SuperKEKB 入射器におけるエミッタンス保存
EMITTANCE PRESERVATION IN SUPERKEKB INJECTOR
風間慎吾 ∗ 、佐藤政則、杉本寛、吉田光宏、小川雄二郎
Shingo Kazama∗ , Masanori Satoh, Hiroshi Sugimoto, Mitsuhiro Yoshida, Yujiro Ogawa
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 305-0801, Japan

Abstract
Injector linac at KEK is now under the way to produce high current and low emittance beams for SuperKEKB.
The target luminosity for SuperKEKB is 40 times higher than that of KEKB. A short-range transverse wakefield and adispersive effect at the linac cause an emittance growth, and a longitudinal wakefield effect enlarges an energy spreadof the beams. In this paper, we presented simulation and experimental studies concerning the emittance preservationand the energy spread issues. As a candidate for the mitigation of the emittance dilution originating from the transverse
wakefield, a method called offset injection is considered. It is demonstrated both in simulation and experiment that theoffset injection remarkably improves the emittance preservation.

1.

INTRODUCTION

SuperKEKB is an electron-positron collider with an energy of 7 GeV and 4 GeV, respectively. The target luminosity is 8×1035 cm2 s−1 , which is 40 times higher than thatof KEKB [1] . SuperKEKB main ring therefore requires ahigh current and low emittance beam. These parameters are
summarized in Table 1. In order to meet the requirement,a photo-cathode RF gun is planed to be installed at the injector linac for the electron beam. For the production of alow emittance positron beam, a damping ring is now underconstruction. Since the target emittance is quite small compared to that of KEKB, much more attention should be paidto the emittance growth through the linac. The short-range
wakefield and the dispersive effect are considered to be themajor sources of the emittance dilution. In this paper, we
report on a design study on SuperKEKB injector for highcurrent, low emittance, and low energy spread beams. We
mainly report on simulation studies concerning the emittance preservation issues and how to suppress the increaseof the energy spread. All simulation presented in this paper is performed with elegant [2] . Experimental results on
the offset injection using a thermionic electron gun is alsoshown.
Table 1: Required parameters for SuperKEKB[ ]Bunch charge nC
Verticalemittance[]
mm mrad[Horizontal emittance]
mm mrad [ ]Energy spread %∗ kazama@post.kek.jp

Phase 2(e+ /e− )Phase 3(e+ /e− )2/2
20 / 20

4/5
20 / 20100 / 50

100 / 500.1

0.1

Figure 1: Schematic of SuperKEKB injector linac.

2.

TRACKING SIMULATION

Figure 1 shows a schematic of SuperKEKB injector
linac. The linac is mainly composed of 9 sections. In thispaper, simulation is performed from the C-sector to the 5sector for simplicity.
2.1

Condition of Simulation

The initial particle distribution in the longitudinal direction at the C-sector is assumed to be a Gaussian of 10 psbunch length (FWHM) with 2 or 5 nC charge and 1.5 GeV
energy. The distributions of transverse phase space and energy spread are both assumed to be Gaussian. The initialemittance in the horizontal and vertical directions and theenergy spread are set to be 10 mm mrad and 0.1 %, respectively. Longitudinal monopole and transverse dipole wakefield are incorporated in the simulation with an analyticalexpression of the wake functions [3] . Long-range wakefield
effects are not taken into account in the simulation. The
electron beam is approximated by 105 macro particles. For
the study of the effect of misalignment on the emittance
growth, alignment errors for quadrupole magnets and acceleration tubes are considered, and their distributions areassumed to be Gaussian.

3.

EMITTANCE PRESERVATION

3.1

Short-Range Wakefield and Misalignment

When a bunch of electron beam passes through a misaligned accelerating structure, the head particles in thebunch will interact with the beam pipe and leave a wakefield to the tail particles. The induced wakefield can deflect the trailing particles further away from the axis, resulting in an increase of the projected beam emittance. Thetransverse wakefield strength can be reduced with a shortbunch length. However, the short bunch length causes thestrong longitudinal wakefield, resulting in a large energy
spread. Therefore, the bunch length has to be optimized
with a detailed simulation. The dependence of the bunch
length on the energy spread will be discussed in the next
section. To achieve the required emittance, the magnitudeof the misalignment must be kept as small as possible. Figure. 2 shows a simulated vertical emittance at the end of the5-sector as a function of magnitude of local misalignment
when the charge of the electron beam is 5 nC. It shows thatthe vertical emittance of 20 mm mrad can be realized if themagnitude of the misalignment is smaller than 0.1 mm insigma.

