Beam-Beam experience at KEKB
M. Tawada, K. Akai, N. Akasaka, K. Bane∗ , A. Enomoto, J. W. Flanagan, H. Fukuma, Y. Funakoshi,
K. Furukawa, J. Haba, S. Hiramatsu, K. Hosoyama, N. Huang † , T. Ieiri, N. Iida, H. Ikeda, T. Kamitani,
S. Kato, M. Kikuchi, E. Kikutani, H. Koiso, S. -I. Kurokawa, M. Masuzawa, T. Matsumoto,
S. Michizono, T. Mimashi, T. Nakamura, Y. Ogawa, K. Ohmi, Y. Ohnishi, S. Ohsawa, N. Ohuchi, K. Oide,
E. A. Perevedentsev‡ , D. Pestrikov‡, K. Satoh, M. Suetake, Y. Suetsugu, T. Suwada, M. Tejima,
M. Tobiyama, S. Uno, Y. Z. Wu† , N. Yamamoto, M. Yoshida, S. Yoshimoto, M. Yoshioka, C. H. Yu † ,F. Zimmermann§ , KEK, 1-1 Oho, Tsukuba-shi, Ibaraki-ken 305-0801, Japan

Abstract
KEKB has achieved the peak luminosity of 4.1×10 33
cm−2 sec−1 and the present capability for delivering integrated luminosity is 224 pb−1/day. This paper describes(1) the recent performance and the problems of KEKB and(2) the comparison of beam-beam simulations with experiments at KEKB.

1INTRODUCTIONKEKB is a double ring electron-positron collider to study
B-meson physics. One ring is an 8 GeV electron ring (HER)
and the other is a 3.5 GeV positron ring (LER). The HER
and LER rings cross at the interaction point (IP) with a ±11
mrad crossing angle. To study B-meson physics, which
deals with very rare processes, KEKB has a high design
luminosity of 1×1034 cm−2 sec−1 and high vertical beambeam parameters (ξy ) of 0.05. The general outline and overall parameters of the KEKB accelerator are given in [1].
Recently, there has been excellent progress in commissioning of the KEKB accelerator. Figure 1 shows the luminosity history of KEKB from the beginning of the commissioning with the Belle detector. The peak luminosity of
4.1×1033 cm−2 sec−1 was achieved and the present capability for delivering integrated luminosity is 224 pb −1/day,
4.7 fb−1/month. The total integrated luminosity of 30 fb −1
was accumulated[2]. Table 1 summarizes the present parameters which are related to the luminosity with the design
parameters.

2

RECENT IMPROVEMENT OF KEKBPERFORMANCEKEKB performance has been improved by several
means: (1) installation of solenoids to LER, (2) a shift ofthe vertical tunes above a half integer for both rings , (3)increasing the HER bunch current after the replacement of
HER movable masks to those of a new type of mask and(4) a continuos tune monitor of pilot bunch.
∗ visiting from SLAC, U.S.A† visiting from IHEP, China‡ visting from BINP, Russia§ visiting from CERN, Switzerland

Horizontal emittanceBeam current
No. of bunches/ring
Bunch current
Bunch spacing
Bunch trainsσx∗
σy∗ 1)
y /xβx /βyξx /ξy 2)νx /νyBeam lifetime
Bunch length
Luminosity (CsI)
Luminosity records
per day/ 7 days / month

LER
18
885
(2600)
1154(5120)
0.77
(0.5)
2.4
(0.6)
1
103
2.9
4.2
0.59/0.0065(0.33/0.01)
0.072/0.045(0.039/0.052)
45.51/44.57(45.52/44.08)
166@854 mA
5.9@8.0
4.1×1033
224/1336/4703

HER
24
748
(1100)
1154(5120)
0.65
(0.2)
2.4
(0.6)
1
123
2.9
3.2
0.63/0.007(0.33/0.01)
0.050/0.028(0.039/0.052)
44.519/42.517(44.52/42.08)
210@675 mA
6.4@11(1×1034 )

unit
nm
mA

mA
m

µm
µm
%
m

min.
mm@MV
/cm2 /sec/pb

Table 1: The present machine parameters and performanceof the KEKB (June 13, 2001). The values in a parenthesis are the design values. 1) Vertical beam sizes of the two
beams are assumed to be equal. 2) An effect of dynamic
beta and dynamic emittance is not considered.

