Compensation of the Crossing Angle with Crab Cavities at KEKB
T. Abe, K. Akai, M. Akemoto, A. Akiyama, M. Arinaga, K. Ebihara, K. Egawa, A. Enomoto,J. Flanagan, S. Fukuda, H. Fukuma, Y. Funakoshi, 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, K. Mori, A. Morita, Y. Morita, H. Nakai, H. Nakajima, T. T. Nakamura,
H. Nakanishi, K. Nakanishi, K. Nakao, S. Ninomiya, 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, N. Yamamoto,Y. Yamamoto,Y. Yano, K. Yokoyama, Ma. Yoshida, Mi. Yoshida, S. Yoshimoto, K. Yoshino,
KEK, Oho, Tsukuba, Ibaraki 305-0801, Japan
E. Perevedentsev, D. N. Shatilov, BINP, Novosibirsk, Russia
Abstract
The crab cavities have been installed in the KEKB B–
Factory rings to compensate the crossing angle at the collision point and thus increase luminosity. The beam operation with crab crossing has been done since February 2007.
This is the first experience with such cavities in colliders
or storage rings. Although these crab cavities have beenworking without serious issues, the gain in the luminosity
has not been much higher than the geometrical gain, andthe reason is under the study.

KEKB B–FACTORYKEKB B–Factory[1] has been operating since 1999 forthe collision experiment mainly at the Υ(4S) resonance.
KEKB consists of the low energy positron ring (LER) at 3.5
GeV, the high energy electron ring (HER) at 8 GeV, and theinjector linac. Two beams collide at the Belle detector. The
machine parameters are listed in Table . The highest luminosity, 1.72 × 1034 cm−2 s−1 , was recorded in Nov. 2006.
The peak luminosity became 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 the Continuous Injection Mode as well as
acceleration of 2 bunches per an rf pulse at the linac. The
electron cloud in the LER, which was much more severe
than thought in the design, has been mitigated up to 1.8 A
with 3.5 bucket spacing by solenoid windings for 2,200 m.

CRAB CROSSING
One of the main design features of KEKB is the horizontal crossing angle, 22 mrad, at the interaction point(IP). Although there are a lot of 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 ≈ 0.055. 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, invented by R. Palmer[2],was an idea to recover the head-on collision with the crossing angle. It has been also shown that the synchrotronbetatron coupling terms associated with the crossing angle
are canceled by crab crossing[3]. The crab crossing scheme
has been considered in the design of KEKB from the beginning as a backup solution for the crossing angle. Whenξy reached 0.05 at KEKB around the year 2000, the crab
crossing once seemed non-urgent. Then soon a prediction
by K. Ohmi’s beam-beam simulation appeared[4], showingthat a very high ξy beyond 0.1, or even higher than 0.2, will
be possible with head-on or crab crossing. Figure 1 shows
the comparison of ξy for the head-on (crab) and crossing
angle with a strong-strong beam-beam simulation. Thenthe development of the crab cavities has been revitalized.

Single Crab Cavity Scheme
The original design of KEKB had two cavities for each
ring, both side of the IP, where the crab kick excited by the
first cavity is absorbed by another one. The new single crab
cavity scheme extends the region with crab orbit until bothcavities eventually merge to each other in a particular location in the ring. Then it needs only one cavity per ring. In
the case of KEKB, this scheme not only saved the cost of
the cavities, but made it possible to use the existing cryogenic system at Nikko for the superconducting accelerating
cavities for the crab cavities. The layout is shown in Fig. 2.
The beam optics was modified for the crab cavities toTable 1: Machine parameters of KEKB at its best before crab crossing, comparing to
the design. All luminosities are recorded values at the Belle detector. The best data
were recorded on Nov. 16, 2006, except for the integrated luminosities.
Best
LER HER
Circumference
Beam Energy
Stored beam current
Number of bunches / ring
Bunch current
Bunch spacing
Horizontal Emittance
Horizontal β at IP
Vertical β at IP
Horizontal size @ IP
Vertical size @ IP
Hor. Beam-beam parameter
Ver. Beam-beam parameter
Bunch length
Horizontal rossing angle
Luminosity
R
R Luminosity / 1, 7, 30 days
Luminosity, total

