XII SuperB Project Workshop LAPP, Annecy, France, March 16-19, 2010 Latest SuperB Lattice Yuri Nosochkov for the SuperB Lattice Design Team XII SuperB Project Workshop LAPP, Annecy, France, March 16-19, 2010

Version 12 lattice modifications Final Focus is shortened and emittance contribution is minimized for a given FF bending angle. Matching section is moved outside of the FF and crab section to maintain automatic match for crab sextupoles. HER injection section is moved inside an arc end combined with arcs crossing section near the left side of the long straight. LER injection section is moved farther into the arc on the right side of the straight. Dogleg is removed, thus providing more space for RF cavities, tune trombone, etc. Two types of bending angle in arc cells reduce the emittance and 2nd order chromaticity. Circumference is reduced by ~65 m. Sextupoles are optimized to increase the energy bandwidth to ±1%. Weak octupoles are included to compensate higher order terms.

Ring layout 66 mrad IR RF LER SR HER arc LER e- e+ C = 1258.3582 m

Final Focus geometry Crossing angle is increased from 60 to 66 mrad for larger separation near IP. Bending asymmetry with respect to IP is made the same in both rings. Total angle per half FF is 490.7±33 mrad. This makes the same FF optics in LER and HER for an easier match, but introduces a slight spin mismatch at the LER IP (~5% polarization reduction). More realistic model of the Final Doublet quadrupoles. FF length for geometry match is adjusted by drifts in the matching sections. IP HER LER

HER FF optics V10 IP V12 b* = 26 / 0.27 mm Shorter X-sextupole section -> reduced chromaticity, emittance. “Spin rotator” optics is replaced with a simpler matching section. The matching section is outside of the FF and crab section for automatic match of the crab and FF optics. IP V10 Y-sext X-sext Crab V12 Match b* = 26 / 0.27 mm

LER FF optics Same modifications as in HER, except that matching section is shorter to provide space for spin rotator optics. ±33 mrad bending asymmetry with respect to IP causes a slight spin mismatch between SR and IP resulting in ~5% polarization reduction. IP V10 Y-sext X-sext Crab V12 Match & SR

FF H-invariant HER V12 HER V10 IP LER V10 LER V12 FF bend locations are better optimized for minimal emittance contribution. HER V10 HER V12 LER V10 LER V12 IP

FF chromaticity HER V12 HER V10 IP LER V12 LER V10 FF optics and sextupoles are optimized for lower W-functions and larger energy bandwidth. HER V10 HER V12 LER V10 LER V12 IP

Long straight section, injection and RF Dogleg is removed and HER injection is moved out of the straight leaving more space for RF, tune trombone, etc. HER injection optics is created by lengthening the last –I arc cell on the left side of the straight. It is also combined with the arcs crossing section. HER chromaticity is reduced by ~3-4 units, and SR is reduced by ~5%. LER injection is moved farther into the arc on the right side of the straight. Injection kickers are moved to attain a higher R12 at septum for a larger bump. FODO cells in the long straight contain 8 RF cavities in LER and 28 in HER. HER injection LER injection HER RF LER RF Crossing 126.3 mrad Arc e+ e- Magnets near the crossing point need to be moved away for better separation.

HER straight and injection optics V10 Dogleg Injection V12 Crossing bx = 266 m Kicker Longer straight

LER straight and injection optics V10 Dogleg Injection bx = 142 m V12 Arc cells

Arc cells q1 q2 HER -I cell HER 3p/2 cell q1 2 types of bending angle for lower emittance and 2nd order chromatic tune shift: q1=67.1 mrad, q2=59.1 mrad. Arc end lattice functions are adjusted to match the last arc sextupole pairs with the other arc sextupoles. Arc length is adjusted by drifts at center of –I cells. HER 3p/2 cell q1 Cell phase advance is optimized to compensate W-functions as local as possible in each arc. Arc sextupoles are adjusted to minimize octupole terms due to interleaved pairs. 2 weak octupoles are added at arc ends for further improvement -> DA increases 20%.

Arc cell H-invariant -I cell HER V10 -I cell HER V12 3p/2 cell HER V10

Complete ring optics HER LER Injection IP

Compensation of W-functions Sextupoles are optimized to compensate W-functions semi-locally in each arc and each half FF. HER LER

Betatron tune and b* versus Dp/p Energy bandwidth is up to ±1%. HER LER

Ring H-invariant HER LER Lower H-invariant yields emittance reduction to 1.97 / 1.82 nm-rad in HER / LER. HER LER

Lattice parameters HER LER Energy Eo, GeV 6.7 4.18 Circumference L, m 1258.3582 Number of particles, *1010 5.08* 6.56* Tune Qx / Qy 40.575 / 17.595 42.575 / 18.595 Emittance Em_0, nm*rad 1.97 1.82 Ratio Em_IBS/Em_0 1.02* 1.35* Coupling, % 0.25 Energy spread, Sig_p 6.3E-04 6.7E-04 Bunch length, mm 4.7 4.3 Damping time x / s, msec 27 / 13 41 / 20 Beta_X/Y_IP, mm 26 / 0.274 Touschek lifetime, min 35* 16* Compaction factor 4.35E-04 4.04E-04 Energy loss, MeV/turn 2.11 0.87 fRF, MHz 476.0 URF, MV 7.0 5.25 Harmonic number 1998 * Values from SuperB parameter table, Feb 25, 2010.