Performance of KEKB with Crab Cavities
Y. Funakoshi, T. Abe, K. Akai, M. Akemoto, A. Akiyama, M. Arinaga, K. Ebihara, K. Egawa,A. Enomoto, J. Flanagan, S. Fukuda, H. Fukuma, K. Furukawa, T. Furuya, K. Hara, T. Higo,
S. Hiramatsu, H. Hisamatsu, H. Honma, T. Honma, K. Hosoyama, T. Ieiri, N. Iida, H. Ikeda,
M. Ikeda, S. Inagaki, S. Isagawa, H. Ishii, A. Kabe, E. Kadokura, T. Kageyama, K. Kakihara,
E. Kako, S. Kamada, T. Kamitani, K. Kanazawa, H. Katagiri, S. Kato, T. Kawamoto,
S. Kazakov, M. Kikuchi, E. Kikutani, K. Kitagawa, H. Koiso, Y. Kojima, I. Komada,T. Kubo, K. Kudo, N. Kudo, K. Marutsuka, M. Masuzawa, S. Matsumoto, T. Matsumoto,
S. Michizono, K. Mikawa, T. Mimashi, S. Mitsunobu, T. Miura, K. Mori, A. Morita, Y. Morita,
H. Nakai, H. Nakajima, T. T. Nakamura, H. Nakanishi, K. Nakanishi, K. Nakao, S. Ninomiya,
M. Nishiwaki, Y. Ogawa, K. Ohmi, S. Ohsawa, Y. Ohsawa,Y. Ohnishi, N. Ohuchi, K. Oide,
M. Ono, T. Ozaki, K. Saito, H. Sakai, Y. Sakamoto, M. Sato, M. Satoh, K. Shibata, T. Shidara,
M. Shirai, A. Shirakawa, T. Sueno, M. Suetake, Y. Suetsugu, R. Sugahara, T. Sugimura,T. Suwada, O. Tajima, S. Takano, S. Takasaki, T. Takenaka, Y. Takeuchi, M. Tawada,
M. Tejima, M. Tobiyama, N. Tokuda, S. Uehara, S. Uno, Y. Yamamoto, Y. Yano, K. Yokoyama,
Ma. Yoshida, Mi. Yoshida, S. Yoshimoto, K. Yoshino
KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
E. Perevedentsev, D. N. Shatilov, BINP, Novosibirsk, Russia
Abstract

Table 1: KEKB Machine Parameters.

20 years after they were initially proposed, in February
2007 crab cavities are for the first time installed in an operating collider, KEKB. The commissioning of KEKB withcrab cavities is reported, and the performance of the collider is compared with the performance without crab cavities and with the beam-beam simulation. Operational experience of the crab cavities with beams is described.

KEKB B-FACTORYKEKB B-Factory [1] has been operating at KEK since1999 for the e+e- collision experiment mainly at the Υ(4S)
resonance. KEKB is composed of the low energy positronring (LER) at 3.5 GeV, the high energy electron ring (HER)
at 8 GeV, and an injector linac. Two beams collide at thephysics detector named “Belle”. The machine parameters
are listed in Table 1. Figure 1 shows the history of KEKB.
The highest luminosity, 1.72×1034cm−2 s−1 , was achievedin Nov. 2006. The peak luminosity is higher than the design by 70 % mainly due to smaller βy∗ (6 mm vs. 10 mm),horizontal betatron tune closer to a half integer (LER:0.505/ HER:0.511 vs. 0.52), and higher stored current in the
HER (1.35 A vs. 1.1 A). The daily integrated luminosity
is as twice high as the design due to Continuous Injection
Mode as well as acceleration of 2 bunches per an rf pulse
at the linac. The electron clouds in the LER have been
mitigated up to 1.8 A with 3.5 bucket spacing by solenoid
windings of 2,200 m.

