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

FIRST BEAM COLLISION IN THE KEKB
Y. Funakoshi∗ , K. Akai, N. Akasaka, A. Enomoto, J. Flanagan, H. Fukuma, K. Furukawa,
S. Hiramatsu, K. Hosoyama, N. Huan, 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, 1-1 Oho, Tsukuba, Ibaraki 305-0801 Japan
Abstract

following expression.
∆y 0 + i∆x0

The first beam collision study was done in the KEKB double ring collider. Beam collision conditions were found by
searching beam-beam deflection curves in a trial-and-error
method. From these curves, beam sizes at IP and a luminoisty was estimated.

1PROCEDURE OF FINDING BEAM
COLLISION CONDITIONSx + iy{w( q)2(Σ2x − Σ2y )Σwhereyp2 ,σx2 + σx∗q2 ,Σy = σy2 + σy∗Σx =Z z222ieξ dξ]w(z) = e−z [1 + √π 0
is the complex error function. Here, x and y denote offsetsof the horizontal and the vertical directions, respectively.
re denotes the classical radius of the electron. Asterisks
in subscripts mean that the values belong to the counterrotating beam. When we can assume that there is an offset
only in the vertical direction, the beam-beam dipole kick isexpressed as:and∆y 0N ∗ re= −γsy22πexp()Σ2x − Σ2y2(Σ2x − Σ2y )ΣxΣy yy) − Erf ( q)}×{Erf ( q2222(Σx − Σy )2(Σx − Σ2y )(1)
When there is an offset only in the horizontal direction, thebeam-beam dipole kick is expressed as:i∆x0N ∗ re= −γ

Bassetti-Erskine formulasx22πexp(−)
Σ2x − Σ2y2(Σ2x − Σ2y )ΣIn analyzing data of the beam-beam deflection, we used
the Bassetti-Erskine formula[2] which gives 2-dimensional
beam-beam kick. This means that we ignored bunch lengtheffects of the beam-beam interaction. With the rigid Gaussian model, the coherent beam-beam kick is given by the−i Σxy x−ix) − Erf ( q)}×{Erf ( q222(Σx − Σy )2(Σ2x − Σ2y )
(2)
where

∗ Email: yoshihiro.funakoshi@kek.jp

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

2π
Σ2x − Σ2yx

To establish a beam collision condition, we have to tune
beams both in longitudinal and in transverse directions. As
for the longitudinal direction, relative timing of the twobeams have to be adjusted so that the two beams collide at
the nominal collision point. As for the transverse direction,
beam positions of the two beams at IP have to coincide witheach other. In addition to this, beam crossing angles should
be removed to ensure a stable beam collision. A verticalcrossing angle is generally important. On the other hand,a horizontal crossing angle is usually less harmful and wehave intentionally introduced a horizontal crossing angleof ±11mrad to simplify an IR design. In this beam study,
however, we did not care the crossing angles and committed ourselves to the beam offset at IP.

2.1sΣxyy2x2
Σ x x + i Σy yq)},)w(−exp(− 2 −2Σx2Σ2y2(Σ2 − Σ2 )INTRODUCTION

Unlike single ring colliders, special cares are needed tobring two beams into collision in double ring colliders likethe KEKB. Generally speaking, there are several methods
to detect beam collision. Among those methods, we havebeen made use of a beam-beam deflection technique, pioneered at the SLC[1], for this purpose. In this report, results of the first beam collision study are described wherethe beam-beam deflection method has been successfully
applied to the KEKB collider to find beam collision conditions.

2N ∗ re= −γ1132

2Erf (x) = √πZ x02e−t dt

Proceedings of the 1999 Particle Accelerator Conference, New York, 1999
is the error function.

2.2

Longitudinal

The collision point can be shifted by changing relative
beam timing between LER (low energy ring) and HER(high energy ring). We adjusted an RF phase of LER sothat relative timing of an LER bunch and an HER bunch atthe BPM’s agrees with a design value. Beam timing wasobserved by monitoring signals from a BPM nearest to IP
with an oscilloscope. The BPMs are located at positions
where it can detect timing of both beams.

2.3Horizontal

We observed a horizontal beam-beam deflection with scanning horizontal orbit offsets at IP. The scan was done bychanging the RF phase of LER by making use of a design
horizontal crossing angle of ±11mrad.
The beam-beam deflection was detected by measuring
orbit change at BPM’s beside quadrupole magnets named”QC2” where betatron phase advances from IP are almost
π/2. A beam-beam kick is obtained from the following
expression.
∆xQC2R∆xQC2L+p ∗∆x0 = p ∗βx βxQC2R
βx βxQC2L
Here, L and R denote the left side and right side viewed
from the ring center, respectively. As shown in the formula,
we took sum of these two BPM’s to cancel out an effect oforbit drifts. A horizontal orbit offset at IP found from thescan was removed by making an orbit bump.

