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