Luminosity Optimization by Controlling a Beam Size Ratio at KEKB
N. Iida, Y. Funakoshi, H. Koiso, M. Masuzawa, K. Oide, M. Tawada
KEK, Japan, 1-1 Oho, Tsukuba, Ibaraki 305-0801
Abstract
KEKB B-Factory is one of second generation electron andpositron colliders. The energies of the two beams are 3.5
GeV(positron) and 8 GeV(electron). In the usual beam operation of KEKB, the Low Energy Ring (LER) beam isweaker than the High Energy Ring (HER) beam. We foundthat the LER vertical beam size can shrink by intentionally making the HER beam size bigger and then luminosity
gets higher when the LER beam is blown up due to thebeam-beam effect. By making use of this mechanism, wehave constructed a feedback system which keeps the vertical beam size ratio of the two beams at some optimum
values where the luminosity is maximum. We found that
this feedback is a very useful tool for increasing the luminosity.

1INTRODUCTION

The KEKB accelerator is a high luminosity e+ e− collider to generate a large amount of B mesons. The designed value of peak luminosity is 1.0 × 1034 cm−2 sec−1
and we have currently the best recorded value of about
3.0 × 1033 cm−2 sec−1 . At KEKB, enlargement of the LER
vertical beam size is the most severe obstacle for increasing
the luminosity.
There are two major processes of the LER beam blowup.
One is a single beam blowup[1] and the other is that due tobeam-beam effect[2]. The former is induced by the photoelectrons which are emitted from the inner surface of LER
beam pipe by the synchrotron radiation from the beam. Thebeam blowup is more likely appeared in the vertical beam
size at KEKB. The latter one, the beam-beam blowup isalso observed in LER. Although we sometimes observe itin the horizontal direction too, we discuss only the vertical blowup of the LER in this report. There are two reasons why the LER beam is weaker at KEKB, both of whichcome from the photoelectron beam blowup. One is that thepresent operating beam currents of KEKB heavily breaks
the energy transparency condition; the HER beam current
is much higher than that of LER even if we consider theenergy difference of the two beam. This is because thehigher HER beam current usually brings the higher luminosity whereas the higher LER beam current is less effective for increasing the luminosity due to the photoelectron
blowup. The other reason is that the LER vertical beam sizeof collision is larger than that of HER due to the photoelectron effect. Because of this beam size difference, particles
in LER feels the nonlinear beam-beam force more likely
than those in HER. This also brings the LER beam-beam

blowup.
We empirically know that the higher luminosity is obtained when the blowing up of the LER vertical beam
size caused by beam-beam effect is suppressed by making the HER beam larger intentionally. We found thatthe luminosity is very sensitive to the ratio of beam sizes,
σyLER /σyHER . We constructed a feedback to keep the vertical beam size ratio to an optimum target value that isobtained empirically. In this paper, the feedback system
which is used for the actual beam operation, called “iSize”
feedback system is described.

22.1

BEAM SIZE FEEDBACK SYSTEMHER Beam Size Control

At KEKB, the non-interleaved sextupole scheme is adopted
for chromaticity correction and many pairs of sextupole
magnets are installed in the arc sections of each KEKBring. At one of the most strong sextupole pairs in HER, ananti-symmetric bump is made by using three dipole correction magnets near them. This bump converts the horizontal
dispersion to the vertical which leaks out around the wholeof the ring. On the other hand, the created XY-coupling isclosed in the bump and never leaks out. By this dispersion
the vertical emittance is enlarged and the HER beam size
can be made larger. The calculated orbits and dispersions

Figure 1: The orbits calculated with iSize bump height of
1mm at the pair of sextupole magnets as shown in the thirdgraph.

around the pair of sextupoles with a bump of 1mm heightis shown in Fig. 1. The emittances calculated with someiSize bump heights are shown in Fig. 2. These calculations
are done with the “sad” code[3] in which a lattice for thecurrent operations is used[4]. The iSize bump heights inthe actual operation are mainly between 0mm and 2mm.
Two controllers of changing the HER vertical beam size
is mentioned in this section.
3.5 10- 9

Vertical Emittance (m)3 10- 92.5 10- 9
2 10- 91.5 10- 9
1 10- 95 10-100-5 10-10-5-4-3-2-1

012345Bump Height (mm)Figure 2: The emittances calculated with some iSize bumpheights.

