SuperKEKB Lattice and Dynamic Aperture H. Koiso Apr. 20, 2005 Super B Factory Workshop in Hawaii

Lattice Parameters LERHER Horizontal emittance24 nm Beta IP200/3 mm Bunch length33mm RF voltage1520 Momentum compaction2.7× ×10 -4 MV Synchrotron tune No major change in arcs. Only the interaction region in Tsukuba straight section (~200m) will be fully reconstructed.

2.5π cell structure  x and α are independently adjustable.  x 10 ~ 36 nm, α -4 ~ 4×10 -4 Noninterleaved sextupoles (52 HER /54 LER pairs)

Geometrical Conditions Both rings are geometrically adjusted in the accuracy of 1> mm. –The position of IP is same as that of KEKB. Crossing angle at IP is satisfied the requirements. e+/e-:before charge switch)

Unit Cell  x =24 nm LER (left), HER(right) Both rings reserve sufficient tuning range of  x and α.

LER ring RF RF IP wiggler RF The horizontal emittance is adjusted as  xarc ~  xwig

HER ring RF IP RF (ARES) (Super)

IR Lattice x-y coupling components and H/V dispersions are all corrected to zero at IP, and are localized on each side of IP with 6(LER)/6(HER) skew quadrupoles and H/V dipoles. SuperBelle solenoid field is compensated on each side of IP. Field distributions of solenoids, QCS are given by 2-cm slices with constant strengths. Conditions for Crab cavities are not satisfied. –Crab cavities can be placed in Nikko straight section if the test at KEKB is successful.

Solenoid Field QCS field gradient (T/m) (top) Solenoid field (T) (bottom) QC2RP (QC1RE) QCSR IP QCSL (QC1LE) QC2LP

QCS Multipole Fields QCS field gradient (T/m) (top) K5(12-pole), K9(20-pole), K13(28-pole) QC2RP (QC1RE) QCSR IP QCSL (QC1LE) QC2LP

LER IR (  x*/  y* = 20/0.3 cm) LER IR with local chromaticity correction. (crab) SL SL IP SL SL (crab) beam→ x/yx/y

Coupling Components (LER IR) x/yx/y

HER IR (  x*/  y* = 20/0.3 cm) (crab) IP (crab) x/yx/y

LER dynamic aperture bare lattice BXBY=20/.3 cm (4cm-thick slices) injection beam Required: H/V 7.5/1.2 ×10 -6 m

HER dynamic aperture bare lattice BXBY=20/.3 cm (4cm-thick slices) injection beam Required: H/V 4.5/0.52 ×10 -6 m

Dynamic Aperture with Beam-Beam Effect Case  y = 0.14, dynamic aperture shrinks in large momentum deviation for LER. Transverse aperture decreases in HER due to beam-beam effect. Touschek lifetime with beam-beam(x y = 0.14): 50 min in LER / 180 min in HER Stored beam J y /J x = 2 % x / y = / No beam-beam  y = 0.07  y = 0.14 * no machine error Stored beam J y /J x = 2 % x / y = /  y = 0.14  y = 0.07 No beam-beam by Y.Onishi

LER dynamic aperture bare lattice BXBY=20/.3 cm (2 cm-thick slices) injection beam Required: H/V 7.5/1.2 ×10 -6 m

LER dynamic aperture lattice with QCS multipoles BXBY=20/.3 cm (2 cm-thick slices) injection beam Required: H/V 7.5/1.2 ×10 -6 m

HER Sextupole Magnet Strengths of 9 SD pairs K2 ~ -14. (the present limit is -12) New sextupole magnets are needed to improved the dynamic apertures. Local chromaticity correction in HER may be needed.

Interactive procedure of measurement + analysis + correction Knobs: ■ Local bumps at sextupoles ■ Fudge factors for quads/skews dispersion XY-coupling beta function Works very well ! Optics measurement and correction

Chromaticity Measurement There are differences from the model in off-momentum optics.

Summary LER dynamic aperture satisfies the requirements for transverse acceptances at injection. Modeling method of QCS and solenoid fields (for example, the thickness of slices) affects the dynamic aperture. –Effect of the edge of quadrupole field? Need to check. QCS multipoles do not change the dynamic aperture significantly. HER aperture still needs improvement. –Local chromaticity correction may be necessary. Dynamic apertures are decreased by the beam-beam effect. Dynamic apertures of both rings will be improved by further optimization of sextupole strengths. –should be estimated at a working point ~(.503,530). Correction methods for off-momentum optics should be developed.

Synchro-betatron Resonance HER(KEKB) by K. Oide, et.al.

LER dynamic aperture bare lattice BXBY=20/.3 cm injection beam Required: H/V 7.5/1.2 ×10 -6 m

Bumps at sextupoles scan Horizontal/Vertical bumps at sextupoles are used for optics correction. 8 vertical bumps at SD sextupoles in each side of IP. Vertical dispersion and its angle, x-y coupling components are independently adjustable. R1,R2,R3,R4,EY, and EPY Sextupole movers will be used instead of vertical bumps.

Merit of Local Chromaticity Correction by A. Morita LER dynamic aperture with a crab cavity (KEKB )

Solenoid Field QCS field gradient (T/m) (top) Solenoid field (T) (bottom) QC2RP (QC1RE) QCSR IP QCSL (QC1LE) QC2LP