LOW EMITTANCE BEAM TRANSPORT FOR e− /e+ LINAC
Y. Seimiya∗ , N. Iida, M. Kikuchi, T. Mori, KEK, Tsukuba, Japan
Abstract
Design luminosity of SuperKEKB is 8 × 1035 cm−2 s−1 ,which is 40 times higher than that of KEKB achieved. To
achieve the design luminosity, the beam have to be transported to the SuperKEKB main ring with the high bunchcharge (4 nC) and low emittance: 40/20 µm for horizontal/vertical electron beam emittance and 100/15 µm forpositron beam emittance in Phase 3 final. In the LINAC andthe beam transport line, the emittance growth is mainly induced by residual dispersion, beam phase space jitter, wakefield in acceleration structure, and radiation excitation. Inthe Phase 2 operation, we have evaluated and, if possible,
corrected these effects on the emittance. Results of the emittance measurement is described.

INTRODUCTION
SuperKEKB is e-/e+ collider for high energy particle
physics in KEK. The design luminosity of SuperKEKB is
40 times higher than that of KEKB achieved [1]. This highluminosity can be realized by both doubling the current andmaking the beam size a one-twentieth compared with thatof KEKB. The Phase 2 commissioning was finished in July
2018. The LINAC was developed for SuperKEKB [2]. During the operation in Phase 2, collimator tuning to reduce
background of Belle-II detector, 𝛽 squeezing for small beam
size at the collision point, collision tuning to maximize thehigh luminosity, and so on have been done [3]. The physics
run is scheduled to start in March 2019 as the Phase 3. Required beam-parameters for Phase 2 and Phase 3 (final) areshown in Fig. 1. In Phase 3 final, requirement to the beam
charge is 4 nC for both beams. Required horizontal/verticalemittance is 100/15 µm for positron beam and 40/20 µm forelectron beam. We have to convey this high-quality beam
to the main ring without emittance degradation as far as
possible. Otherwise, the injection rate would be worse andthe luminosity would not be able to reach the target value.
A footprint of the LINAC and the beam transport line
(BT) is shown in Fig. 2. The LINAC is composed of Sector
A, B, J-ARC, C, and 1-5. The LINAC has two kinds ofelectron gun; a thermionic gun to obtain high-current beam
used for positron production and a photocathode RF gun for
low emittance electron beam. The large emittance of thepositron beam emittance for LER is reduced by a damping
ring (DR), which is placed beside the end of Sector 2. The
beam is extracted from the end of Sector 2 to the LTR line
at 1.1 GeV and injected to the DR. After two cycles of theLINAC pulse, the damped beam is, through the RTL line,
resumed to the start of Sector 3 in the LINAC. Positron
beam is accelerated up to 4 GeV and transported throughthe positron BT line and finally reaches the low energy ring∗ seimiya@post.kek.jp

Figure 1: Required beam-parameters for SuperKEKB injector LINAC and the beam transport line.
(LER). Low emittance electron beam is accelerated up to7 GeV and transported through the electron BT line andfinally reaches the high energy ring (HER). To maintain thelow emittance, fine tuning is necessary in every place of thesystem.

SOURCES OF EMITTANCE GROWTH
We have evaluated several conceivable kinds of sourcesof the emittance growth.

Residual Dispersion
Through the residual dispersion, the energy spread converts to the beam size. First, an example of the dispersion
correction at J-ARC section in the LINAC are shown inFig. 3. where the horizontal axis shows path length along
the beam line, blue and red lines show horizontal and vertical dispersion function, respectively. Before correction,
large residual dispersion had emerged after the J-ARC asshown in the left inset of Fig. 3. By tuning the strengthof quadrupole magnets, horizontal/vertical residual dispersion became small from 0.429/0.092 m to 0.024/0.017 m asshown in the right inset of Fig. 3.
In the same manner, we corrected dispersion in the RTL.
In the RTL, there are two ARCs. For example, Fig. 4 shows
before and after the dispersion correction in first ARC. The
bottom figure in Fig. 4 shows residual dispersion. Blue andred lines show horizontal and vertical residual dispersion,respectively. After the dispersion correction, residual dispersion became smaller. Figure 5 shows values of residual
dispersion before and after correction. In both ARCs, residual dispersion became smaller after the dispersion correction.
But, the residual dispersion in the first ARC is still not smallenough. We need more studies in detail on this issue.
Figure 6 shows improvement of the emittance due to dispersion correction. The emittance was measured with wire
scanner (WS). First, we corrected the dispersion in the second ARC. By the correction, emittance was improved from

Figure 2: A footprint of SuperKEKB injector LINAC and the beam transport line.