2.1

Installation of solenoid to LER

A vertical beam blowup has been observed in LER since
early operation. The main characteristics of the blowup are
explained by single-beam head-tail instability caused by anelectron cloud. About 4600 solenoids were installed to LER
in order to suppress the electron cloud. Its total length isabout 1.23 km and about 40 % of the ring circumference
was covered by solenoid field. The calculated field strength
was 45 Gauss at the center of the solenoid when the maximum current of 5 A was applied. Figure 2 shows the luminosity as a function of the bunch current product with andwithout solenoid field.
The averaged vertical beam size over all bunches areFigure 1: This figure shows the luminosity history from the beginning of the commissioning with Belle detector (July 16,2001).
measured by a synchrotron radiation interferometer [3].
The beam size is transformed from the source point of thesynchrotron radiation to IP. The threshold current of blowup
was also increased when solenoids were excited[4]. The
problem is improved but not solved yet. The vertical beam
size is still large at the higher beam current than 700 mA
with 1154 bunch mode.

2.2

Tune Survey and Continuous Tune Monitor

We have moved to the vertical tune above the half integer
for both rings at February, 2001. The reason is as follows.
(1) The closed orbit at the tune above the half integer is not
so sensitive to the machine errors as that with a tune justabove the integer. (2) The strong-strong beam-beam simulations have predicted a tune region above the half integer
would bring a better luminosity[5].
The machine stability was also improved by the continuos tune monitor of pilot bunches. This monitor can measure the tune during both injection and physics time by using un-collided bunches.

2.3

ground of a detector. Sixteen movable masks were installed for each ring of KEKB. Heating problems of movable masks have limited the stored beam currents for HER.
New movable masks have been designed employing RF
technologies for HOM damping[6].
After replacement of the HER movable masks to a new
type[7] at April, 2001, we could increase the beam currents
gradually.

HER current

The movable mask is a device that cuts off spent electrons/positrons just near the beam orbit and reduces back-3

PRESENT LUMINOSITY LIMITATION
AND PROBLEM AT KEKBThe luminosity of KEKB has been limited by the several
problems. (1) Installation of the solenoids to suppress theelectron cloud instability has improved the problem as described before but not resolved it completely. (2) It turned
out that the LER single beam blowup is sensitive to the filling pattern. We have tried various filling patterns to increase the number of bunches. But we could not get higher
luminosity than that with 4 rf bucket spacing. (3) The total beam current is limited by the heating of vacuum components due to the synchrotron radiation or HOM. And thebunch current is also limited by the heating of the HOM
damper of the superconducting cavity for HER. (4) beam
background for Belle detector.

then the luminosity is recovered.
F. Zimmermann have explained that ”egure” problem
comes from a significant tune dependence and the existenceof flip-flop solutions for head-on collisions by evaluating asimplified linear model of beam-beam interaction[8].

Figure 2: Specific luminosity per bunch as a function of thebunch current product in the case of all solenoid OFF(●),
solenoid of 400 m OFF(●) and All solenoid ON(●).

Figure 4: This figure shows a typical ”Egure” pattern.

4

Figure 3: The data for the 3 rf bucket (●,●) spacing patternshow lower specific luminosity than that for the 4 rf bucket(●) pattern.

3.1”Egure” problem

Sudden drops of the luminosity, so called ”Egure” at
KEKB, are frequently observed. Figure 4 shows a typical”Egure” pattern. The ”Egure” accompanies the LER horizontal beam size growth. (sometimes accompanies verticalbeam size growth.) When ”Egure” is occurred, we make thehorizontal beam separation (∼ 50 µm ) for short time and