CRAB CROSSING SCHEME
One of the main design features of KEKB is the horizontal crossing angle of 22 mrad, at the interaction point

EnergyCircum.
φcrossIbeam
Nbunches
Ibunch
εx
βx∗
βy∗
σy∗
Vc
νx
νy
νs
ξx
ξy
Lifetime
Lumi.
Lum/day

May 2008
LER
HER
3.5
8.0
3016
crab crossing
1619
854
1584
1.02
0.539
15
24
90
90
5.9
5.9
1.1
1,1
8.0
13.0
.505
.509
.567
.596
-.0240 -.0204
.099
.119
.097
.092
94
158
16.10
1.092

Nov. 2006
LER
HER
3.5
8.0
3016
22
1662
1340
1387
1.20
0.965
18
24
59
56
6.5
5.9
1.9
1.9
8.0
15.0
.505
.509
.534
.565
-.0246 -.0226
.117
.070
.105
.056
110
180
17.12
1.232

GeV
m
mrad
mA
mA
nm
cm
mm
µm
MV

min.
/nb/s
/fb

(IP). Although there are many merits in the crossing angle scheme, the beam-beam performance may degrade.
The design of KEKB predicted that the vertical beambeam parameter ξy is as high as 0.05 if betatron tunes areproperly chosen and actually KEKB has already achievedξy ∼ 0.056. Thus the beam-beam issues associated withthe crossing angle was not critical if ξy is lower than 0.05
or so. The crab crossing scheme was proposed in 1988
by R. Palmer[2] as an idea to recover the head-on collision with the crossing angle for linear colliders. It has

Figure 1: History of KEKB.

Figure 2: Predicted beam-beam parameters by the strongstrong beam-beam simulations with the crossing angle of
22mrad (purple) and the head-on(crab crossing) (red).
Some experimental data are also shown with closed circles.
been also shown that the synchro-betatron coupling terms
associated with the crossing angle in ring colliders are canceled by the crab crossing[3]. The crab crossing scheme
has been considered in the design of KEKB from the beginning as a backup measure against the crossing angle.
Once, the crab cavities seemed non-urgent because KEKB
achieved ξy > 0.05 at the early stage of the operation (in2003). However, recently an interesting beam-beam simulation results appeared[4], predicting that the head-on or
the crab crossing provides higher ξy > 0.1, if combinedwith the horizontal tune very close to the half integer. Figure 2 shows the comparison of ξy for the head-on (crabcrossing) and the crossing angle with a strong-strong beambeam simulation. Then the development of the crab cavities has been revitalized. The original design of KEKB had

two cavities for each ring on both sides of the IP so that the
crab kick excited by the first cavity is absorbed by anotherone. The new single crab cavity scheme extends the region
with crab orbit until both cavities eventually merge to eachother in a particular location in the ring. Then it needs only
one cavity per ring. The layout is shown in Figure 3. This
scheme not only saved the cost of the cavities, but made it
possible to use the existing cryogenic system at Nikko forthe superconducting accelerating cavities also for the crab
cavities. The beam optics was modified for the crab cavities to provide necessary magnitude of the beta functions at
the cavities and the proper phase between the cavities andthe IP. A number of quadrupoles have switched the polarityand became to have independent power supplies.

Figure 3: Layout of the crab cavities in the KEKB rings.

Table 2: Typical parameters for crab cavities. The crossing
angle, the horizontal beta functions at the IP and the crab
cavities, the horizontal tunes, the horizontal phase advancefrom the cavities to the IP, the crab voltage and the RF frequency are shown.
LER
HER
φcross22
mrad
βx∗
80 ∼ 90 80 ∼ 90
cm
βxC
68
130
m
νx
45.50644.511
ψxC /2π
0.25
0.25
VC
0.83
1.37
MV
fRF
508.89MHz

