A NEW WORKING POINT FOR THE KEKB
*Y. Z. Wu , Y. Funakoshi, M. Tawada, K. Ohmi, KEK Tsukuba, JapanAbstract
In order to improve the beam-beam performance andto increase the luminosity of the KEKB [1,2], a newworking point with a tune above the half integer in bothplanes has been proposed. The strong-strong beam-beamsimulations with a code developed by K. Ohmi [3] areused for the luminosity scan. In this paper, we discuss
the simulation results in the new tune space region, andsuggest a new working point as a candidate for theoperation of the KEKB machine.

1 INTRODUCTION
The performance of a collider and the luminosity
depend sensitively on the working point. So choosing agood working point is very important for high luminosity
operation. The KEKB B-factory has been well operated
for more than two years since December 1998. At theearly stage of the operation, the KEKB used the working
points with the tunes above the integer in both planes,
later on the horizontal tunes for both rings were moved
to the values above the half integer, while keeping thevertical tunes above the integer [4].
The KEKB machine is now working with fractional
tunes ∆νx =0.52, just above half integer in horizontal, and∆νy=0.08, just above integer in vertical (Jan. 2001).
These tunes gave a good beam-beam performance andbetter luminosity, and there are still some potential toreach higher luminosity with them. But it seems that thetunes are very sensitive to the machine setting and could
substantially effect the beam lifetime and luminosity,
even their variations are small as 0.002∼0.003. Also thebeam-beam blowup has been observed even at the lowbeam currents [5].
For the present working point of the KEKB (Jan.
2001), the vertical tune is rather close to the integer, andits location in the tune plane is near the sextupole
resonance 2νx-νy=47 (LER), these may cause the closed
orbit and dynamic aperture more sensitive to the machine
errors, therefore the luminosity and beam lifetime could
be reduced.
Above considerations pushed us to perform a study
aimed to find a new working point situated far from
integer and from sextupole resonance, improving thebeam–beam performance and increasing the luminosity.
*Visiting from IHEP, China

2 BASIC CONSIDERATIONS FORCHOICE OF A NEW TUNE
From the point of view of beam-beam dynamics, thefractional tunes between interaction points in a colliding
beam storage ring would be better if they are close to,but above, an integer or half integer [6]. These tunes
would give a good beam-beam performance, but result in
the dynamic beta effect having a noticeable effect on theoperation. Other effects to be considered for the choiceinclude: the lower order resonance lines are less aroundit; the orbit distortion and dynamic aperture with thetunes should be less sensitive to the machine errors.
Comparing with the tune just above the integer, thetune above the half integer has some advantages. First,
the closed orbit is not so sensitive to the machine errors
as that with a tune just above the integer. This is due tothe orbit distortion ∆x ∝ δθ/sinπν, where δθ is an error
kick. Second, if we look at the tune plane and plot all theresonance lines up to fifth order, we could see that there
is simply more space in the neighborhood of the halfinteger and coupling resonance than that with a tune justabove integer. Third, Several existing colliders operate inthe region of tune plane, just above the half integer. For
the CESR machine, after switching to single interaction
point operation with a crossing angle, it was found thatthe best working point is very close to the coupling
resonance and just above the half integer [7]. Theseexperiences are good examples.
Based on above considerations, we try to explore anew tune space region and find a more suitable working
point for the KEKB machine.

3 STRONG-STRONG BEAM-BEAM
SIMULATION IN A NEW TUNE REGION
We have used a strong-strong beam-beam simulation
code developed by K. Ohmi [3] to perform luminosity
scans in a new tune space region. The simulation isperformed with 100,000 macro-particles divided into 5
slices in longitudinal, using a 64×128 mesh withhorizontal and vertical sizes of 20µm×0.4µm. The
particles are tracked for 45,000 turns. In the simulations,the horizontal tunes for both rings are kept almost sameas present, i. e. νx=44.52 in the HER and νx=45.52 in theLER. For the vertical planes, we lower the integer tunes
from 42 to 41 for the HER, and from 44 to 43 for theLER. This would decrease the nature chromaticity, andtherefore reduce the sextupole strengths for thechromaticity correction.
The tune scans are mainly carried out for the LER. Inorder to determine the HER tunes quickly, a roughsimulation is done by keeping a same fractional tune ineach plane for both rings.
As the strong-strong beam-beam simulation quite
costs computer time, so we only perform a rough scan ina limited tune space region which we are interested in.
The tune survey area covers fractional tunes in therange of ∆νx=0.510~0.550, and ∆νy=0.560~0.655. Thetune scan step is 0.005 in both planes.
At first, the simulation is done based on a set of old
operation parameters of the KEKB. With theseparameters we have accumulated more simulation date
for the vertical tunes above the integer [8], so we cancompare them with that using new tunes. Second, thepresent operating parameters are used in the simulations.

in the vertical plane to form a safe area spreading from∆νy=0.565 to 0.655. The largest safe region around thebest tunes of ∆νx=0.515, ∆νy=0.635 covers the tune
dimensions larger than 0.05 in both planes. The best
luminosity in this set of simulations could reach30-2 -1
1.65×10 cm s .
The results also show that in the three tune regions, theluminosity is very stable and is not sensitive to the*variations of βx in the LER, even it is changed from thevalue of 0.7 m to 0.33 m. But for the other regions, the*luminosity could be improved while using a lower βxvalue in the LER. For example, the luminosity could be
increased about 10% by decreasing its value from 0.7m
*to 0.5m. With βx of 0.33m in the LER, the luminosity30-2 -1
could reach 1.50×10 cm s for almost the whole tune
survey region, as showed in Fig. 2.

