INVESTIGATION OF BEAM VARIATION AND EMITTANCE GROWTHSIMULATION WITH BOTH MISALIGNMENTS AND THE BEAM JITTERFOR SUPERKEKB INJECTOR LINAC
Y. Seimiya∗† , M. Satoh, T. Higo, T. Suwada, F. Miyahara, K. Furukawa, KEK, Ibaraki
Abstract
The SuperKEKB is e+/e- circular collider for high luminosity, 8 × 1035 as a target value. For the high luminosity, the injector linac is required to transport low emittancehigh-charged electron beam and positron beam to the ring.
A charged beam with an oﬀset from a center of cavity isaﬀected by the wakefield depending on both the oﬀset sizein the cavity and longitudinal particle position in the beam.
The wakefield causes emittance growth. This growth can besuppressed by appropriate orbit control so as to cancel thewakefield eﬀect of the cavities in total. On the other hands,
the beam variation in 6-dimensional phase space also induces the emittance growth. Emittance growth by both misalignments and 6-dimensional beam jitter was evaluated byparticle tracking simulation. Investigation of beam jitterand drift was also performed by correlation analysis between beam position and measured parameter, charge ortemperature.

INTRODUCTION
SuperKEKB is e+/e- collider for high energy particle
physics in KEK. Design luminosity of the SuperKEKB is8 × 1035 , which is 40 times higher than that of KEKB
achieved [1]. This high luminosity can be realized by twice
current and one-twentieth beam size compared with that ofKEKB. For the high luminosity, high intensity low emittance beam is necessary for the injector linac. If beam phasespace is larger than SuperKEKB ring acceptance, the particles over the acceptance are lost and lifetime of the beam in
the ring become short and luminosity go down. Therefore,
we have to transport high charged low emittance beam toSuperKEKB ring.
Phase 1 of SuperKEKB project started from Feb. 2016.
Various devices check, software operation check, and vacuum scrubbing were done successfully. Last run of the linac
before DR (Damping Ring) commissioning was finished as
mentioned reference [2]. DR commissioning will start fromAutumn 2017 and phase 2 will start from 2018 for tuning
to low emittance beam and low background with Belle IIdetector, which was installed April 2017. Physics run isplanned in the phase 3 from Winter 2018. Low emittancebeam tuning has to be established in the phase 2.
Schematic layout of the linac is shown as Fig. 1. The
linac is composed of sector A, B, J-ARC, C, and 1∼5. Normalized horizontal/vertical emittance less than 40/20 µm at
the end of linac is required in the phase 3. The linac has∗ yuji.seimiya@kek.jp† This work is supported by JSPS KAKENHI Grant Number 16K17545.

two kinds of electron gun: thermionic gun for high-current
electron beam for positron generation and photocathode RF
gun for low emittance electron beam. Positron beam is accelerated up to 4 GeV and transported to LER (Low Energy Ring). Low emittance electron beam is accelerated
up to 7 GeV and transported to HER (High Energy Ring).
Two-bunch operation will be performed at 50 Hz with 96
ns bunch space. Positron beam emittance for LER is reduced by DR, which is placed between sector 2 and sector
3. There is not major emittance reduction mechanism aboutelectron beam for HER because there is not DR for electronbeam. Emittance preservation of the electron beam in theSuperKEKB injector linac was studied by Ref. [3–5]. A
charged beam with an oﬀset from a center of cavity is affected by the wakefield depending on both the oﬀset sizein the cavity and longitudinal particle position in the beam.
The wakefield causes emittance growth. This growth canbe suppressed by appropriate orbit control so as to cancel the wakefield eﬀect of the cavities in total. However
not only misalignments of accelerator components but also
beam variation cause emittance growth statistically, which
simulation was performed after ARC section in the reference [6]. In this paper, we evaluate the emittance growthfrom after electron gun (merged point of two electron gunprecisely) to the end of linac by as follows: misalignmentsof quadrupole magnets and acceleration cavities, magnetic
jitters of quadrupole and steering magnets, 6-dimensional
beam jitter. We also investigate the reason of the beam variation (jitter and drift).