BEAM-BEAM SIMULATION

Newly, a strong-strong beam-beam simulation code wasdeveloped by K. Ohmi[9] to study beam-beam effect. In
that simulation, both of the colliding beams are represented
by macro-particles. The electron-magnetic fields of eachrelativistic beam are obtained by solving the Poisson equation for the charge distribution of the macro-particles. At
each turn, the electron-magnetic fields are calculated foreach beam, and then these beams are allowed to interact
with each other through the fields. A transformation of thecollided bunch across one revolution through the ring is calculated by using a beam transfer matrix. The effects of radiation damping are quantum excitation are included in thiscode. The machine errors can be included.
We have carried out simulations for the KEKB parameters which were used in operation and compared theseresults with experiments. A 64×128 mesh with horizontal and vertical sizes of 20×0.4 µm mesh was used, respectively. Both beams are represented by 100,000 macroparticles, typically. The macro-particles are tracked for
45,000 turns. Due to the fast progress in computing power,
the strong-strong beam-beam simulation becomes feasible.
But it still requires a large amount of computer resources.
Figure 5 shows the longitudinal slice number dependence of specific luminosity. Although the slice number
should be bigger than 20, but we usually used 5 longitudinal slices due to the limited computing resources. Even if
longitudinal slice number is 5, the simulation results are in
reasonable agreement with measurements qualitatively inmany cases. For a simulation for one tune point, it takes

25

30

35

Specific luminosity versus current productBeam-beam effects cause an increase in vertical beam
size and subsequent decreases in specific luminosity. Figure 7 shows the simulation of the specific luminosity versus the beam current products. The measured bunch current and bunch length are also used as input parameters for
simulations. The simulation is in good agreement with theexperiment.

Vertical emittance dependence of Luminosity

As shown in the Figure 8, the beam-beam simulation
predicted that (1) the vertical emittance of HER can be optimized to get a higher luminosity and (2) the vertical emit-

1.2

1.1

0.56

2

0.51

0.52

1.1
1.2

1.3

1.5

1.9

1.8
1.8
1.5 1.6 1.7
1.7
1.8
1.7
1.9
2
1.9
2
2
1.8
2
2.1
1.9
1.8
2
2.1 2.1
2
1.7
2 1.9
1.8

1

1.1
1.2

0.9

1.1 1.1
1.2

1.3
1.5
1.5
1.6

1.8

0.58

1.1
1.1

1.5

0.53

1.4
1.5

1.1

1.2
1.2

1.3

0.54

0.55

LER νxFigure 6: The result of LER tune survey by the strongstrong beam-beam simulation without errors (Top graph)and with the error of the vertical crossing angle of 0.1 mrad
(Bottom graph).
12x10

Lspec /bunch [/cm2/sec]

Tune Survey

1.4

0.60

1.1
0.9

1.1

20

1.6
1.8

1.3 1.2
1.1
1 1
1.2
1.4
1.4
1.7
1.5

1.2

15

1.8
1.7
1.6
1.9 1.8

1.1

10

1.5

1.3
1.2

1.3
1.4

1.9

5

2

0.62

1.7 1.6
1.6
1.6
1.7 1.6

1.8
2 2 1.9
1.9
1.8
1.5
1.6
1.7

0.55

2.1

0

0

0.64

LER νy0

1.8 1.7

0.54

1.2

1.8

0.66

0.53

LER νx

1.2

2

0.52

1.3

1.2

2

0.51

1.4
1.5

1.4

4

1.5
1.6

1.5

4

2

2 2
1.9
1.8

1.3

6

2.1

1.4

6

2.1

1.4

2

1.8

Since the luminosity at KEKB is sensitive to the tune,
the tune survey is a very important tuning issue. We haveshifted the vertical tunes above a half integer for both rings
as described before.
The beam-beam simulation without errors shows thatνx ∼45.51, νy ∼44.64 is the best point in that area(theupper graph of Figure 6). We have tried to the LER
vertical tune of 44.64 several times. But the luminositywith that tune is lower than that with the present working
point(νx ∼45.51, νy ∼44.57), which is found by a trial anderror method.
The simulation with the error of vertical crossing angle
explains the lower luminosity at the tune of ν x ∼45.51,
νy ∼44.64 is caused by machine error(the bottom graph of
Figure 6).

4.3

0.60

0.56

Figure 5: Longitudinal slice number dependence of specificluminosity. They were tracked for 20,000 turns, respectively. The yellow filled circle is(●) is the luminosity perbunch, the red filled triangle (▲) and the filled box (■) is
the vertical beam size of LER and HER, respectively.

