Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

LATTICE ANALYSIS OF THE KEKB COLLIDING RINGS
K. Akai, N. Akasaka, A. Enomoto, J. Flanagan, H. Fukuma,Y. Funakoshi, K. Furukawa,
S. Hiramatsu, K. Hosoyama, N. Huang∗ , T. Ieiri, N. Iida, T. Kamitani, S. Kato, M. Kikuchi,
E. Kikutani, H. Koiso, M. Masuzawa, S. Michizono, T. Mimashi, T. Nakamura, Y. Ogawa,K. Ohmi, Y. Ohnishi, S. Ohsawa, N. Ohuchi, K. Oide, D. Pestrikov† , K. Satoh,M. Suetake,Y. Suetsugu, T. Suwada, M. Tawada, M. Tejima,M. Tobiyama, N. Yamamoto, M. Yoshida,
S. Yoshimoto, KEK, Tsukuba, Ibaraki, 305-0801, JananAbstract
A low beta lattice with βx∗ /βy∗ =100/1 cm has been realized
in the KEKB colliding rings. The basic optical parameters
have been measured and compared with the model.

1MODELINGKEKB[1]is an 8 GeV electron + 3.5 GeV positron doublering collider (HER and LER) with a single interaction point(IP) for the Belle detector. The beta function at IP is designed to be 1 cm in the vertical plane (βy∗ = 1 cm) and ahorizontal beam crossing angle of 22 mrad is adopted forcollisions at a bunch spacing of 59 cm. Following countersolenoids which locally compensate the detector solenoid®eld, eight special quadrupole magnets, listed Table 1, areinstalled around IP. QCSR and QCSL are superconducting
magnets which are common in both rings. The other normal magnets have special shapes with ®eld free space forthe counter-rotating beams. The modeling of those special
magnets is one of the most important issues in the lattice design. The results of magnetic ®eld measurements have beentaken into account in the model as much as possible. Designand simulation works have been done by the code SAD[2]developed at KEK.
Magnet(Type)
QC2LE (N)QC2LP (N)QC1LE (N)QCSL (S)IP
QCSR (S)QC1RE (N)QC2RP (N)QC2RE (N)rb(mm)
60
4538704260

B0(T/m)3.2
6.1-14.2-21

xm /ym(mm)
68/13
57/10
22/21
13/20

e− ↓e+ ↑e− ↓−e ↓ e+ ↑-21-13.2
2.9
10.8

14/24
29/27
69/12
69/16

e− ↓ e+ ↑e− ↓e+ ↑e− ↓† visiting from BINP, Russia

0-7803-5573-3/99/$10.00@1999 IEEE.

QCS and solenoid

The ®eld distribution along the longitudinal direction in thesolenoid area is given by 4 cm-thick slices with a constant®eld. Both QCSs are included in this area, and are also divided into slices with normal and skew multipoles up to the32-th pole. The magnitude of multipole components were
estimated from the results of ®eld measurements[3]. Since
the outgoing beams pass the QCSs at off-axis, it is necessaryto express the transverse distribution with suf®cient accuracy at ∼ 60 mm away from the center. To optimize the x-y
coupling, the QCSR and QCSL are set to be rotated by 35.6
and -10.8 mrad, respectively.

(a)

(b)

QCSR

Beam

ECSR

IP

ECSL

QCSL

Figure 1: Model of QCS and compensation solenoid system.

1.2

Table 1: Special quadrupole magnets near IP. rb is the bore
radius, B 0 the ®eld gradient, xm andym the maximum amplitudes of the injected beams in the horizontal and verticalplanes.

∗ visiting from IHEP, China

1.1

QC1RE and Others

QC1RE is a half quadrupole for HER. The beam passes
through 45 mm off-axis of the virtual center of QC1RE in
the horizontal plane. The integrated dipole ®eld obtained
from the ®eld measurement along the beam trajectory isconsistent with 3-dimensional calculation and amounts toan additional kick of 1.1 mrad, which is incorporated asthin dipole magnets attached at both edges of QC1RE. The
dynamic aperture with measured values of the higher multipoles was checked for some of the normal quadrupoles,
which was found to be marginal compared with the requirements.

