BEAM-BEAM EFFECT OBSERVED IN THE KEKB
Y. Funakoshi, K. Akai, K. Ebihara, K. Egawa, A. Enomoto, J. Flanagan, H. Fukuma,
K. Furukawa, S. Hiramatsu, T. Ieiri, N. Iida, H. Ikeda, T. Kageyama, S. Kamada, T. Kamitani,
G. Katano, S. Kato, M. Kikuchi, E. Kikutani, H. Koiso, M. Masuzawa, T. Matsumoto,T. Mimashi, T. T. Nakamura, H. Nakayama, Y. Ogawa, K. Ohmi, Y. Ohnishi, S. Ohsawa, N. Ohuchi,K. Oide, E. A. Perevedentsev∗ , S. Stanic, M. Suetake, Y. Suetsugu, T. Suwada, M. Tawada,M. Tejima, M. Tobiyama, N. Yamamoto, M. Yoshida, S. Yoshimoto, S. Win, Y. Wu† , Y. Yano,
F. Zimmermann‡ , KEK, Ibaraki 305-0801, Japan
Abstract
This report summarizes observed phenomena related tothe beam-beam effects in the KEKB collider. A general
performance of the beam-beam effect is described. An emphasis is put on the reduction of the specific luminositywith shorter bunch spacing.

1INTRODUCTION

Table 1 shows a parameter list of the KEKB at the recordpeak luminosity. This table tells some characteristic features of the KEKB. The present KEKB is filled with beams
at every 4th RF bucket. In the design[1], the number ofbunches was assumed to be around 5000 which means thatevery RF bucket is filled with particles (except for someabort gap). In the present KEKB, the specific luminosity isdecreased when the number of bunches is increased fromthe every 4th RF bucket case by reducing bunch spacing.
The 5 RF bucket spacing pattern is inhibited at the KEKB,
since this pattern induces a heating problem of the IP chamber. Although we once tried 6 bucket spacing, we could not
get higher specific luminosity than with 4 bucket spacing.
Therefore, 4 RF bucket spacing (∼8nsec) is the best choiceat the present KEKB. The other parameters are chosen under this restriction of bunch spacing.
It is notable that the bunch currents of the present KEKB
are much higher compared with the design values particularly in the HER (high energy ring). This is also a consequence of the bunch spacing restriction. To compensate
this unusually high bunch current to some extent, the horizontal emittance of the HER is enlarged compared with thedesign. On the other hand, the LER bunch current is not sohigh as the HER. Until very recent operations, the luminosity did not increase with a higher LER beam current thansome threshold current. It is believed that this luminosity saturation with the LER beam current arose from thebeam blowup due to the electron cloud. In this situation,
the LER beam current was limited by the electron cloudinstability in the sense that the luminosity did not increasewith a higher LER beam current. However, as a result ofcumulative installations of solenoid windings in the LER,
the single beam blowup from the electron cloud is not vis∗ visiting from BINP, Russia† visiting from IHEP, China‡ visiting from CERN, Switzerland

ible with the present maximum beam current. The scrubbing effect of the chamber wall also possibly contributed tosuppress the blowup. The present beam current limitation
comes from a heating problem in the IR region.
Another feature of the KEKB is that working points arevery close to the half integer resonance particularly in thehorizontal direction as is seen in the table. These horizontal tunes make the horizontal emittance large and the horizonal beta functions small to a large extent. This large emittance compensates the large bunch currents and contributes
to stabilize the beams against the beam-beam effect. As isseen in the table, both of the horizontal and vertical tunes ofthe both rings are located above the half integer resonance,
while the vertical tunes are above the integer resonance inthe design. In the early days of the KEKB, the verticaltunes were above the integer resonance. In February 2001,
the vertical tunes moved to above the half integer based on
results of new beam-beam simulations. This change of thetunes brought some increase of the luminosity.

