EMITTANCE PRESERVATION IN SUPERKEKB INJECTOR
S. Kazama∗ , M. Satoh, H. Sugimoto, M. Yoshida, Y. 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 thanthat of KEKB. A short-range transverse wakefield and adispersive effect at the linac cause an emittance growth, anda longitudinal wakefield effect enlarges an energy spread ofthe beams. In this paper, we presented simulation studies
concerning the emittance preservation and the energy spread
issues. As a candidate for the mitigation of the emittance dilution originating from the transverse wakefield, a so-called"offset injection" method using steering coils is considered.
It is demonstrated that the offset injection remarkably improves the emittance preservation.

INTRODUCTION

Table 1: Required parameters for SuperKEKB∗ kazama@post.kek.jp

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 C-sector to 5-sector
for sim-plicity.

Condition of simulation

SuperKEKB is an electron-positron collider with an energy of 7 GeV and 4 GeV, respectively. The target luminosity is 8×1035cm2s−1, which is 40 times higher than thatof KEKB [1]. SuperKEKB main ring therefore requires ahigh current and low emittance beam. These parameters aresummarized in Table 1. In order to meet the requirement,
photo-cathode RF guns are now installed at the injector linac
for the electron beam. For the production of a low emittancepositron beam, a damping ring is now under construction.
Since the target emittance is quite small compared to that of
KEKB, much more attention should be paid to the emittance
growth through the linac. The Short-range wakefield and thedispersive effect are considered to be the major sources ofthe emittance dilution. In this paper, we report on a design
study on SuperKEKB injector for high current, low emittance, and low energy spread beams. We mainly report on
simulation studies concerning the emittance preservation
issues and how to suppress the increase of the energy spread.
All simulation presented in this paper is performed withelegant [2].

 Bunch charge nC
Vertical emittance
mm mradHorizontal emittance
mm mrad Energy spread %Figure 1: Schematic of SuperKEKB injector linac.

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

4/5
20 / 20100 / 50

100 / 500.1

0.1

The initial particle distribution in the longitudinal direction at the C-sector is a Gaussian of 10 ps bunch length(FWHM) with 2 or 5 nC charge and 1.5 GeV energy. The
distributions of transverse phase space and energy spread areboth assumed to be Gaussian. The initial emittance in thehorizontal and vertical directions and the energy spread are
set to be 10 mm mrad and 0.1 %, respectively. Longitudinalmonopole and transverse dipole wakefield are incorporated
in the simulation with an analytical expression 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 emiitance growth, alignment errors for
quadrupole magnets and acceleration tubes are considered,and their distributions are assumed to be Gaussian.

EMITTANCE PRESERVATION
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 tothe tail particles. The induced wakefield can deflect thetrailing particles further away from the axis, resulting in an
increase of the projected beam emittance. A small amountof misalignment and a short bunch length can reduce thetransverse wakefield strength. However, the short bunch
length causes the strong longitudinal wakefield, resulting ina large energy spread. Therefore, the bunch length has tobe optimized with a detailed simulation. The dependenceof the bunch length on the energy spread will be discussed
in the next section. To achieve the required emittance, themagnitude of the misalignment must be kept as small aspossible. Figure. 2 shows a simulated vertical emittance at

Figure 2: Vertical emittance at the end of 5-sector as afunction of the magnitude of misalignment.

In the SuperKEKB injector linac, the local alignment of
the accelerator structures at the 3, 4, and 5-sector has been
performed with a laser tracker during summer shutdown in2014 [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 100 µm seems to be already achieved.
Systematic uncertainties on the measurement are now underinvestigation. The most important error is expected to comefrom the uncertainty of the alignment of the girders on which
accelerator structures are placed.