MACHINE STUDY AND PHYSIC RUN
WITH CRAB CAVITIESThe crab cavities were installed at KEKB during the winter shutdown in FY 2006[5]. A dedicated machine timefrom Feb. 13 2007 to the end of June 2007 was devoted tothe commissioning of the crab cavity system and the machine study with the crab crossing.[6] In most cases, thebeam study was done with relatively small beam currents
typically 100mA (LER) and 50mA (HER). The crabbing
motion of the beams by the crab cavities was confirmed
by observing tilts of bunches with the streak camera[7]. A
high beam current operation of the crab cavities was also
tried for different two purposes. Firstly, we hoped to confirm that a high luminosity is actually achieved with the
crab on. In the high beam current operation, the peak luminosity exceeded the design luminosity of 1×1034cm−2 s−1 .
Secondary, we confirmed that the nominal beam currents
before the installation of the crab cavities can be storedwith the crab cavities detuned. This means that we can return to the situation before the crab installation by detuning
them in case that the crabs are serious obstacles for the highluminosity. In the autumn run in 2007 following the beam
study, the physics operation started with the crab cavity on.
Since then, we have been operating KEKB with the crab
cavities on. So far, the highest luminosity with the crab
crossing is 1.61 × 1034 cm−2 s−1 . This value is somewhat
lower than before the crab installation. However, the value
was achieved with much lower beam currents, particularlyfor HER. A comparison of machine parameters before andafter the crab installation is also shown in Table 1.

Beam-beam performance with crab crossing
Figure 4 shows the specific luminosity as function of thebunch current product. In the figure, the points in thin-blue
are data of the 22mrad crossing angle in the physics run.
The red points denote data of the crab crossing taken in the
dedicated beam study and in most cases the bunch spacing
was as long as 49 RF buckets. The data in green was takenin the physics run with the crab crossing when the highest luminosity was achieved with the crab crossing. In thiscase, averaged bunch spacing was 3.06 RF buckets. Since

Figure 4: Beam current dependence of specific luminosity.
there is no big difference between the long and short bunch
spacings, effects depending on the bunch spacing such as
the electron clouds are not very important for the specificluminosity in the present operation condition. In the figure, also shown is the specific luminosity predicted by thebeam-beam simulations. Both predictions with and without the crab crossing are shown. As seen in the figure, theexperimental data are consistent with the simulation in caseof the 22mrad crossing angle. On the other hand, in case of
the crab crossing, the experimental values are much lower
than the predictions particularly at the high bunch currents,
although at the low bunch currents there is a good agreement between them. This low specific luminosity at highbunch currents is a serious problem. Another problem withthe crab crossing is that the bunch current product is limited at around 0.85mA2 due to decreases of beam lifetime.
This problem is also serious, since the design value of theSuperKEKB is 1.53mA2 . This beam current limitation is
not predicted by the beam-beam simulation. In Figure 1,
some experimental values of the vertical beam-beam parameter are shown. As seen in the figure, the experimentvalue of the 22mrad crossing angle is consistent with thesimulation. In case of the crab crossing, however, the experimental value is much lower than the simulation at thehigh bunch currents. The maximum vertical beam-beam
parameter with the crab crossing exceeds 0.093. This value
is very high in a usual sense, which indicates the potential
superiority of the crab crossing.

POSSIBLE CAUSES OF LUMINOSITY
RESTRICTION
We have not yet identified the cause of the low specificluminosity at the high bunch currents, although we havebeen struggling with the problem. Our efforts are discussed
in more details elsewhere [8]. In this section, we briefly
summarize our efforts to solve the problem.
Too many tuning parameters? In the routine luminosity tuning of KEKB, we make tuning on many parameters such as the orbital offsets at the IP and the crossing
angles in both horizontal and vertical directions, the local
x-y coupling at the IP, the horizontal and vertical dispersion

at the IP and their slopes, the vertical waist points at the IP,
the crab voltages, the x-y coupling parameters at the crab
cavities, the betatron tunes and so on. In the conventional
method of tuning at KEKB, most of these parameters (except for the parameters optimized by observing their own
observables) are scanned one by one just observing the luminosity and the beam sizes. One possibility of the low
specific luminosity is that we have not yet reached an optimum parameter set due to too wide parameter space. As amore efficient method of parameter search, we introducedin autumn 2007 the downhill simplex method for 12 parameters of the x-y coupling parameters at the IP and thevertical dispersions at the IP and their slopes. These 12 parameters can be searched at the same time in this method.
We have been using this method since then. However,even with this method an achievable specific luminosity
has not been improved, although the speed of the parametersearch seems to be rather improved. Our method of parameter search was examined by the beam-beam simulation.
The same procedures as the parameter scan or the simplex
search were performed in the simulation with intentionallyintroduced errors for the 12 parameters. The simulation
showed that we can reach the parameter set which gives asatisfactory luminosity, if the errors are in the range of ourusual tuning.