2SPECIFIC LUMINOSITY AND
BEAM-BEAM PARAMETERS

To assess beam-beam performance, a common way is
to record the specific luminosity and the beam-beam parameters. In the following, these parameters are discussed.
One thing that one should note here is that these parameters
do not necessarily describe only beam-beam performance.
They could be affected by other beam blowup mechanisms
such as the electron cloud instability.
In Fig. 1 and 2, the specific luminosity per bunch isshown as function of a square root of a bunch current product. The specific luminosity (per bunch) is defined by apeak luminosity divided by a number of bunches and also
divided by a bunch current product of the two beams. The
specific luminosity should be constant, if the beam sizes do
not change. The slopes in the figures mean that the sizes
continuously shrink as the beam currents decrease in thecourse of the fills. The figures show comparisons of thespecific luminosity with 3 RF bucket spacing to that with 4
RF bucket spacing. The data in Fig. 1 was taken before thesummer shutdown in 2001 and that in Fig. 2 was after theshutdown. During the shutdown, additional solenoid coilsof about 800m in total were installed in LER. In Fig. 1, thespecific luminosity with 3 bucket spacing is much lower

εx (nm)βx∗ /βy∗ (m)bunch current
(mA)

LER
18
(18)
0.59/0.0062(0.33/0.010 )
1365(2600)

1223(5000)# of bunches
bunch current(mA)bunch spacing(nsec)
bunch length(mm@MV)ξx /ξyνx /νyLifetime(min@mA)
Luminosity(/cm2 /sec)

HER
24(18)
0.63/0.007(0.33/0.010 )918(1100)

1.12(0.52)

0.750(0.22)
8(2)5.3@6.6(calculation)
0.082/0.050(0.039/0.052)
45.512/43.566(45.52/44.08)

5.5@12.0(calculation)
0.073/0.041(0.039/0.052)
44.512/41.586(44.52/42.08)

106@1365

Figure 2: A specific luminosity as function of a square rootof the bunch current product. The data was taken on Nov.
9 and 10 in 2001 (after the summer shutdown).

299@91833

7.35 × 10(1.0 × 1034 )Table 1: Present performance compared with the design.
(Values in parentheses are the design values.)

4-bucket spacing

3-bucket spacing

Figure 1: A specific luminosity as function of a square rootof the bunch current product. The data was taken on July 11and 12 in 2001 (before the summer shutdown). The green
and red dots denote the data with 4 bucket spacing and 3bucket spacing, respectively.
than that with 4 bucket spacing. If the beam blowup is
induced purely by the beam-beam effect, the two curves inthis graph should overlap. Therefore, the different behaviorof the two curves indicates that a beam blowup mechanism
other than the beam-beam effect plays a part in the blowup.
Since the beam blowup is usually observed in the verticaldirection of the LER beam, the electron cloud instability is
the first candidate for this mechanism. However, even below the threshold beam current of this instability, the specific luminosity with 3 bucket spacing is much lower thanthat with 4 bucket spacing. Therefore, we can not attribute
this difference to the electron cloud instability alone. We

Figure 3: A current dependence of the specific luminosity with different bunch spacing of 4 bucket (red) and 24
bucket (green). These two data sets were taken in the sameday (March 10 2001).
might have to consider a synergistic effect of the beambeam effect and the electron cloud instability. Recently, E.
A. Perevedentsev et al. and K. Ohmi independently proposed a model in which a coherent beam-beam instabilityof the head-tail type could be induced by the beam-beameffect combined with some ring impedance [4] [5]. Thismodel might be applicable to the present case by considering the electron cloud as the impedance source. After
addition of solenoid coils during the summer shutdown in
2001, the situation changed. As is seen in Fig. 2, the specific luminosity with 3 bucket spacing is much improved,
while the improvement with 4 bucket spacing is small.
A more fundamental question is that the origin of thesteep slopes of the curves in Fig. 1 and 2. Since the continuous beam blowup during the fill seems quite unusualcompared with conventional colliders, the origin of thesebeam size enlargements has been controversial. There has
been some doubt that the beam blowup comes not fromthe beam-beam effect but from the electron cloud instability. This doubt seemed to be supported by an observationthat the beam blowup is mainly observed in the verticaldirection of the LER. To distinguish these two effects, anexperiment with longer bunch spacing of 24 RF buckets

Specific Luminosity /bunch [*1030 /cm2/sec/mA2]