Offset Injection
As discussed in the previous section, accelerator elements
cannot be perfectly aligned. Hence, even when the beam is
injected without an offset, the misalignment will induce
the transverse wakefield. In order to reduce the emittance
growth, a compensation method ("offset injection") has been
investigated in this paper. In the actual experiment, thiscan be performed by adjusting the current of steering coil.
Electron beams are then injected into the next section witha certain kick angle and a certain offset. The kick angle canbe tuned in units of 0.1 µrad, and the effect originating fromthe instability of a power source is estimated to benegligible. We simulated the effect of the offset injection in
the case of Phase 2 and 3 using a lattice with an alignment
error of 0.1 mm in sigma. Figure 4 and 5 show the verticalemittance at the end of 5-sector as a function of the offset
and the kick angle when the beam charge is 2 and 5 nC,respectively. In both cases, optimal offsets and kick angles
are estimated to be relatively small, 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 ofoffsets and kick angles satisfy the requirement in Phase 2.
On the other hand, only a few parameters satisfy therequirement in the case of 5 nC, therefore the orbit control
in Phase 3 will be quite challenging.

γ ∈y @ 5-sector End [m rad]the end of 5-sector as a function of the magnitude of local
misalignment when the charge of the electron beam is 5 nC.
It shows that the vertical emittance of 20 mm mrad can berealized if the magnitude of the misalignment is smaller than
0.1 mm in sigma.

×10−30.14

Kick Angle = 0 [µ rad]0.12

Kick Angle = -18 [µ rad]
Kick Angle = -28 [µ rad]0.1

Kick Angle = -38 [µ rad]

0.08
0.06
0.04
0.02
0−0.1 −0.05

00.05

0.1

0.15

0.2

0.25 0.3
offset [mm]Figure 4: Vertical emittance as a function of the offset andthe kick angle when the beam charge is 2 nC.

ENERGY SPREAD

Figure 3: Measured misalignment of the accelerator structures on the girders in the horizontal (black) and vertical(red) direction.

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 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 is set tobe 0 to confirm how much energy spread is induced.

Kick Angle = 0 [µ rad]
Kick Angle = -16 [µ rad]0.4

Kick Angle = -26 [µ rad]0.3

σE/E [%]γ ∈y @ 5-sector End [m rad]−3

0.5 ×10

2 nC, gaussian

12 nC, rectangular
5 nC, gaussian

0.8

5 nC, rectangular

Kick Angle = -36 [µ rad]

0.6
0.2
0.4
0.1
0.2
0−0.1

−0.05

00.05

0.1

0.15
0.2
offset [mm]002468101214 16 18 20bunch length [ps]Figure 7: Energy spread at the end of 5-sector as a functionof the bunch length with optimal RF phase.

Figure 6 shows the energy spread at the end of 5-sector
as a function of the 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.

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

σE/E [%]

Figure 5: Vertical emittance as a function of the offset andthe kick angle when the beam charge is 5 nC.

1.4
2 nC, gaussian

1.2

2 nC, rectangular
5 nC, gaussian

15 nC, rectangular

0.8
0.6
0.4

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 forthe mitigation of the transverse wakefield effects, the offset
injection method using steering coils is considered. It is numerically shown that the requirement in Phase 2 and 3 can besatisfied with this method, although it is necessary to control
the orbit stably in a high precision at Phase 3. The energy
spread of 0.1 % also can be achieved if beams are placedon the optimal off-crest RF phase and the longitudinal beam
distribution is rectangular. An experimental demonstrationof the offset injection method and more systematic studies
between the emittance preservation and the energy spread
are under study.

0.2002468101214 16 18 20bunch length [ps]REFERENCES[1] KEKB Design Report, KEK Report 95-7.

Figure 6: Energy spread at the end of 5-sector as a functionof the bunch length with on-crest RF phase.

[2] M. Borland, "elegant: A Flexible SDDS-Compliant Code forAccelerator Simulation", Advanced Photon Source LS-287,
September 2000

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 wecould change the RF phase up to 20 degree. Figure 7 showsthe energy spread as a function of the bunch length withoptimal 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, onlyrectangular beam distribution satisfies the requirement inPhase 3. Therefore, it is crucial to make such an optimal[3] K. Yokoya, "Short-Range Wake Formulas for Infinite Periodic
Pill-Box", May 13, 1998
[4] The 18th KEKB Accelerator Review: http://www-kekb.
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.