SuperB Lattice Studies

M. BiaginiLNF-INFN

ILCDR07 Workshop, LNF-FrascatiMar. 5-7, 2007

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 1x1036 luminosity while keeping wall power requirements as low as possible !

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

OCS ILC 4 GeV ring ILCDR-like

Wiggler cell

7 GeV ring ILCDR-like

Arc cell

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

2.4 Km with FF

Comparison of parameters for different circumferences

4 GeV 7 GeV

C (m) 6114. 3251. 2392. 6114. 3251. 2392.

Bw (T) 1.6 1.4 1.4 1.6 1.4 1.4

Lbend(m) 5.6 5.6 6.72 11.2 10.6 6.72

N. bends 96 96 100 96 96 100

Bbend (T) 0.078 0.155 0.125 0.136 0.144 0.218

Uo (MeV/turn) 5.7 4.4 3.5 10.7 6.4 7.

N. wigg. cells 8 8 8 4 4 4

x (ms) 28.8 19.8 18.2 26. 24. 15.8

s (ms) 14.4 10. 9.1 13 12. 7.9

x (nm) 0.5 0.38 0.37 0.5 0.565 0.64

E 1.1x10-3 1.1x10-3 1.x10-3 1.3x10-3 1.32x10-3 1.35x10-3

Ibeam (A) 2.5 2.5 2.5 1.4 1.4 1.4

Pbeam(MW) 14. 11. 8.8 15. 9. 9.8

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

Cells with PEP-II HER magnets, x=0.375,y=0.125 (TME)2 HER dipoles

Side by side

4 LER dipolesside by side

7 GeV HER with PEP-II magnets

x = 0.84 nms = 19.6 msecUo = 4. MeV/turnC =3.111 KmBw = 1.4 T2 wiggler section

4 GeV LER with PEP-II magnets

x = 0.58 nms = 18 msecUo =2.3 MeV/turnC =3.111 KmBw = 1.5 T4 wiggler sections

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: Qx’ from -80 to -55

Qy’ 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

Schematic layout of 6-fold ring

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

LER HER

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• Bwig = 1.05 T• 2 dipoles/cell,

(,0.4phase 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• Bwig = 1.05 T• We can use leftover dipoles from

HER, but the ring loses its symmetry, the matching sections are not “optically beautiful”

Ring Parameters

Energy (GeV) 4 7

C (m) 1975.5 1975.5

Bw (T) 1.19 1.05

Lbend(m) (Arc/FF) 0.9/5.4/5.4 10.8/5.4

N. Bends (Arc/FF) 160/40/16 120/16

Uo (MeV/turn) 2.3 4.5

Wiggler sections: N, Ltot(m) 4, 100 4, 100

z (mm) 6. 5.4

s (ms) 10.3 10.3

x (nm) 1.2 1.

Emittance ratio 0.25% 0.25%

E 1.x10-3 1.x10-3

Momentum compaction 2.7x10-4 4.1x10-4

s 0.014 0.022

Vrf (MV), Ncav 6, 8 18, 24

Npart (x1010) 3.31 1.89

Ibeam (A) 2.5 1.44

Pbeam(MW) 5.7 6.5

Frf (MHz) 476

Nbunches 3000

Gap 5%

Pwall (MW) (50% eff) 2 rings 24.4

x 20mm

x 4m

x’ 200rad

y 200m

y 20nm

y’ 100rad

z 7mm

2* 30mrad

IP Parameters

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)

Upgrade pathC(m) s(ms) x (nm) z (nm) Power

10 Cells arc

4 wig

1970 10.5 1.0 5.3 23.2

12 Cells arc 4 wig

2240 12.5 0.6 5.0 21.0

12 Cells arc

2 wig

2240 15.8 0.8 4.7 17.0

12 Cells arc

No wig

2240 21.5 1.05 4.2 11.5

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

LER 12 cells

Chromatic functions

No FF

With FF

HER 12 cells

Chromatic functions

No FF

With FF

“12 cells” Ring Parameters

Energy (GeV) 4 7

C (m) 2250 2250

Bw (T) 1. 0.83

Lbend(m) (Arc/FF) 0.45/0.75/5.4 5.4/5.4

N. Bends (Arc/FF) 120/120/16 120/16

Uo (MeV/turn) 1.9 3.3

Wiggler sections: N, Ltot(m) 4, 100 2, 100

z (mm) 4.7 5.

s (ms) 16. 16.

x (nm) 0.8 0.8

Emittance ratio 0.25% 0.25%

E 1.x10-3 1.x10-3

Momentum compaction 1.8x10-4 3.x10-4

s 0.011 0.02

Vrf (MV), Ncav 6, 8 18, 24

Npart (x1010) 6.16 3.52

Ibeam (A) 2.3 1.3

Pbeam(MW) 4.4 4.3

Frf (MHz) 476

Nbunches 1733

Gap 5%

Pwall (MW) (50% eff) 2 rings 17

x 20mm

x 4m

x’ 200rad

y 200m

y 20nm

y’ 100rad

z 7mm

2* 30mrad

IP Parameters

• 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)

FFTB-stile Final Focus

IP phasesexts

Sf Sf

Sd Sd

Sd Sf

Ring+FF Bandwidth

Sf Sf

-I restoring “weak” sextupoles

FF with IP-phase

sexts

Minimum betay at the IP phase becomes a maximumfor off momenta

HER ring with FFlattice

Chromaticity through the ring

IBS in LER (A. Wolski)Blu: betatron coupling makes a 10 % contribution to the vertical emittance, with vertical dispersioncontributing 50%

Red: betatron coupling and vertical dispersion make equal contribution to the vertical emittance

x

E

y

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%)

IBS in HER (A. Wolski)

Blu: betatron coupling makes a 10 % contribution to the vertical emittance, with vertical dispersioncontributing 50%

Red: betatron coupling and vertical dispersion make equal contribution to the vertical emittance

x y

z E

Lower bunch charge, higher E:better results

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

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

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

]4

1[)1(2

2222yxyx pppp

H

23 y full coupling

21 x no coupling

42 x no coupling

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.

Dynamic aperture of LER lattice with FF and multipole errors

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

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