SuperKEKB Lattice and Dynamic Aperture

H. KoisoApr. 20, 2005

Super B Factory Workshop in Hawaii

Lattice ParametersLER HER

Horizontal emittance 24 24 nm

Beta function @ IP 200/3 200/3 mm

Bunch length 3 3 mm

RF voltage 15 20

Momentum compaction

2.7×10-4 1.8×10-4 MV

Synchrotron tune -.031 -.019

•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 (52HER/54LER pairs)

Geometrical Conditions • Both rings are geometrically adjusted in the a

ccuracy of 1> mm.– The position of IP is same as that of KEKB.

• Crossing angle at IP is satisfied the requirements.e-e+ now, Belle solenoide+ SuperKEKB22mrad8mradSuperKEKB

beam pipe axis

7mrad

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 te

st 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

Coupling Components (LER IR)

x/y

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

(crab) IP (crab)

x/y

LER dynamic aperture bare lattice BXBY=20/.3 cm (4cm-thick slices)

injection beam

Required: H/V 7.5/1.2 ×10-6m

HER dynamic aperture bare lattice BXBY=20/.3 cm (4cm-thick slices)

injection beam

Required: H/V 4.5/0.52 ×10-6m

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(xy= 0.14): 50 min in LER / 180 min in HER

Stored beam Jy/Jx = 2 %

x/y = 45.510/43.545

No beam-beam

y = 0.07

y = 0.14

* no machine errorStored beam Jy/Jx = 2 %

x/y = 45.510/43.570

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 ×10-6m

LER dynamic aperture lattice with QCS multipoles BXBY=20/.3 cm (2 cm-thick slices)

injection beam

Required: H/V 7.5/1.2 ×10-6m

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 ofmeasurement + 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 a

cceptances at injection. • Modeling method of QCS and solenoid fields (for example, the thi

ckness 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 optimi

zation of sextupole strengths. – should be estimated at a working point ~(.503 ,530) .

• Correction methods for off-momentum optics should be developed.

Synchro-betatron ResonanceHER(KEKB)

by K. Oide, et.al.

LER dynamic aperture bare lattice BXBY=20/.3 cm

injection beam

Required: H/V 7.5/1.2 ×10-6m

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 adjustab

le. 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