DESIGN STUDY ON KEK INJECTOR LINAC UPGRADE
FOR HIGH-CURRENT AND LOW-EMITTANCE BEAMS
H. Sugimoto, M. Satoh, M. Yoshida, KEK, Tsukuba, Japan
Abstract
Injector linac at KEK is now under upgrading toproduce high current and low emittance beams to a
SuperB factory, named SuperKEKB. Emittance growth
resulted from both wakefield and dispersive effects at thelinac are troublesome in keeping the beam quality during
the acceleration. In this paper, we report recent simulation
study for the emittance preservation issue. As a candidate
for mitigation of the emittance dilution originated fromthe transverse wakefield, a bunch compression using an
existing bending section is considered. It is demonstrated
that the bunch compression remarkably improves theemittance preservation through the linac.

INTRODUCTION
SuperKEKB is a 7 GeV electron and 4 GeV positron
collider based on a nano-beam scheme[1]. The target
luminosity is 8x1035 cm−2 s−1, which is 40 times higher
than that of KEKB[2]. In the interaction point, a nanoscale sized beam is essential for the design luminosity.
SuperKEKB main ring therefore requires a high currentand low emittance beam (5nC, 20 mm mrad for electron,4nC, 6 mm mrad for positron). To meet the requirement,
new photo-cathode rf guns will be installed to the injector
linac for the electron beam. For the low emittancepositron beam, a damping ring is now under construction.
Since the target emittance required by SuperKEKB isvery small compared to that of KEKB main ring, much
more attention should be paid to emittance growththrough the linac. Short-range wakefield and dispersive
effects are considered to be the major source of emittance
dilution.
In this paper, we report design study on SuperKEKB
injector for high current and low emittance beams. We
mainly report numerical simulations on the emittancepreservation. All simulation presented in this paper isperformed by an accelerator simulation code, named“SAD”[3].

EMITTANCE PRESERVATION
The word “emittance” has many definitions inaccelerator physics, thus it sometimes causes confusion
when the emittance preservation is discussed. The
definition of the emittance in this paper isε x ≡ γβx2p x2 − xp x, where γ and β are the Lorentz

factors. The canonical variables x and px are sum ofbetatron motion and motion related to the momentum
dispersion, namely, longitudinal beam dynamics.
Therefore the emittance is, in general not preserved andincreased by unexpected dispersion due to magnet
misalignment even when wakefield is absent.

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Figure 1: Schematic of SuperKEKB injector linac(upper figure) and beam optical functions (lowerfigure).
In the case of high current beam, the wakefield cause
serious emittance dilution. The longitudinal wakefield
induces energy spread to the beam and enhances
emittance growth due to the dispersive effect. The
enhanced energy spread also involves nonlinear dynamics.
The nonlinear force increases the beam emittance due tothe filamentation of the beam distribution. The transverse
wakefield is excited when a beam passes through off-axisof an acceleration structure and deflects tail particles. This
process cause serious beam instability in the high current
beam.
Therefore, in order to keep beam quality during theacceleration through the linac, the beam optics including
operation parameters should be carefully chosen tominimize these unexpected emittance degradations.

TRACKING SIMULATION
Figure 1 shows a schematic of SuperKEKB injector
linac and linear beam optics used in the tracking
simulations. The linac is mainly composed of 9 sections.
A one unique feature related to this paper is that there is abending section, named J-Arc. An application of thisexisting bending section to the emittance preservation is
the main topics of this paper.

Simulation Condition
The initial particle distribution is a rectangular pulse of
10 ps bunch length (FWHM) with 5nC charge assuming
an electron beam. Gaussian distributions are employed tothe transverse phase space and energy spread. The initial    ! "#$    % ! "#$    ! "#$          ! " #  " #

 

Figure 2: Horizontal emittance at the end of Sector B
as a function of rf phase of the acceleration tubes.
Each dot and vertical bar represents mean value andstandard deviation of 100 simulations, respectively.
On-crest is defined by 0 degree, and positive phasemeans bunch head gains higher energy from the rf
wave compared to bunch tail.
emittance is 6 mm mrad for both horizontal and verticaldirections, and the energy spread is 0.4 %. These
parameters are chosen from a numerical simulation for a
photo-cathode rf gun to be installed.
Longitudinal monopole and transverse dipole wakefield
are incorporated in the simulation by using an analyticalexpression of the wake functions[4]. Long-range
wakefield effects are not taken into account. The beam isapproximated by 105 macro particles.
Alignment error of quadrupole magnet and acceleration
tube is considered. All alignment errors are Gaussian
distributed with rms 0.3 mm without particularly noted.
Global orbit correction is carried out with singular value
decomposition using 81 BPMs and 194 steering magnets.
Each BPM is attached to the quadrupole magnets.
Therefore the orbit correction is done not by minimizing
actual beam offset to the design beam line, but by
minimizing the BPM readings. The jitter error of BPM
and beam is not included.