C
E
I
Nb
Ib
sb
εx
βx∗
βy∗
σx∗
σy∗
ξx
ξy
σz
θx
L

DesignLER HER

3014
8
3.5
8
1.33
2.6
1.1
1389
5000
1.19
0.96
0.52
0.22
1.8–2.4
0.6
18
24
18
18
59
56
33
33
0.65
0.59
1.0
1.0
103
116
77
77
1.9
1.9
1.9
1.9
0.115
0.075
.039
.039
0.101
0.056
.052
.052
7
6
4
4
22
17.12
10
1.23, 7.82, 30.21∼ 0.6, −, −720
100 for 3 years
3.5
1.65

m
GeV
A

Table 2: Typical parameters for the crab
mA
m
nm
cm
cm
µm
µm

mm
mrad
/nb/s
/fb
/fb

crossing.
Ring
θx
βx∗
βxC
µx /2πψxC /2πVCωrf /2π

LER

HER
22

80
80
73
162
0.505
0.511
∼ 0.25 ∼ 0.25
0.95
1.45
509

mrad
cm
m

V
MHz

Figure 1: Enhancement of the vertical beam-beam parameter by
a head-on (crab) collision (upper curve) comparing to the crossing
angle of 22 mrad (lower curve), obtained by a strong-strong beambeam simulation. Parameters are same as the present KEKB.

provide necessary magnitude of the β-functions at the cavities and the proper phase between the cavities and the IP[5].
A number of quadrupoles have switched the polarity andbecame to have independent power supplies. The necessary
horizontal kick voltage of the crab cavity Vc must satisfy
θx
=
2

p

βxC βx∗ cos(ψxC − µx /2) VC ωrf
2 sin(µx /2)

Ec

,

(1)

where βxC , ψxC , µx , and ωrf are the horizontal β function
and the betatron phase relative to the IP at the crab cavity,
tune of the ring, and the rf frequency of the crab cavity,
respectively. The actual crab cavity may deflect the beam
by a magnetic field, but we can define “crab kick voltage”
by the effective change in the transverse momentum. The
resulting parameters for the crab cavities and beam optics
are shown in Table 2. The rf frequency of the crav cavity is
chosen equal to the accelerating cavities.

Figure 2: The layout of the crab cavities at KEKB with the LER(red) and the HER (green). Each ring has one crab cavity at the
Nikko straight section where the cryogenics already exists for theaccelerating cavities. Each ring is equipped with a streak camera.

CRAB CAVITIESDesign and Production
The crab cavity (CC) for KEKB was originally designed
by K. Akai since 1991[6] and has been already includedin KEKB Design Report. It is a superconducting cavity
at 4K to use the lowest transverse mode to give the horizontal crab kick. The main components of the crab cavity
is shown in Fig. 3.The cavity is horizontally squashed so
as to make the frequency of the vertical kick mode higher
enough than the horizontal mode that is tuned to the accelerating rf frequency, 509 MHz. As it has an accelerating mode lower than the crab mode, a coaxial beam pipe isequipped to make it propagate out. The coax is also used as
the frequency tuning of the crab mode by changing the in-sertion depth with a tuner rod externally driven by a piezo
device and a pulsed motor located in room temperature.
The higher order modes are basically damped by two absorbers made of ferrite, one in the large beam pipe and theother at the end of the coax. Some parasitic modes excitedaround the coax was mitigated by tilting the rod in the notch
filter[8]. The engineering design of the crab cavity, cryostat, and periferal devices was done by K. Hosoyama anda number of prototypes have been tested since 1994 by hisgroup[7], and finally converged into the present one.

ond. An independent measurement with a spectrum analyzer was done to detect faster phase fluctuation. The results of the phase fluctuation were within ±0.01 degree forfrequency region higher than 2 kHz, and within ±0.1 degree between about 20 Hz and 2 kHz for the both rings.
These results indicate that the high fluctuation in the LER
in Fig. 4 was in frequency region lower than 1 Hz. Bothmeasurement of the phase fluctuation with the data logger
and the spectrum analyzer were well below the requirement. The measurement by the data logger involves additional noise in phase detectors.

Figure 4: Phase distribution of the crab cavities for the LER (left)
and the HER (right) with the rf feedback. The standard deviationsof the phases are 0.023 deg and 0.010 deg for the LER and the
HER, respectively.

Figure 3: KEKB crab cavity consists of cavity cell (a), input
coupler (b), coaxial beam pipe made of Nb (c) and its stub support(d), ferrite higher order mode (HOM) absorbers (e), notch filter (f)to reflect back the crab mode, tuning rod (g) of the coax, jacket
type He vessels (h), and the support rods (i). The length in thez-direction shown in this figure is about 3 m, and the total system
including the cryostat is about 6 m.