Figure 2: Vertical emittance at the end of the 5-sector as afunction of magnitude of misalignment.
In the SuperKEKB injector linac, the local alignment of
the accelerator structures at the 3, 4, and 5-sector was performed with a laser tracker during a shutdown in summer
2014 [4] . As shown in Fig. 3, measured local alignment errors in the horizontal and vertical directions are estimatedto be about 15 µm and 40 µm, respectively. Therefore,
the initial goal of the local alignment seems to be alreadyachieved. However, systematic uncertainties on the measurement have to be well investigated. The most important error is expected to come from the uncertainty of thealignment of the girders on which accelerator structures areplaced.
3.2

Offset Injection: SimulationAs discussed in the previous section, accelerator elements cannot be perfectly aligned. Hence, even when thebeam is injected without any offsets, the misalignment will
induce the transverse wakefield. In order to reduce theFigure 3: Measured misalignment of the accelerator structures on the girders in the horizontal (black) and vertical(red) direction.

emittance growth, a compensation method called offset injection has been investigated in this paper. In the actual
experiment, this can be performed by adjusting currents of
two steering coils to some optimal values. Electron beams
are then injected into the next section with a certain kickangle and a certain offset. The kick angle can be tuned inunits of 0.1 µrad, and the effect originating from the instability of a power source is estimated to be negligible. We
simulated the effect of the offset injection in the case of
Phase 2 and 3 using twenty different lattices with an alignment error of 0.1 mm in sigma. Figure 4 and 5 show oneof the twenty results of the offset injection. As shown in
the figures, optimal offsets and kick angles are estimatedto be relatively small in both cases, which means that it isnecessary to control the orbit stably in a high precision. In
the case of 2 nC, a large number of combinations of offsets
and kick angles satisfy the requirement in Phase 2. On theother hand, only a few parameters satisfy the requirementin the case of 5 nC, therefore the orbit control in Phase 3
will be quite challenging. In order to satisfy the requirement of SuperKEKB, the deviation of a beam offset and akick angle has to be kept smaller than 0.05 mm and 2 µ rad,respectively.
3.3

Offset Injection: Experiment

The photo-cathode RF gun is now in a development
phase, therefore the thermionic electron gun used in theKEKB was re-installed at the injector to investigate the performance of the SuperKEKB LINAC. The offset injection
was performed from the A-sector to the end of the B-sector
with the thermionic electron gun. Figure 6 shows the horizontal emittance as a function of currents in two steeringcoils placed at the start of the A-sector. It is experimentallydemonstrated that the emittance can be reduced by changing the currents in the two steering coils. However, it takes
about ten minutes to measure the emittance with Q-scanfor each points, which means that half a day is necessary
to search for the most optimal currents of steering coils.
Since the time available for the experiment was limited, thecurrents which can preserve the initial emittance could not×10−3

0.01

0.14

1100

00.12

−0.01

−0.02

0.1

−0.03

0.08

−0.04

0.06

−0.05

0.04

−0.06
−0.07
−0.2−0.15−0.1−0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
offset [mm]

0.02

×10−6

×10−30.14−200.12−22−240.1−260.08−280.06−300.04−32−34−0.05

SX_A2_1 = -1.089 [A]1000

SX_A2_1 = -1.129 [A]900

SX_A2_1 = -1.149 [A]800

SX_A2_1 = -1.169 [A]SX_A2_1 = -1.189 [A]

700
600
500
400
300

2000.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

1 1.05 1.1
SX_A2_2 [A]Figure 6: Horizontal emittance as a function of currents in
two steering coils placed at the start of the A-sector.
is set to be 0 to confirm how much energy spread is inducedby the longitudinal wakefield.
Figure 7 shows the energy spread at the end of the 5sector as a function of bunch length with on-crest RF phasefor various types of longitudinal beam distributions. Gaussian and rectangular shapes are considered as a longitudinalbeam distribution in this simulation, and the bunch length
for a rectangular distribution is defined by its full width. As
shown in the figure, there is no solution which satisfies therequirement in both Phase 2 and 3.