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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

1.3

Lattice for BEAST

The commissioning has commenced with βx∗ /βy∗ =100/2cm, and the reduction of βy∗ to =1 cm has been succeeded

in both rings[4]. The chromaticity correction has fully utilized 52-family noninterleaved sextupole pairs and vertical 2-family pairs for the local correction only in LER. The
commissioning lattice has slightly modi®ed for the BEAST
detector, removing the detector solenoid. Because QCSs
are already rotated, the x-y coupling should be correctedeven without the detector solenoid. The rotations of normal
IR quadrupoles have also been changed and the compensation solenoids have been excited to 10% of the nominal values to minimize strengths of skew quadrupoles. In order toadjust orbits and dispersions, local orbit bumps have been
applied in the interaction region (IR) as shown in Fig. 2.

on the vertical orbit. The vertical dispersion has been decreased to a reasonable level by adequate tuning of the vertical orbit, in particular, at sextupoles.
Source(a) Flat rectangular dipole(b) Edge angle(c) Slope of By , By = By (s)(d) Integrated quadrupole(e)Integratedsextupole,R 00
By (s)x(s)ds

SLRSLRSLLβy∗ =2 cm
Adjust energy, QCS
LER dipole modelAwith fudge factors (*)
LER dipole modelB(no fudge factors)
Adjust QCSβy∗ =1 cm
Adjust tunes, orbits,chromaticity, etc.

SLL

Figure 2: LER optical functions in IR. SLL and SLR are
sextupoles for the local chromaticity correction.

22.1

MEASUREMENT OF BASIC
PARAMETERS-0.112

LER∆νx ,∆νyHER∆νx ,∆νy-0.01, -0.30

0.12, -0.08+0.04, -0.10-0.14, -0.20-0.13, -0.19

0.12, -0.09-0.07, -0.22+0.07, -0.06

Closed Orbit

Transverse tune

Even a few steps of improvements of the model lattice aslisted Tables 2 and 3, the measured tunes still have some difference from the model in both rings. It is necessary to precise calibration between various magnets (superconducting,normal, IR quadrupoles with special shapes) to identify error sources.

2.3

0.114

Table 3: History of tune deviations from the model lattice.
(*)Fudge factors of -0.4% and -0.8% were applied for tow
families of quadrupole magnets in unit cells, QD3P(40) andQD5P(48), respectively.

The global closed orbit has been successfully corrected withconventional methods (SVD and MICADO) better than 0.6mm rms. The local bumps has also been used for ®ne tuning
and for diagnostics of machine errors.

2.2∆νy00.40-0.037-0.056

Table 2: Model of LER dipole magnet. The quadrupoleand sextupole components are estimated from the results of®eld measurements[5]. ModelB and A are with and withoutSource(e).

IPbeam∆νx0000.057

Dispersion

The measured values of horizontal dispersions agree withthe model within 16% in LER and 6% in HER. Sometimes alarge vertical dispersion has been observed, which depends

2.4

Chromaticity

The examples of the chromaticity measurement are shown
Fig.4. The differences from the model are not so big, butamount to 5 in the vertical direction in the βy∗ =1cm case. It
is necessary to adjust tunes of the model lattice to the measured ones in ®nding solution of strengths of sextupoles.

2.5β Function

Big mismatch of LER optics in the vertical direction wasobserved both in the response of single kick orbits [6] andin measurements with trim coils of normal quadrupoles asshown in Fig.6. The matching was greatly recovered by adjusting ®eld strengths of QCSs by +0.8%, which was determined by analyzing the leakage orbit of the local bumpat QCSs. After recent re®nements of the QCS model by
subtracting effects of the return yoke of the Belle detector,

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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999
QCSs still look stronger by 0.37% than other quadrupole
magnets in LER. In HER, βy at QCSs and QC1s are consistent with the model in 10%. Further measurements andanalysis are now being in progress.
The authors thank K. Egawa, S.-I. Kurokawa,K. Nakayama, K. Tsuchiya for helpful discussions
and comments.

Figure 5: Calculated chromaticities of LER in the case ofβx∗ /βy∗ =100/1 cm.

Figure 3:
Measured and(above:LER, below:HER).

LER

Dnx

dispersions

D nx

00-0.005

Dny-0.005
D ny-0.01
-0.4

-0.2

-0.01
0.4

0.2

HER

0.01

0.04

D nx

0.005
Dnx

0Dp/p (%)

0.02

00-0.005-0.01-0.4

D ny-0.2

0Dp/p [%]

0.2

30
20
10120

DnyFuji

OhoTsukuba

Nikko

OhoTsukuba

Nikko

designedmeasured

100806040
200
Nikko

Fuji

Figure 6: Measurement of β-function with trim coils ofquadrupole magnets in the case of βx∗ /βy∗ =100/2 cm. The®eld strength of each quadrupole was changed typically
1.5% by the trim coil.

-0.02
-0.04
0.4

Figure 4: Measured chromaticities (above:LER, below:HER) in the case of βx∗ /βy∗ =100/1 cm.

3401400.005

designedmeasured

50

0Nikko0.01

Vertical beta function (m)

0.01
0.005

calculated

Horizontal beta function (m)60[2] http://www-acc-theory.kek.jp/SAD/sad.html[3] N. Ohuchi et al., Proc. of EPAC98 (1998).
[4] K. Oide et al

REFERENCES[1] KEKB B-Factory Design Report, KEK-Report 95-7, (1995).

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