellent bandwidth. Since they are placed at a minimum betas location, they do not reduce the dynamic aperture
Geometric aberrations reduced, added a x-sextupole to cancel residual geometric aberrations from off-phase sextupoles
Radiative Bhabhas hitting the IR beam pipes are a lot
Sychrotron radiation power is large
A solution with a septum QD0 is being studied

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

19. Off energy behaviour Chromatic functions bx byx10-3 Bandwidths ay axSD SF
crab
Min. IP phase
becomes a max.
for off momenta
particles
Chromatic
functions bx
byx10-3
Bandwidths ay ax

20. IP layout M.Sullivan QD0 is common to HER and LER
QD0 axis displaced toward incoming beams to reduce synchrotron radiation fan on SVT
Dipolar component due to off-axis QD0 induces, as in all crossing angle geometries, an over-bending of low energy out-coming particles eventually hitting the pipe or detector
New QD0 design based on SC “helical-type” windings

21. S. Bettoni, E. Paoloni

22. S. Bettoni, E. Paoloni

23. Rings optical functions
LER
HER
No spin rotator
here

24. Chromatic functions (zoom)FF

25. Dynamic Aperture optimization (1)
Dynamic Aperture (DA) represents the stability area of particles over many turns. It depends on lattice non-linearities, mainly the sextupoles used for chromaticity correction
Large chromaticity and strong sextupoles are a characteristics of very low emittance lattices
The Tousheck lifetime is affected by it
It is very important to have a large stable region possibly for different working points (WP) in the tunes plane
It is also important that a good DA WP corresponds to good beam-beam WP !
For low symmetry lattices, as SuperB, a dense net of structural resonances arises

26. Dynamic Aperture optimization (2)
For SuperB a large perturbation comes from the Final Focus region, where strong sextupoles are used to correct the large chromaticity produced at the IP, and where the CW sextupoles are placed
Very nice work for SuperB HER has been performed at BINP (P. Piminov) with the Acceleraticum code which allows for optimization of DA and WP at the same time
The method is called “Best sextupole pair” (BSP)
A DA tune scan and matching of the tune WP is performed
Work is still in progress and will continue for off-momentum DA, as well as for the LER. DA with the inclusion of machine errors need also to be computed
P.Piminov, BINP

27. SuperB HER DA tune scan Blue: bad Red: good Old WP (.575/.595)
New WP (.569/.638)
Horizontal DA
Vertical DA
Cross check of DA and luminosity tune scans is very important
Iterative method allows to choose best WP for both
P.Piminov, BINP

28. HER DA optimization for new WP
130 σy
80 σx
Black: original DA at WP (.575/.595)
Red: optimized at WP (.575/.595)
Green: DA for the new WP (.569/.638), same sextupoles
Blue: DA re-optimized in the new WP (.569/.638)
P.Piminov, BINP

29. One ring layout
280 m
20 m
No spin rotator here

30. Conclusions
New cell layout is more flexible in terms of emittance, allowing for the same target luminosity of 1036 cm-2 s-1
Rings are shorter and cheaper
Longer Tousheck lifetime in LER
Lower vertical tune shift
More relaxed LER beam parameters
Lower currents
Longer damping times
Possible to run Phase #1 without wigglers
Upgrade parameters possible with wiggler installation
All PEP-II magnets used
Final Focus design to be optimized for backgrounds
Dynamic aperture optimization in progress
Space for spin rotators provided, matching into lattice in progress (see Uli’s talk)