0.0200.05

0.1
0.15
offset [mm]Figure 5: Vertical emittance in m-rad as a function of offset
and kick angle when the beam charge is 5 nC.

σE/E [%]

kick angle [rad]Figure 4: Vertical emittance in m-rad as a function of offset
and kick angle when the beam charge is 2 nC.

−18

γ ∈x @ B-sector End [µm rad]−3

kick angle [rad]0.02 ×10

1.4
2 nC, gaussian

1.2

2 nC, rectangular
5 nC, gaussian

1

5 nC, rectangular

0.8

be found out. Therefore, it is quite important to measure
the emittance in a short period of time. The beam size isstrongly correlated to the emittance of beams and it can bemeasured in a one-shot, therefore an instant feedback canbe performed by measuring the beam size instead of measuring the emittance. In the coming operation scheduled
at autumn 2015, the offset injection will be performed bymeasuring the beam size.

4.

ENERGY SPREAD

As another possible way to mitigate the emittance degradation, a bunch compression using J-Arc section is now under investigation [5] . Since the transverse wakefield effectcan be reduced by a shorter bunch length, a bunch compression system with non-isochronous J-arc could be a solution
to achieve a lower emittance. However, the shorter bunch
length causes the stronger longitudinal wakefield, resulting
in a large energy spread. Therefore, it has to be well studied with detailed simulation. In this section, the relation
between the bunch length and the energy spread is investigated. In the following simulation, the initial energy spread

0.60.40.2002468101214 16 18 20bunch length [ps]Figure 7: Energy spread at the end of the 5-sector as a function of bunch length with on-crest RF phase.
In order to suppress the energy spread, the ”off-crest”
method is studied in this paper. Since the beam energy inSuperKEKB is much smaller than that in KEKB, there is a
5 % margin in the accelerating voltage, which means that
the RF phase can be changed to off-crest phases. Figure 8
shows the energy spread as a function of bunch length with
an optimal RF phase. In the case of 2 nC, the energy spreadof 0.1 % can be achieved even when the Gaussian beam
distribution is assumed. However, in the case of 5 nC, only
rectangular beam distribution satisfies the requirement inPhase 3. Therefore, it is crucial to make such an optimal

σE/E [%]

beam shape, and the study concerning a laser pulse shaping
is now on-going [6] .

2 nC, gaussian

12 nC, rectangular
5 nC, gaussian

0.8

5 nC, rectangular

0.6
0.4
0.2
002468101214 16 18 20bunch length [ps]Figure 8: Energy spread at the end of the 5-sector as a function of bunch length with an optimal RF phase.

5.

CONCLUSION

Design study on the KEK injector linac upgrade is reported focusing on numerical simulation for the emittancepreservation and the beam energy spread. As a candidate
for the mitigation of the transverse wakefield effects, theoffset injection method using steering coils is considered.
It is numerically shown that the requirement in Phase 2 and3 can be satisfied with this method, although it is necessary
to control the orbit stably in a high precision at Phase 3.
Experimental demonstration of the offset injection method
is also performed with a thermionic electron gun. The energy spread of 0.1 % also can be achieved if beams areplaced on the optimal off-crest RF phase and the longitudinal beam distribution is rectangular. More systematicstudies between the emittance preservation and the energy
spread are under study.

REFERENCES[1] KEKB Design Report, KEK Report 95-7.
[2] M. Borland, ”elegant: A Flexible SDDS-Compliant Code forAccelerator Simulation”, Advanced Photon Source LS-287,
September 2000
[3] K. Yokoya, ”Short-Range Wake Formulas for Infinite Periodic Pill-Box”, May 13, 1998
[4] The 18th KEKB Accelerator Review:
http://wwwkekb.kek.jp/MAC/2015/[5] H. Sugimoto et al, ”Design study on KEK injector linac upgrade for high-current and low-emittance beams”, IPAC’12,Louisiana, USA 2014.
[6] M. Yoshida et al, ”Generation and Acceleration of Lowemittance, High-current Electron Beams for SuperKEKB”,
LINAC’14, Geneva, Switzerland, 2014.