Figure 5: Beam current dependence of specific luminositywith different horizontal beta functions at the IP.
Beam lifetime issue In the luminosity tuning, wesometimes encounter the situation that we can not set parameters giving a higher luminosity due to poor beam lifetime. We have been suspecting that poor beam lifetime
brings the low specific luminosity at high bunch currents.
As for the process which affects beam lifetime, we recently
found a process which might be responsible for the lifetime decrease. This is the dynamic beam-beam effects; i.e.
the dynamic beta effect and the dynamic emittance effect.
Since the horizontal tune of KEKB is very close to the half
integer (typically .506), the effects are very large. The horizontal beta function at the IP (βx∗ ) shrinks from 0.9m to0.2m and the horizontal emittance (εx ) is enlarged from
18nm to 55nm with νx of .506 and the unperturbed beambeam parameter (ξx0 ) of 0.09. The change of the beta function at the IP means a large beta beat all around the ring.

In this situation, we found that the horizontal beam sizes ataround the crab cavity in both rings are very large (typically7mm) at the high bunch currents and the physical aperture
there is only around 5 σx . Therefore, there is a possibility
that the physical aperture around the crab cavities affects
the beam lifetime seriously. If this is true, we can mitigate the situation by lowering the horizontal beta function
at the crab cavities, which is possible by enlarging βx∗ without changing the crab voltages. We performed an experiment where we enlarged βx∗ from 0.8m to 1.5m for bothrings. The experimental result is shown in Figure 5. The
specific luminosity with βx∗ = 1.5m is shown in the magenta color. The values of the beam-beam simulation are
also plotted with two different values of the global x-y coupling. A remarkable thing with this new optics is that the
maximum bunch currents increased. It seems that the causeof this bunch current limitation is physical aperture aroundthe crab cavities associated with the dynamic beam-beameffects. However, the tendency that the specific luminosity
agrees with the simulation at the low bunch currents anddisagrees at the high bunch currents still exists even withthis new optics. Therefore, we can not conclude that thebeam lifetime issue creates the steeper slope of the specificluminosity than the beam-beam simulation.
Synchro-betatron resonance In the course of KEKB
operation, it turned out that the synchro-betatron resonances of (2νx + νs = integer) and (2νx + 2νs = integer)
affects the KEKB performance seriously. Nature of theresonance lines was studied in details during the machine
study on the crab crossing last year. We found that the resonances affect (1) single-beam lifetime, (2) single-beam
beam sizes (both in horizontal and vertical directions),(3) two-beam lifetime and (4) two-beam beam sizes (bothin horizontal and vertical directions) and the effects arebeam current dependent. The effects lower the luminosity directly or indirectly through the beam-size blowup,
the beam current limitation due to poor beam lifetime orsmaller variable range of the tunes. The resonance lines
in HER are stronger than those in LER, since we do nothave a local chromaticity correction in HER. In the usual
operation, the horizontal tune of LER can be set below theresonance of (2νx + νs = integer), while that of HER is
just above the resonance line, although the lower tune ispreferable according to the beam-beam simulation.
The strength of the resonance lines is strongly dependent on the choice of sextupole magnets. A large amountof efforts has been devoted for searching a better set of sextupole magnets [9][8] and they contributed to the increaseof the luminosity. At present, there is no direct evidence
that the synchro-betatron resonances are responsible for the
low specific luminosity at the high bunch currents. However, we still think that they are a possible candidate.
Phase errors of crab cavity Fast noises may induce
some loss in the luminosity. According to the beam-beamsimulation, allowed phase error of the crab cavities for N√turn correlation is 0.1× N degrees. On the other hand, themeasured error under the presence of the beams was lessthem 0.01 degree for fast fluctuation ( 1kHz) and lessthan 0.1 degree for slow fluctuation (from ten to several
hundreds Hz). Then, the measured phase error is muchsmaller than the allowed values given by the beam-beamsimulation.
Other possibilities There are yet other possibilities
that may degrade the specific luminosity.
• The vertical crab at the IP, which is created by someerrors related to the crab kick such as a mis-alignmentof the crab cavity and the local x-y coupling at the crab
cavity, degrades the luminosity?
• An unexpectedly large vertical single-beam emittancedegrades the luminosity?