Figure 5: Residual dispersion before and after correction inthe RTL.
Figure 3: Dispersion measurement before and after the dispersion correction in the LINAC.

Figure 6: Emittance improvement due to dispersion correction.

Beam Phase Space JitterFigure 4: Dispersion measurement before and after the dispersion correction in the RTL.

about 300 µm to 200 µm. Then, we corrected the dispersion
in the first ARC. By the correction, emittance was improved
to 130 µm. Though the horizontal emittance became lessthan half, it is still twice as large as design value. Reference [4] mention this issue.
In the same manner, we corrected dispersion in each ARCof the BT. Figure 7 shows residual dispersion before andafter correction for electron and positron beam. The order ofARC names are from the upstream to downstream of the BT.
In the upstream of the WSs, dispersion correction was done.
In some ARCs, dispersion correction is not completed.

The extent of the transported beam to the main ring must
be stable so that the beam can be injected inside the main
ring acceptance. The emittance that includes beam phasespace jitter, called as effective emittance, must be satisfy therequirement. We evaluated the emittance growth due to thebeam phase space jitter and investigated their sources.
To evaluate the emittance growth due to beam phase space
jitter, we introduce following effective emittance,𝜖𝑒𝑓 𝑓 = √⟨𝑋 2 ⟩ ⟨𝑋 ′2 ⟩ − ⟨𝑋𝑋 ′ ⟩2= √𝜖20 + 𝜖2𝑗 + 2𝜖0 𝜖𝑗 𝐵𝑚𝑎𝑔 ,where𝑋 = 𝑥 + Δ𝑥, 𝑋 ′ = 𝑥 ′ + Δ𝑥 ′ ,2𝜖0 = √⟨𝑥 2 ⟩ ⟨𝑥 ′2 ⟩ − ⟨𝑥𝑥 ′ ⟩ ,2𝜖𝑗 = √⟨Δ𝑥 2 ⟩ ⟨Δ𝑥 ′2 ⟩ − ⟨Δ𝑥Δ𝑥 ′ ⟩ ,𝐵𝑚𝑎𝑔 =𝛾0 𝛽 − 2𝛼0 𝛼 + 𝛽0 𝛾,
2Figure 7: Residual dispersion before and after correction forboth electron and positron beam in the BT.

Figure 8: Measured beam position jitter and jitter emittancein the LINAC before and after dispersion correction. Theelectron beam was 1 nC and generated by RF gun.
Table 1: Basic Parameter Set

𝜖0 and 𝜖𝑗 are nominal emittance and emittance growth induced by beam phase space jitter (jitter emittance), respectively. 𝐵𝑚𝑎𝑔 is a phase space mismatch between the beamand the jitter. The value is equal to or larger than 1. If
𝐵𝑚𝑎𝑔 = 1, there is no mismatch and the effective emittanceequals just the nominal emittance plus the jitter emittance.
𝐵𝑚𝑎𝑔 is measured to be about 1-2 in the usual LINAC operation, which is measured with WS. From the beam position,assuming the transfer matrix between two BPMs, beam angle can be estimated. Jitter emittance can thus be derived
from the beam position jitter and beam angle jitter.
We have measured the beam position jitter at BPM in
the LINAC. Figure 8 shows the beam position jitter andthe jitter emittance. Horizontal axis shows the path length
after the electron gun. Position jitter is defined as standard
deviation of measured beam position. Around the 140 m
point of the figure, there is J-ARC section. Because the JARC section is dispersive, beam energy jitter is converted tobeam position jitter in this section. Dispersion and position
jitter were about 0.8 m and 360 µm at the center of thissection, respectively, then energy jitter is estimated to beabout 0.045%. In addition to the J-ARC, behind the positrontarget placed in about 290 m point, beam position jitterand jitter emittance were observed to increase as shown in
the left figure in Fig. 8. In this case, horizontal/verticaljitter emittance was about 28/7 µm at the end of the LINAC.
Target value of the horizontal/vertical emittance in Phase
3 is 40/20 µm. Therefore, the effect of jitter emittance on
effective emittance was very large. On the other hand, after
the dispersion correction, horizontal/vertical jitter emittancewas decreased to about 1.8/0.9 µm at the end of the LINAC
as shown in the right figure in Fig. 8. Beam phase space
jitter was successfully reduced by the dispersion correction.
Small emittance growth still remains behind the target evenafter the correction. This result is obtained in case of 1 nC,
therefore we should understand origin of the beam phasespace jitter to prepare for the 4 nC beam.