2.4

VerticalA vertical collision condition was searched by scanning asize of an orbit bump made in one of the rings. BeamBeam deflection was detected by measuring orbit change
at BPM’s beside quadrupole magnets named ”QCS” wherebetatron phase advances from IP are almost π/2. A beambeam kick is obtained from the following expression.
∆yQCSR∆yQCSL+p ∗∆y 0 = p ∗βy βyQCSR
βy βyQCSL
To avoid an effect of orbit drift, we took sum of thesetwo BPM’s. The scan was continued until we obtained adeflection pattern which characterizes a beam-beam kick.

Figure 1: Horizontal Beam-beam scan with large verticaloffset.
then, beam collision timing was adjusted finely by changing an RF phase of LER. An amount of phase adjustment
was 7 degree in this study. Since resolution of the timing
measurement was around 10 ∼ 20psec, an error of the tuning was considered to be less than 3mm (10psec).

3.2

The collision study has been done twice. One was donein a single bunch mode and the other was with multibunch
beams. Thereinafter in this report, we will only mention
about the multibunch beam collision study most recentlyperformed. Typical machine parameters relevant to thepresent study are summarized in Table 1. Figure 1 showsa typical result of the horizontal (RF phase) scan. In thiscase, there remained a relatively large vertical offset. The
deflection curve was fitted by formula (2) to find a horizontal offset. To remove the horizontal offset, a horizontal
orbit bump was made in LER. This process was repeatedseveral times until the center of the curve coincides with
the nominal RF phase (-7 degree in the present case). This
iteration was needed since the beam-beam kick itself makessome orbit changes and we did not take this effect into account.
After removing the vertical offset (see below), the horizontal scan was done again. Figure 2 shows a result. Again
the defelection curve was fitted by formula (2). From thefit, a horizontal beam size was estimated as shown in Table
1. We should note that the estimated value include someerror, since we have not yet estimated the effect of the orbitchange due to the beam-beam kick.

3.3
3
3.1

RESULTS OF COLLISION STUDYLongitudinal

Beam collision timing was observed by monitoring signals
from one of the electrodes of the BPM closest to IP under the condition that a single bunch is stored in each ring.
First, RF buckets of the bunches was adjusted so that thebunches collide roughly at the nominal collision point. AndHorizontal

VerticalAfter the horizontal beam offset was removed, a verticalbeam-beam scan was done to search for an optimum collision condition by scanning a size of an orbit bump made in
HER. A result of the search is shown in Fig. 3. As is seenin the figure, a relatively large offset of 0.73mm was observed. The vertical beam size was estimated by a fit usingformula (1). Again we should note that the estimated beam
size includes some error from the beam-beam kick itself.

1133

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

Figure 2: Horizontal Beam-beam scan without vertical offset.

of LER. An offset was removed by making an orbit bumpin LER. A vertical beam-beam scan was done by scanninga size of an orbit bump made at IP in HER. A relatively
large vertical offset of 0.73 mm was observed. From thebeam-beam deflection curves, beam sizes at IP and a luminosity were estimated. The first multibunch beam collision
was done on 25th March with an estimated luminosity of
1.7 × 1031 cm−2 s−1 . We will do more precise analysis onthe beam-beam deflection including a self-consistent orbitchange due to a beam-beam effect.
The next step of the study is to keep the beam collisioncondition once found. For this purpose, we are preparing aspecial orbit feedback system also based on the beam-beam
deflection technique.

5REFERENCES[1] P. Bambade and R. Erickson, SLAC-PUB-3979 (1986).
[2] M. Bassetti and R. Erickson, CERN-ISR-TH/80-06 (1980).

Figure 3: Vertical Beam-beam deflection.

3.4

Luminosity

From the horizontal and vertical beam sizes estimated fromthe deflection data, a luminosity was estimated to be around
1.7 × 1031 with an assumption that the two beam collide
head-on. After removing the orbit offsets in both horizontal and vertical directions, a physics detector (BEAST) tookdata. Although beam collision was confirmed by events
taken with EFC (Extremely Forward Calorimeter) in theBEAST detector, we could not make quantitative comparison due to a low event rate.
Table 1: Machine parameters used in the study
βx∗ /βy∗Beam current
Number of bunches
Beam size (Σx /Σy )Lifetime
Estimated luminosity

4HER LER
1/0.011365200
200
278/5.640200
1.7 × 1031

mmAµm
mim.
/cm2 /sec

SUMMARY AND FUTURE PLAN

A fine tuning on a collision timing was done by measuring a time difference of two beams. An error of the tuning
was considered to be less than 3mm (10psec). A horizontal
orbit offset at IP was measured by scanning an RF phase1134