we were troubled with frequent trips of the HER crab cavity. This problem was solved by lowering the crab voltage,
which was possible by enlarging the horizontal beta function at the crab cavity, and RF conditioning. In the wintershutdown following Period 2, the cavities were warmed up
once again to the room temperature. During Period 3, thetrip rate of the HER crab cavity seems to be more or lessstable, while that of the LER crab has a tendency to increase slowly after the warm-up. Generally speaking, theHER crab cavity shows a higher trip rate than that of LER
corresponding to the higher crab voltage as shown in Table
2. It seems that the situation of the trip rate has reached amore or less stationary state and the similar situation willcontinue from now on. As for causes of the trips, mostof HER cases are breakdowns of superconductivity due todischarge in the cavity. On the other hand, causes of LER
cavity are discharge in the coaxial coupler or at the input
coupler.

• The cross talk between the beam-beam effects and thelattice non-linearity affects the luminosity? [10]• Fast noises from the transverse bunch-by-bunch feedback system degrades the beam-beam performance?
These possibilities have been investigated by experiments and/or beam-beam simulations. However, we have
not yet found a promising explanation for the degradationof the specific luminosity.

EXPERIENCE OF CRAB CAVITYOPERATION WITH BEAMS
The initial goal of the beam study of the crab cavities wasto prove that the high beam-beam parameters predicted by
the simulation is actually achieved in a real machine. This
study could be done with relatively low beam currents witha fewer number of bunches. A high beam current operationof the crab cavities had the second priority, since their tolerance against the high beam currents was unknown. However, they have been working much more stably than theinitial expectation and are presently being used in the usualphysics run. Figure 6 shows a history of the trip rate of the
crab cavities. Period 1 in the figure was a dedicated machine time for the study of the crab cavities and the crab
crossing. In most of cases, the beam currents are rather
low, typically 100mA (LER) and 50mA (HER). Around the
6th week, the maximum attainable kick voltage of the LER
crab cavity dropped suddenly from ∼ 1.5MV to ∼ 1.1MV
for an unknown reason. In the middle of this period, we had
to warm up the system up to the room temperature to recover from frequent trips of LER carb cavities. It was also
expected that the performance degradation of the LER crab
cavity was recovered with the warm-up. However, the performance was not improved and this problem has not beensolved since then. In the summer shutdown following Period 1, the cavities were warmed up again to the room temperature. From Period 2, the use of the crab cavities in theusual physic run started. At the beginning of this period,

Figure 6: Trip rate of crab cavity system.

ACKNOWLEDGMENTS
The authors thank H. Sugawara, Y. Totsuka, A. Suzuki,
F. Takasaki, Y. Kamiya, S.-I. Kurokawa, M. Yamauchi,
and the Belle Collaboration for supporting this program,
A. Hutton and the members of the KEKB Accelerator Review Committee for various suggestions for years, and R.
Calaga, F. Zimmermann and M. Zobov for useful discussions.

REFERENCES[1] KEKB B-Factory Design Report, KEK-Report-95-7, June
1995.
[2] R. B. Palmer, SLAC PUB-4707 (1988); In Proc. DPF Summer Study Snowmass 88, Snowmass, CO, 1988, ed. S.
Jensen. Singapore: World Sci. (1988), p.613.
[3] K. Oide and K. Yokoya, Phys.Rev.A40:315 (1989).
[4] K. Ohmi et al, Proc. of EPAC06, 616 (2006).
[5] K. Hosoyama et al., SRF2007, Peking University, Beijing,
China, MO405 (2007).
[6] T. Abe et al., Proc. of PAC07 (2007).
[7] H. Ikeda et al., Proc. of PAC07 (2007).
[8] Y. Funakoshi, Proc. Of Factories Workshop08, BINP(2008).
[9] A. Morita et al., Proc. of PAC07 (2007).
[10] K. Ohmi et al., in these proceedings.