Wakefield in Acceleration Structure
Wakefield, generated by a head of bunch, kicks its own tail.
Thus if the beam is off-centered in the structure, the transverse wakefield increases beam emittance. This effect canParameter

Value

Unit

Initial emittance
Initial bunch length
Initial energy spread
ChargeDistribution
S-band acc. cavity aperture

103/2.35
0.004
5Gaussian
𝜙20µmmm–nC–mm

be minimized by a proper orbit correction. We performed
particle tracking simulation to evaluate emittance growth
induced by wakefield in acceleration structure. The particle
tracking is simulated by the SAD program [5]. Misalignment of the components had been measured by laser-basedalignment system [6, 7]. The measured misalignment values
were used for this simulation. Table 1 shows basic parameterset of the simulation. Left figure in Fig. 9 shows emittanceafter orbit displacement was minimized. Blue and red dotsshow horizontal and vertical emittance, respectively. Blueand red lines show the horizontal and vertical requirements
for Phase 3, respectively. As the beam went down to theLINAC end, the horizontal/vertical emittance grew up to240/120 µm at the end of the LINAC. On the other hand,right figure in Fig. 9 shows emittance minimized at the endof the LINAC. Emittance growth, in this case, occurred at
Sector C and corrected at Sector 2. By an orbit correction
for emittance preservation, emittance growth induced by anaccelerator structure could be cancelled by the other accelerator structure. In this case, the horizontal/vertical emittanceis 22/11 µm at the end of the LINAC. These emittances areless than Phase 3 requirements. Especially, the vertical emittance is almost same as initial emittance. In the simulation,transmission rate was almost 1.

Radiation Excitation
Radiation excitation effect on emittance is proportional
to both Lorenz gamma to the fifth power and inverse ofcurvature radius to the third power. Especially, electron
beam (7 GeV) is strongly affected by the radiation excitation
effect. Particle tracking was performed from beginning toend of the BT. Figure 10 shows the simulation results. Initialknown emittance growth sources in the BT are in progress.

Figure 9: Emittance change due to different orbit correctionin the LINAC.

Figure 11: Emittance measurement result for electron beamat each sector.

Figure 10: Radiation excitation effect on emittance in theBT.
horizontal emittance of electron/positron beam is 20/64 µm.
These emittances are increased by radiation excitation andreach 69/77 µm at the end of the BT. Especially, electron
beam emittance at the end of the BT is larger than Phase
3 requirement. We are reconsidering the requirement by
taking into account of the actual injection system and beam
optics.

EMITTANCE MEASUREMENTFirst, we show emittance measurement result of electron
beam as Fig. 11. Left and right figures show horizontal
and vertical emittance measured at each sector, respectively.
Purple dots show emittance of electron beam generated withthermionic gun. Green and blue dots show emittance ofelectron beam generated with RF gun. Green dots measured
in 29 June 2018 and blue dots measured in the next day.
Clearly, beam emittance with the RF gun was smaller thanthat with thermionic gun. Blue and orange dashed lines
show Phase 2 and Phase 3 requirement value, respectively.
The requirement emittance of electron beam at the end of theLINAC is satisfied for Phase 2, but not for Phase 3. Currently,
we performed orbit correction algorithm only to reduce orbit
distortion. We will introduce the orbit correction programfor emittance preservation in this Winter. Large emittance
growth was observed at the BT though dispersion correction
was done. This emittance growth is irrelevant to radiation
excitation because used WSs in the BT are placed where thetotal bending angle from the beginning of the BT is small.
Finally, we show emittance measurement result ofpositron beam in Fig. 12. In Phase 2, the requirement emittance of positron beam at the end of the LINAC was alsosatisfied though the requirement for Phase 3 was also notsatisfied. Emittance was also increased in the BT thoughdispersion correction was done. Investigations for these un-Figure 12: Emittance measurement result for positron beamat each sector.

SUMMARY
In the LINAC and the BT, transport of high current and low
emittance beam is necessary for SuperKEKB. In the LINAC,emittance requirement for Phase 2 was satisfied after applying dispersion correction, reduction of beam phase space
jitter, and orbit correction. To suppress the emittance growthmore, automatic orbit correction for minimizing emittance
growth is desired. We plan to introduce such an emittancecontrol program in this Winter. Large emittance growth wasobserved in the BT. Emittance requirement in Phase 2 was
not satisfied in the BT. Investigations of the issues are inprogress.

ACKNOWLEDGEMENTS
This work was partly supported by JSPS KAKENHI Grant
Number 16K17545.

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