2.2iSize Controllers

Feedback The feedback routine uses a ratio
σyLER /σyHER as an input parameter. The aim of thefeedback is to keep the ratio around a target value. Thebeam sizes are measured by Synchrotron RadiationMonitors(SRM’s)[5] which are located at the arc sectionsof both rings. The SRM can take data at about 5Hz which
are averaged every five data. Measured beam sizes aretransferred to those at the interaction point. The iSize
feedback obtains the beam size of each ring at about 1Hz.
However calibrations for absolute values of beam sizes
are under study now. Based on the ratio, a bump height isdetermined.
The blue line at the lower right of Fig. 3 shows a hyperbolic curve fit with the plots and the red line indicates thetarget value for σyHER which is calculated σyLER divided by
the target ratio. The bump height to be set is obtained as anintersection point of the two lines. The actual bump heightchange is decreased by multiplying a damping factor. Thisfactor is necessary for stabilizing the feedback action. The
typical damping factor is about 0.01. The bumps are madeby the dipole magnets exclusively used for the iSize controllers.
Trend graphs of parameters used for the iSize feedback
on one day are shown in Fig. 3. The beam currents wereabout 740mA and 580mA for HER and LER, respectively.
At the beginning of these graphs the iSize bump height wasFigure 3: The top two trend graphs correspond to the iSize
bump heights for LER( not used here) and HER. The middle two correspond to σx and σy . The red and blue lines
express those of LER and HER for each direction. The
fifth graph shows the vertical size ratio( green line ) andthe target value( yellow line ). The bottom shows luminosity measured by a CsI calorimetry in the BELLE detector.
The lower left and right of the figure show correlations ofluminosity with the ratio and σyHER with the bump height,respectively.
set at an value far from an optimum and the feedback wasintentionally turned off. At the time of 15h04m45m thefeedback was turned on and the bump height gradually increased. The HER vertical size enlarged and on the contrary the LER shrank. Simultaneously the vertical size ratioof LER to HER approached to an optimum target value of0.8. When the ratio reached the target value at 05m40s, theluminosity recorded the maximum value. It took about one
minute from turning on the feedback. The response of thefeedback depends on the machine tuning situation.
The optimum target values are obtained by a trial and error method. The target value is changed as a function of theLER beam current as shown in Fig. 4. At the higher beam
current, the LER beam blowup is severer and the bump getshigher.
“Tool” We have one more controller named “iSizeTool” also using iSize bump. This tool moves iSize bumpheight little by little and observes luminosity changing at
each point. The bump height of the next step is determinedso that the highest luminosity is expected from the past

0.78

6-2 -1

0.76
0.75
0.74
0.73
0.72

2.65
2.44
2.2
32.00.71

20.7
400-9450500

550600650

700750800

σy (µm)iSize Ratio Target

Luminoisty / Bunch (cm s )Experiment
Injection

0.77

0.5

1.0

1.5

2.0

2.5

3.0x10HER Vertical Emittance (m)LER Current (mA)

Figure 4: The target value is changed according the theLER beam current. The red line is used for BELLE experiment and the green one is for injection time.
two data. The calculation is done with a one-dimensional
Downhill Simplex method. This tool is useful when themachine is stable. However it has two weak points, one isthat the measurement of luminosity is slow( about 0.1Hz )and the other is that it is easy to be disturbed by the othercollision tunings. This tool is mainly used as an auxiliary
tool of iSize Feedback when the SRM does not work wellfor some reasons.

3βx /βybunch current
Bunch lengthνx /νyzero-crossing.
We can not compare directly the results of simulation
with actual measurements from some reasons. One reason is that the simulations only deal with the beam-beam
blowup and we take no account of the LER single beam
blowup. Another reason is that a calibration of the SRM is
not complete yet. However, it is qualitatively shown by thesimulations that there is an optimum value of HER emittance for luminosity.

SIMULATION

If there is no iSize feedback system, the weaker beamwould be blown up and the luminosity would be lower.
To see the effectiveness of iSize feedback system, wehave performed beam-beam simulations for the present
working parameters of KEKB with a code developed by
K. Ohmi [6][7].
Energyxy /x

Figure 5: This figure shows Luminosity(yellow•),σy (red (LER), blue  (HER)) and Σy (green-) for crossing angle of 22mrad and Luminosity(yellow ◦) for zerocrossing angle as a function of HER vertical emittance.

LER
3.5
182
(1)
0.63/0.007
0.66(0.87)
5.5@6.0
45.518/44.063

HER
8.024
(controlled byiSize Feedback)(1)
0.8/0.007
0.50(0.37)
5.7@11.0
44.525/42.135

unit
GeV
nm%mmA
mm@MV4

CONCLUSION

We found that the luminosity strongly depends on the vertical size ratio of LER to that of HER. The iSize controller isa very important tool for KEKB to get a high luminosity. In
actual beam operation, iSize feedback is always turned on.
The simulation also shows that the luminosity maximum isrealized at an optimum value of the vertical size ratio.

5REFERENCES[1] H. Fukuma et al.“Observation of Vertical Beam Blow-up in
KEKB Low Energy Ring”, Proceedings of EPAC 2000, Vienna, Austria[2] K. Akai et al.,“Beam-Beam Performance and Luminosity Optimization at KEKB”, Proceedings of Factories’99, Tsukuba,Japan[3] http://acc-physics.kek.jp/SAD/sad.html

Table 1: Parameters for the simulations. The values in ()are the designed values.
The simulation parameters are shown in Table 1. Fig. 5
shows the luminosity and the vertical beam sizes of bothrings as a function of the HER vertical emittance in thecases of crossing angle of 22mrad (KEKB) and 0mrad. The
highest luminosity is obtained around the minimum valueof Σy . And the HER vertical emittance dependence on theluminosity for KEKB is stronger than that for the case of[4] H. Koiso and K. Oide, in Proc. of 16th IEEE PAC95, Dallas,Texas, TAG11, 2780(1995)[5] N. Mitsuhashi et al.,“Optical Diagnostics System for KEKB
B-Factory”, Proceedings of EPAC 2000, Vienna, Austria[6] K. Ohmi, K. Hirata and K. Oide, Phys. Rev. E49 751, 1994.
[7] M. Tawada, Y. Funakoshi, M. Masuzawa and H. Ohmi,“Comparison of beam-beam simulation with experiments at
the KEKB”, EPAC 2000, 1193, Vienna, Austria