Performance
The crab cavity for the HER was first assembled andtested in June 2006. Although the volage and Q-values satisfied the requirement, the cavity frequency were out of thetunable range. The reason was that the estimation of the relative thermal contraction between the cavity and the coax
was not quite adequate. After the correction of the alignment, the second test was done in October 2006, then all
performance satisfied the goal. The cavity for the LER was
assembled and tested in December 2006, and the result was
satisfactory. Both cavities were conditioned up to 1.8 MV
kick voltage, with the unloaded Q–values higher than 109
at the design voltage, 1.4 MV. The conditioning took lessthan a few days for the both cases.
As an example to show the performace of the crab cavities, Fig. 4 shows the rf phase stability achieved with the
rf feedback. The achieved level of the phase fluctuation
was well below the requirement even for the worse one (theLER). The reason why the LER was worse than the HER
was that the movement of the coax for the LER was not
smooth enough, showing some friction or backlash, whose
real cause has not yet been identified. The data in Fig. 4
were taken by a data logger with a time constant of 1 sec-

Figure 5: Crab cavities were installed in the HER (left) and theLER (right), one for each ring.

The both cavities were installed in the rings in the wintershutdown from the end of December 2006 through January
2007, as shown in Fig. 5. More conditioning was done after the installation. These cavities have been working withbeam showing enough stability. These cavities have been
warmed up a few times to 80K, and once to 300K to remove the absorbed gas. The number of trips per day per
cavity was about twice before the warm up to 300K, andreduced to about once and 1/2 for the HER and the LER,
respectively, after that.

FIRST BEAM TEST OF CRAB CROSSING
The first beam test of the crab cavities started on February 14, 2007. After beam storage without crab voltage
for a few days, the crab voltage was applied one by one.
The tuning were mostly done with 50 or 100 bunches perring in collision. The highest bunch current was kept below 1.5 mA in the LER, which was limited to protect the
BPM electronics, and 0.5 to 0.7 mA in the HER. The maximum luminosity with crab crossing was 1034 cm−2 s−1

with 1,000 mA and 540 mA in the LER and the HER, respectively, with 1091 bunches so far.

Observation of Crabbing
The very first test with the crab cavity was the observation of the kick in the horizontal orbit, changing the phaseof the crab rf. It fits to a sine curve very well and the resulting kick voltages agree with estimation from the rf powerin both rings within a few % errors.
Then the tilts of the bunches were observed by streak
cameras located in the rings. One of the merits of thesingle-cavity scheme is such an observation is possible, as
the tilt is everywhere in the ring. Figure 6 shows tilt ofbunches. The response of the tilt to the phase of the crab
cavities were right.

Figure 7: Specific luminosity per bunch with crab crossing (red)comparing to crossing angle (blue) as a function of the product ofbunch current. The highest ξy ∼ 0.088 was achieved at the arrow.

Figure 6: Images taken by streak cameras, which locate as Fig. 2,
show tilt of the bunches in the LER (left) and the HER (right)[11].

Effective Head-on Collision
As a result of the crab crossing, the response of the horizontal offset between two beams were greatly changed
from with the crossing angle. With the crossing angle, thebehavior of the beam, especially the vertical beam size of
the LER was not symmetric to the sign of the offset[9].
The vertical beam size blows up drastically when the HER
beam comes inside at the IP relative to the LER. In thiscase the head of the LER beam collides to the HER beamwith more horizontal offset, as both beams comes from theinside to the outside at the IP. The longitudinal asymmetryof the LER bunch charge caused by the impedance, morecharge at the head than the tail, is suspected as the causeof the asymmetry. Actually this asymmetry in the verticalbeam size has been utilized to control the horizontal offset,
as it has even better sensitivity than the horizontal beambeam kick.
By the introduction of the crab crossing, such asymmetry
disappeared or greatly reduced, since one of the sources of
the asymmetry, the crossing angle, went away. Then the
feedback looking at the vertical size became unusable andfeedback with horizontal beam-beam kick took place. Thisis a clear indication of the effective head-on collision.

Specific Luminosity
Figure 7 shows the achieved specific luminosity perbunch as a function of the product of bunch currents, comparing the crab crossing and the crossing angle. The high-est beam-beam parameter achieved with the crab crossing
was 0.088, while it was 0.055 with crossing angle. The
slope for the crab crossing data roughly follows a curvewith ξy =constant, for the current product between 0.4 to
0.8 mA2 . The curve may seem steeper below 0.4, but thereason is not known. The product of the bunch did not become higher than 0.9, as the lifetimes dropped rapidly. The
gain in the specific luminosity was not much higher thanthe expected geometrical gain, ∼ 15%.