From SectorA to B
Before proceeding simulation including whole linac
sections, emittance preservation from the Sector A to B isexamined. The emittance at the end of Sector B as afunction of acceleration phase is shown in Fig. 2, where 3
different simulation conditions are assumed to find out
the most dominant source of the emittance growth.
The emittance is well preserved if linac is perfectlyaligned or wakefield is turned off. When themisalignments are introduced to the linac, resultant orbit
distortion induces the transverse wakefield and causes
emittance degradation. Considering that the orbit 

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

   

Figure 3: Longitudinal beam profile with and withoutbunch compression.
correction is done so that the beam passes through thequadrupole center, the dispersive effect due to quadrupole
misalignment is minimized after the optics correction. On
the other hand, the beam may passes through the off-axisof the acceleration tubes, thus the transverse wakefield isinevitably excited. These simulation results indicate thatthe most dominant source of the emittance growth iswakefield as long as orbit correction is performed by thepresented procedure.
To mitigate the wakefield effects, an application ofBNS damping[5] has been considered. BNS damping,
however, results a relatively large energy spread at theend of Sector B and leads to serious beam losses at avertical slit installed to the following J-Arc bendingsection. One of other possible solution is offset injection
scheme[6]. Both experimental and numerical simulation
studies at KEKB injector shows that the offset injection
effectively reduces the emittance dilution[7].

Bunch Compression Using J-Arc Section
As a possible way for mitigation of the emittancedegradation due to transverse wakefield, we here consider
a bunch compression using J-Arc section.
Our linac has a bending section named J-Arc as alreadymentioned. J-Arc currently is an isochronous bending
section and the (5,6) element R56 of the transfer matrix is0. The transverse wakefield effect can be reduced if
shorter bunch length is attained. A bunch compression
system with non-isochroous J-arc has been investigated.
Longitudinal phase space plot at the end of J-arc
section with and without the bunch compression are
shown in Fig. 3. It is confirmed from Fig. 3 that the nonisochronous J-arc works well as a bunch compression
system. The bunch compression in J-Arc reduces theemittance dilution after J-Arc section as shown in the next
section.

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Figure 4: Horizontal emittance history along the linac.
Figure 6: Horizontal emittance at the end of the linac
as a function of transfer matrix element R56 of J-arc
Section, where 3 alignment precisions are considered.
same seed of random number in the all simulation shownin Fig. 6. The non-isochronous J-Arc remarkably
improves emittance preservation.

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SUMMARY    

Figure 5: Horizontal phase space plot at the end of thelinac with and without the bunch compression.

From Sector A to Sector 5
We finally perform simulations of emittancepreservation through the whole linac section to see how
effective the bunch compression is. In the presented
simulation, we assume that J-Arc section is perfectlyaligned in order to focus on the emittance dilution
originated from the transverse wakefield. J-Arc
imperfection leaks a large dispersion to the downstream
and causes emittance growth. The effect on the emittance
dilution from the dispersion leakage will be investigatedin the near future.
Figure 4 shows the horizontal emittance history along
the linac with and without bunch compression. The
emittance rises at J-Arc section due to the energy
dispersion. A huge emittance growth is observed after
400 m. This is simply because that betatron function islarge compared to that of before 400 m and the large
betatron function enhances the transverse wakefield effect.
The emittance dilution after J-Arc section dramatically
improved when the bunch compression is preformed asexpected. Transverse phase space plot shown in Fig. 5clearly shows that the phase space distortion is improved.
The relation between the final emittance and R56 valueof J-Arc is shown in Fig. 6, where 3 different amplitudesof alignment errors are considered. Since the finalemittance may strongly depend on the seed of random
number used in the generation of misalignment, we use a

Design study on the KEK injector linac upgrade isreported focusing on numerical simulation for theemittance preservation through the linac.
The simulation revealed that the most dominant sourceof the emittance degradation from Sector A to B is thetransverse wakefield rather than dispersive effect fromquadrupole misalignment. This is because the orbit
correction is performed so that the beam passes though
the quadrupole center.
As a candidate for the mitigation of the transverse
wakefield effects, a bunch compression system using an
existing bending section is considered. It is numericallyshown that the beam is successfully compressed with thenon-isochronous J-Arc.
The tracking simulation of the emittance preservation iscarried to see effectiveness of the bunch compression.
The simulation shows that the emittance dilution isdramatically improved owing to the shorter bunch length.
More systematic and comprehensive study on theemittance preservation issue is under study.

REFERENCES[1] C. P. Raimondi, 2nd SuperB Workshop, Frascati,Italy, Mar. 16-18, 2006.
[2] “KEKB Design Report, “ KEK Report 95-7.
[3] K. Oide, Nucl. Inst. Meth. A 276, 427 (1989).
http://acc-physics.kek.jp/SAD/[4] K. Yokoya, “Short-Range Wake Formulas forInfinite Periodic Pill-Box”, May 13, 1998
[5] V. Balakin, S. Novpkhatsky,and V. Smirnov, Proc. of12th Int. Conf. on High Energy Accel., Fermilab,
1983, p.119.
[6] A.W Chao, B. Richter and C.Y. Yao, Nucl. Inst.
Meth. A 178, 1 (1980)[7] L. Zang et al., Proc. of IPAC2011, San Sebastian,Spain, p. 739 (2011)