3.1 Simulation with old parameters
Table 1 gives a set of parameters of KEKB earlier
operation which are related to the simulation.
Table 1 Earlier operating parameters of the KEKBLERHERHorizontal emittance
28.99
29.45(nm)Vertical emittance
0.59730.6072(nm)**
70/0.770/0.7β x /β y (cm)Particales/bunch
3.63395E10 2.34809E10
Bunch length
5.9@5.0
6.4@9(mm@MV)(a) Luminosity contour diagram for the verticaltunes above the integer (Tawada,EPAC’2000).

HER tune survey:
After a rough tune scan with same tune in each plane
for both rings, it’s found that a higher luminosity could
be reached with fractional tunes of ∆νx=0.52, ∆νy=0.635.
So we fixed the HER working point as νx=45.52,
νy=41.635 when surveying the LER tunes.
LER tune survey:
The simulation results show that the predicative
luminosity in single bunch in the above tune space regionis larger than that with present tunes. Fig. 1 shows thesimulation results and compares them with that ofvertical tunes above integer [8].
We can see that for the present tune region used for
the KEKB, the best tunes are ∆νx=0.52, ∆νy=0.08, but thedimensions of the safe area around it are not so large.
Also we could see that a luminosity reduction due tobeam-beam driven resonance of νx-νy-νs=47. The
simulation results with new tunes show that there are 3tune space regions in which the luminosity is larger than30-2 -11.50×10 cm s , and they are almost connected together(b) Luminosity contour diagram for the tunes above
half integer in both planes, the unit of luminosity30-2 -1in the figure is 10 cm s .
Fig. 1 Simulation results comparison for the two tune
space regions.

Fig. 2 Luminosity contour diagram with βx* of 0.33 m
in the LER.

3.2 Simulation with present operation
parameters (Jan. 2001)
Table 2 shows the parameters of KEKB at present.
Compared them with the parameters in the table 1, thebeam currents have been increased obviously.
Table 2 Operating parameters of KEKB at presentLERHER
Horizontal
1824emittance (nm)**63/0.7
80/0.7β x / β y (cm)
Emittance ratio
21y /x (%)
Beam current (mA)760
580
Particales/bunch
4.15E10
3.16E10
Bunch length
5.5@6.0
5.7@11(mm@MV)
In this set of simulations, the HER working point isfixed as νx=44.52, νy=41.625, and the tune space regionof ∆νx=0.505~0.550, ∆νy=0.560~0.665 is covered for theLER tune scans. The simulation results with above
parameters are presented in the Fig. 3, which shows thatthe behavior of the luminosity contour is similar as thatin the (b) of the Fig.1. One can see that the expected30-2 -1
luminosity is larger than 2.0×10 cm s in quite a large
area of ∆ν =0.513~0.530, and ∆νy=0.560~0.665. The best
tune space region is around the tune pint (0.510, 0.635),
where they are the horizontal and vertical tunes,respectively, having a single bunch luminosity of
30-2 -1
2.94×10 cm s which corresponds a peak luminosity of
33-2 -1
3.4×10 cm s with 1153 bunches. Another better tune
space region is around the tune point (0.510, 0.575), andthe predictive luminosity per bunch at this point is30-2 -1
2.47×10 cm s .
x

Fig.3 Luminosity contour diagram for the present
operation parameters of KEKB (Jan., 2001).

4 SUMMARY
It’s reasonable to explore a new working point with atune above the half integer in both planes for the KEKB.
The simulation studies demonstrate that a larger safe
tune space area could be found, and a higher luminosity
could be reached in the new tune space region which wechose. The fractional tune points (∆νx=0.505~0.530,∆νy= 0.560~0.660) for both beams could be tested in theKEKB machine.

5 ACKNOWLEDGEMENTS
The authors would like to thank S. Kurokawa, K. Oide,
H. Koiso, H. Fukuma for the very helpful discussions
and support.

6 REFERENCE[1] KEKB B-Factory design report, KEK-Report-95-7,
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1994,[4] Y. Funakoshi, Beam-Beam performance andluminosity optimization, KEK proceeding 99-24,
Feb. 2000,[5] Y. Funakoshi, et al. KEKB performance,EPAC’2000,[6] M. Tigner, Private communication,[7] B. Richer, Proc. Int. Sym. Electron and positronstorage rings, Saclay, 1996,[8] W. Tawada, Y. Funakoshi, M. Masuzawa, K. Ohmi,
Comparison of beam-beam simulation withexperiments at the KEKB, EPAC’2000.