Tuning Parameters
There are a number of knobs to tune up the crab crossing. Only a few of them can be tuned up with independent
observables besides the luminosity. Table 3 lists the tuning
parameters and its observables.
The issue is that so many knobs are optimized only by
the luminosity and the beam size. The number of suchknobs is about 30. It is in question that such multidimensional optimization actually reach the optimum startingwith the large unknown errors. The tuning process of theseknobs are slow due to the statistical error of the luminosity
monitor especially at low current. Another slowing factor
is that the data must be taken with the same beam currents
to minimize the current dependence for each setting of theknobs.
In many cases, the optimum setting of the knob is different for the luminosity maximum from the size minimumof the beam with the knob. Usually the size minima are
pursued for a few days scanning all knobs for a few cycles,
then switch to luminosity optimum. It is not clear that thiskind of algorithm is adequate.
One of the peculiar knobs for the crab crossing is to control the vertical crabbing at the IP. There are conceivablesources of the vertical crabbing such as x-y coupling at the
IP and at the crab cavities, tilt of the accelerating cavities.
The x-y coupling knobs at the IP and at the crab cavities

Table 3: Tuning knobs for the crab crossing and their observables. Many depend only on the beam size σy at thesynchrotron radiation monitor (SRM), besides the luminosity L.
Knob
Relative beam offset IP
Relative beam angle IP
Global closed orbit
Beam offset at crab cavities[10]Betatron tunes
Relative rf phase
Global couplig, dispersion, beta-beat
LER to HER crab voltage ratio
Rf phase of crab cavity
Vertical waist position
Local x-y couplings and dispersions at IP
Sextupole settings
X-y coupling parameter at the crab cavities
Crab kick voltage

ObservableBeam-beam kick measured by BPMs around the IP
BPMs around the IP
All ∼ 450 BPMs
BPMs around the crab cavity
tunes of non-colliding pilot bunches
center of gravity of the vertex
orbit response to kicks & rf frequency
response in the hor. beam-beam kick. vs. crab rf phasehor. kick vs. crab voltage response
L and σy at the SRM
L and σy at the SRM
L and lifetime
L and σy at the SRM
L and σy at the SRM

can basically compensate such effects, but again there is no
independent observable on this effect besides the luminosity and the beam sizes.

Discussions
The crab crossing has been tested at KEKB for about 4
months. The crab cavities has been working basically very
well providing the necessary kick voltage stably. Although
there are a lot of indications of the effective head-on collision, the specific luminosity has not reached the predictedvalue yet. There are a few speculation on the reason:• Too many knobs are tuned only by the luminosity andthe vertical beam size as described above.
• The horizontal tunes are close to the synchrotronbetatron resonance line 2νx + νz = integer. Actually single-beam blowup of the horizontal and verticalbeam sizes and drop of the beam lifetime were observed when the betatron tunes cross the resonanceline.[13] The magnitude of the blowup strongly depend on the setting of the sextupoles. It is possible toestimate the blowup in the model by considering of theequilibrium horizontal emittance in the synchrotron
phase space[12]. Such an optimization as well as the
dynamic aperture has been tried to find out a good solution of sextupoles.
• Negative momentum compaction factors have been
tried in both rings to examine the effect of the resonance above, expecting a sum and difference resonances may behave differently. It was not successful,
however, a longitudinal oscillation was found in the
LER caused by a single bunch microwave instability.

frequency: every
1 sec
1 sec
15 sec1 sec∼ 20 sec
10 min.
∼ 14 days∼ 7 days∼ 7 days∼1 day∼1 day each∼ 3 days∼ 3 days∼ 7 daysand 0.511). If the lattice has errors in the x–y coupling, such horizontal dynamic emittance may diluteto the vertical emittance. On the other hand, this effect can be cancelled if the local coupling at the IP isproperly corrected.

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 and F. Zimmermann for useful discussions.

REFERENCES[1] KEKB Design Report, KEK Report 95–7(1995), available at
http://kekb.jp.
[2] R. B. Palmer, Proc. of Snowmass DPF Summer Study
1988:0613(1988).
[3] K. Oide and K. Yokoya, Phys.Rev.A40:315(1989).
[4] K. Ohmi et al, Proc. of EPAC06, 616-618(2006)[5] A. Morita et al, Knoxville 2005, Particle Accelerator Conference* 865(2005).
[6] K. Akai et al., Proc. of B Factories, SLAC, U.S.A. 610 April 1992, SLAC–400 pp.181–188(1992), and also K.
Akai et al., Proc. of HEACC’92, p. 757(1992).
[7] K. Hosoyama et al, Asian Particle Accelerator Conference(APAC 98), Tsukuba, Japan, 23–27 Mar 1998, pp 828(1998).
[8] Y. Morita, et al, Proc. of the APAC 2007, Indore, INDIA,
Jan. 29 – Feb. 2, (2007).
[9] Y. Funakoshi, Proc. Of Factories Workshop, Cornell(2001).
[10] M. Masuzawa et al, Proc. of EPAC06, pp.613–615(2006).

• There was a speculation related to the dynamic emittance effect caused by the beam-beam effect as thehorizontal emittance largely increases when the horizontal tune is close to a half integer as KEKB (0.505[11] H. Ikeda et al, in these proceedings.
[12] K. Oide and H. Koiso, Phys.Rev.E49:4474-4479(1994).
[13] Y. Funakoshi et al, in these proceedings.