Figure 1: Schematic layout of the SuperKEKB injector
linac.

WAKE FUNCTION AND POTENTIAL
We performed particle tracking simulation for SuperKEKB linac. Transverse and longitudinal wake field inacceleration cavity were taken into account. Short range
wake functions were derived K. Yokoya [7]. Analyticalwake function and numerical wake function in short-range
were also derived by K. Bane [8]. These wake functions
and the wake potentials are shown as Fig. 2, 3, respectively.
Beam distribution is gaussian and σ = 3 mm/2.35, which
is typical bunch length in the linac, was assumed in wakepotential calculation, which is normalized by charge (nC)//((/ )/ / )in this paper. In Fig. 3, wake potential calculated by CST
studio [9] is also plotted. Though the CST wake potential
is less than others by about 20%, these behaviors are almost same. In this paper, Yokoya wake was used in particle
tracking simulation. Only short-range wake field is treatedbecause bunch space of two-bunch operation is 96 ns andthe space is long enough to ignore middle-range wake fieldin our S-band accelerator cavity.

(()

/(()

Value
1053/2.350.004
10000
Gauusian10UnitµmnCmmmm))/ )/(--Parameter
Initial emittance
Initial charge
Initial σ z
Initial δ# of initial particles
Distribution
S-band accelerator apertureevaluated at the end of linac where wire scanner is placed.
In this paper, definition of emittance is RMS emittance.

Figure 2: Comparison of wake functions. Right and left
figures show transverse and longitudinal wake function, respectively. Green, red, and blue lines show K. Yokoya, K.
Bane, and analytical wake function, respectively.

-Table 1: Basic parameter set. Aperture values indicate theradius. δ is relative momentum deviation.

()

Figure 3: Comparison of wake potentials. Right and left
figures show transverse and longitudinal wake function, respectively. Green, red, blue, and purple lines show K.
Yokoya, K. Bane, analytical, and calculated wake function(CST), respectively.

EMITTANCE GROWTH
One of the simulation result for low emittance is shown as
Fig. 4 under the conditions we mentioned previous section
without magnetic and beam jitters. Blue and red show horizontal and vertical parameters, respectively. From the topof the figure, emittance, the number of transported particles,
beam orbit, misalignments of quadrupole magnets, misalignments of acceleration cavities, and K value of steering
magnet, respectively. Horizontal emittance increases temporally in ARC sector since there is large dispersion in theplace. In the result, normalized horizontal/vertical emittance at the end of linac is about 24/10 µm, which is lessthan target value, 40/20 µm.

PARTICLE TRACKING SETUP
Particle tracking simulation was performed by the Strategic Accelerator Design program [10]. Procedure of lowemittance tuning is as following. First, orbit correction isperformed so as to minimize beam position measured byBPM. Second, oﬀset injection, which is one of emittancecontrol method by 4 steering magnets [11], is performed.
In the linac, reference point of BPM is calibrated to centerof quadrupole magnet by Quad-BPM method [12]. In oursimulation, we assume that BPM have same misalignment
as that of nearest quadrupole magnet. We also assume that
doublet or triplet quadrupole magnets have same misalignment values and acceleration cavities on same frame havesame misalignment from A sector to ARC sector. Standard
deviation of these gaussian misalignments is 0.2mm at from
A to B sector and 0.1mm at ARC sector. Since emittance
growth at the end of linac is more sensitive to misalignment
at ARC section than that at other sectors, misalignment requirement at the sector is higher. From after C sector, misalignments measured by laser PD [13] were used. Realistic
limited steering magnetic force was taken into account. Table 1 is basic parameters of our simulation. Oﬀset injection
was performed both at after merged point of sector A forthermal&RF gun and at the start of sector C. Emittance was