4.2

0.62

8

No. of longitudinal slice

4.1

1.9

0.64

0.58

Luminosity w/o beam-beam effect
8

2.1

2.2

1.8

10

1.9
2
1.5
1.7
1.4
2.1
1.5
1.9
2.2
2 1.9
1.3 1.2
1.5
1.3
2.4
1.4
1.1 1
1
2.5
2.3
2.3
1.2 1.1
2
2.1
1.4
1.8
2 1.9
1.3
1.2
1.7
1.6
1.9
1.9 1.9
1.7 1.6
1.4
2
1.8
1.9
1.8
1.8
1.6
1.6
1.7
1.3
1.5
1.1
1.7
1.5
1.9
1.2 1.1
1.8
2
1.7
1.6
2
2.1
1.2
1.9
2.1
1.1
1.8
2

σy [µm]Luminosity /bunch [/cm2/sec]

30

10x10

0.66

LER νyabout 5 days on the Unix workstation of AP3000 (Sun) andabout 4 hours on the supercomputer of SR8000F1 (Hitachi),which have 12 GFLOPS for each node under above conditions.

-3

10
8
6
4
2
300

350

400

450

500

550x10

3

2

LER_Cur*HER_Cur [mA ]Figure 7: Specific luminosity/bunch as a function of thecurrent products. The red solid line is the experimental result(May 2, 2001, Fill 4811) and the blue filled box (■) is
the simulation result. The longitudinal slice number is 10
in this simulation.

tance dependence of the luminosity for KEKB is stronger
than that for the case of zero-crossing angle.
The vertical emittance feedback system is realized by socalled ”iSize” feedback system at KEKB[10]. At one of thestrongest non-interleaved sextupole pairs in the arc sectionof HER, an anti-symmetric bump is made by three dipole
correction magnets. This bump converts the horizontal dispersion to the vertical. It leaks out around the whole of thering. The created xy-coupling is closed in the bump. Thisdispersion enlarges the vertical emittance. ” iSize” system
at KEKB works well.

2.65σy [µm]Luminoisty / Bunch [cm-2sec-1]

6

2.4

4
2.2

3

[5] Y. Z. Wu, Y. Funakoshi, M. Tawada, K. Ohmi ”A new working point for the KEKB”, HEACC2001, Tsukuba, March(2001).
[6] K. Kanazawa, K. Sato, N. Akasaka, T. Kageyama, Y. Suetsugu, Y. Takeuchi, ”Development of the Movable Mask System for KEKB”, EPAC2000, 2301 (2000).
[7] Y. Suetsugu et. al., HEACC2001, Tsukuba, March (2001).

2.0

2
5

10

15

20

25

30x10

[8] F. Zimmermann, in these proceedings.

-10

HER Vertical Emittance [m][9] K. Ohmi, K. Hirata and K. Oide, Phys. Rev. E49 751, 1994.
[10] N. Iida et. al. , HEACC2001, Tsukuba, March (2001)

Figure 8: Vertical emittance dependence of luminosity.
Vertical beam size of LER(4), HER( ), and Σ(blue solidline), Luminosity with a crossing angle of ± 11 mrad (●),
Luminosity without a crossing angle( ).

5SUMMARY

The peak luminosity of 4.1×1033 cm−2 sec−1 wasachieved at KEKB and the present capability for delivering
integrated luminosity is about 4.7 fb−1/month. Installationof the solenoids to suppress the electron cloud instability
has improved the situation but not resolved the problem.
The machine stability has been improved by moving to thetune above a half integer and the continuos tune monitor ofpilot bunches. The beam-beam simulation is in reasonableagreement with measurement in many cases.

6 FUTURE PLAN
(1) Since KEKB has a crossing angle, a shorter bunch
length is favorable for a geometrical luminosity reduction.
But we are afraid that the shorter bunch for HER may cause
more heating of HOM dampers. Anyway, we will try to domachine study to shorten the LER bunch length.
(2) As we mentioned above, installation of the solenoids
to suppress the electron cloud instability has improved the
problem but not resolved it. During this summer shutdown,
we will add more solenoid to LER.
(3) The injection rate for positron beams is 1.5 mA,
which is the design value. We will try to introduce thetwo-bunch acceleration in order to minimize injection time.
This plan would almost double the injection rate, and the injection time would be reduced by 1/2.

7 ACKNOWLEDGEMENTS
The authors would like to acknowledge the members of
KEKB accelerator group and Belle group.

8 REFERENCES[1] KEKB B-Factory Design Report, KEK Report 95-7, (1995).
[2] http://www-acc.kek.jp/WWW-ACC-exp/KEKB/KEKBhome.html[3] J. W. Flanagann et. al. PAC97.
[4] H. Fukuma et. al., HEACC2001, Tsukuba, March (2001).