40

exp. (F4108-4117, 3/10/2001)
simulation
initial condition of the simulation
30

20

100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sqrt(Bunch Current Product) [mA]Figure 4: A comparison of a measured specific luminositywith 24 bucket bunch spacing to that from the the beambeam simulation using a strong-strong code.
was done. With this bunch spacing, the effects of the electron cloud should be much smaller. In this experiment, weobserved the luminosity with beam currents lower than inusual physics operations. The result is shown in Fig. 3. As
shown in the figure, the specific luminosity with 24 bucket
spacing is almost the same as that with 4 bucket spacing.
This result indicates that the beam blowup in the beam current region of the usual physics run is originated not fromthe electron cloud instability but from the beam-beam effect. This explanation is also supported by a beam-beamsimulation. In Fig. 4, a result of the beam-beam simulationby using a strong-strong simulation code[3] is also shown.
Although a quantitative agreement between the simulationand the experiment is not so good, the simulation reproduces the tendency of the beam current dependence of thespecific luminosity. Fig. 4 also shows that the specific luminosity does not become constant even at a very low beam
current and this is also supported by the simulation. As forthe reason of the strong current dependence of the specificluminosity, we suspected that it may come from the crossing angle. However, even when we temporarily turned off
the crossing angle in the simulation, the current dependent
was still there. After that we suspected that the horizontal tune close to the half integer resonance may bring thestrong current dependence. However, the simulation result did not change very much with tunes which are offfrom the resonance. Therefore, we have not yet understoodthe origin of the strong current dependence of the specificluminosity. There still remains one more question. Theabove conclusion is that the main mechanism of the beam
blowup with 4 bucket spacing is the beam-beam effect. On
the other hand, with 3 bucket spacing, another mechanism(or the synergistic effect) plays some role. These two conclusions seem somewhat contradictory. This question isstill controversial.
The beam-beam parameters are commonly used as anindex of beam-beam performance. The beam-beam parameters at the record peak luminosity are also shown in
Table 1. The horizontal beam-beam parameters are calculated with the design emittance, since no serious horizontal
blowup is observed. Due to the large dynamic emittance ef-Figure 5: Specific luminosity with higher beam currents.
The red and green dots denote an usual physics run with 4
bucket spacing and an experiment with 24 bucket spacing,respectively. The LER and HER beam currents in the experiments were 300mA and 183mA at maximum, respectively.
fect, the actual horizontal tune shifts are much smaller thanthe beam-beam parameters in the table [2]. This may be
the reason why the unusually high horizontal beam-beam
parameters are possible at the KEKB. The vertical beambeam parameters are calculated from the measured luminosity on the assumption that the vertical beam sizes of thetwo beams are equal. We believe that this assumption ismore or less valid, since we rely on the beam size feedback
system [6] for maximizing the luminosity in the usual operation. The“hourglass” effect from a finite bunch lengthand degradation of the beam-beam parameters due to a finite crossing angle are also considered. As for the bunch
length, 7mm is assumed. The vertical beam-beam parameter of the HER is somewhat lower than the design. During
the summer shutdown of 2002, we will reinforce the cooling power of the IR radiation masks. After that we expectthat more beam current can be stored in the rings. Recently,
we made an experiment for the purpose of examining thebeam-beam effects with higher bunch currents. The resultof the experiment is shown in Fig. 5 together with a dataof a usual physics run. As is seen in the figure, the specificluminosity with higher bunch currents is on the extensionof the line corresponding to the usual operation. We observed no serious lifetime decrease even with the higherbunch currents. With still 4 bucket spacing, we can expect
a higher luminosity with higher beam currents.

3REFERENCES[1] KEKB B-Factory Design Report, KEKReport957, June 1995.
[2] Y. Funakoshi et al., ”Factories 2001”, Ithaca, 2001.
[3] K. Ohmi et al., Phys. Rev. E49 751, 1994.
[4] E. A. Perevedentsev and A. A. Valishev, Phys. Rev. SPECIAL
TOPICS4 024403, 2001.
[5] K. Ohmi, private communication.
[6] N. Iida et al., HEACC 2001, Tsukuba, March 2001.