Figure 4: An example of simulation settings and results.
Jitter simulation was performed on the base of this setting. 6-dimensional beam jitters are {x, x ′, y, y ′, z, δ} = {10µm,1 µ, 10 µm, 1 µ, 0.03 mm, 0.03%}. Transverse position
jitters are consistent with measured jitter at start point of thissimulation. Angle jitters are expected to be about one-tenth
the position jitters since BPMs are placed at about 10 m interval. Longitudinal position jitter is roughly corresponded
to required phase jitter of acceleration cavity. Longitudinal momentum deviation is corresponded to that at ARCsector. Quadrupole and steering magnetic have relatively
8 × 10−4 and 10−4 jitters to peak magnetic force of thesemagnet, respectively. These jitters have gaussian distributions. Emittance growth by these jitters are described by
Fig. 5. The figure shows steering jitter is most sensitive
to emittance growth. Total horizontal/vertical emittance,
which is described as an emittance about all particles of injected beam, is 27/15 µm only with beam jitter , 37/16 µm

only with quadrupole jitter, 54/22 µm only with steering jitter, and 74/28 µm with all jitters.

Figure 5: Emittance growth by beam, quadrupole, andsteering jitters.

INVESTIGATION OF BEAM VARIATION
Beam position jitters influence directly total emittance.
Therefore, reduction of the beam position jitters is important for low emittance tuning. Measured beam position jitters are shown at top of Fig. 6 and correlations between
beam positions and charge are shown at bottom of Fig. 6.
From the start of linac to before ARC section, averaged
beam position jitter was about 25 µm (BPM resolution isabout 10 µm). Horizontal beam position jitter was enlarged
at ARC section (around 150m point in the figure). Longitudinal momentum jitter in the presence of horizontal dispersion induces horizontal beam position jitter. If dispersion isleaked, beam position jitter is enlarged as shown top of theFig. 6. SP15T and SP165 are placed at before and after target where beam position jitters increase. Electron beam for
HER passes through tungsten target hole, which diameter is
2 mm. In the correlation plot, correlations also increase atthese points. This result suggests beam lost at the small holeand beam position jitters are enhanced. To reduce the beam
position jitters, dispersion suppression and momentum jitter reduction have to be done. If the beam position jittersafter ARC section, beam loss at the target hole should besmall and enhancement of the beam position jitters shouldbe also small after the target. The operation for the position
jitter reduction will be done at the next run of linac.

Figure 6: Beam position jitter in the linac and correlations
between beam positions and charge. Blue and red show horizontal and vertical correlations, respectively.

Temperature drifts at upstream of A sector and at HV station for electron gun were measured as top of Fig. 7, coloredgreen and red, respectively. In the same time, beam positions were also measured as middle of Fig. 7. From theshape of these figures, it can be found that these temperatures have correlations to beam position (BPM picked uprandomly). In fact, correlations between temperature andbeam positions are large as shown at bottom of Fig. 7. Thesethree figures show the correlations at BPMs in one-third of
the time taken in temperature measurement of HV station.
Blue and red show horizontal and vertical correlations, respectively. Time passes from the left to right figure. Temperature of HV station was stable at the first one-third time,and correlation value is not large. However, at the second
and third one-third time, temperature of HV station drift,
and correlation value became large. This result shows temperature drift around electron gun influence beam position
drift.

Figure 7: Temperature around electron gun, beam position
jitter, and these correlations.

CONCLUSION
Particle tracking simulation for HER electron beam wasperformed. In this simulation, 0.2 mm RMS misalignments
between sector A to B, 0.1 mm RMS misalignments at
ARC sector, measured misalignment between sector C to 5,0.01% steering magnetic jitter, 0.08% quadrupole magnetic
jitter, and {10 µm, 1 µ, 10 µm, 1 µ, 0.03 mm, 0.03%} as 6dimensional beam jitter were included. In these conditions,steering magnetic jitter is dominant for emittance growth.
Low emittance tuning method could be developed so as toreduce sensitivity of steering jitter to emittance growth, forexample optimization of dispersion suppression, otherwise
power supply with higher precision is necessary. Beam position jitter aﬀects growth of total emittance directly; therefore investigation of beam jitter was also performed. Dispersion after ARC section has to be suppressed to reducebeam jitter for high charged low emittance beam. Temperature drift also aﬀects beam position drift. Air conditioning
with more performance is desired in linac.

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