BEAM PHASE SPACE JITTER AND EFFECTIVE EMITTANCEFOR SuperKEKB INJECTOR LINAC∗
Y. Seimiya† , N. Iida, T. Kamitani, M. Satoh, KEK, Ibaraki, Japan
Abstract

Table 1: Target Values of Linac for SuperKEKB

In SuperKEKB linac, stable high charged low emittancebeam is necessary. Transported beam to SuperKEKB Main
Ring (MR) must be stable to the extent that the beam can beinjected inside MR acceptance. SuperKEKB requirement
must be satisﬁed for emittance including beam phase space
jitter, called as eﬀective emittance. Large amplitude beam
position jitter has been measured at linac end. We evaluated that the eﬀect of the beam position jitter to eﬀective
emittance and investigated the cause of the beam position
jitter.

INTRODUCTION
SuperKEKB is e+/e- collider for high energy particle
physics in KEK. Design luminosity of the SuperKEKB
is 8 × 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 emittancebeam is necessary for the injector linac. If beam phase spaceis larger than SuperKEKB ring acceptance, the particles
over the acceptance are lost and lifetime of the beam in thering become short and luminosity goes down. Therefore,
we have to transport high charged low emittance beam toSuperKEKB ring.
Phase 2 commissioning of SuperKEKB project started
from Spring 2018. Collision and luminosity tuning is undergoing in May 2018 as mentioned reference [2]. Physics run
is planned in the phase 3 from Winter 2018. Our target
values of the phase 2 and phase 3 are shown as Table 1.
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 endof linac is required in the phase 3. The linac has two kinds ofelectron gun: thermionic gun for high-current electron beamfor 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). Lowemittance 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 about electron beam for HER because
there is not DR for electron beam. Emittance preservationof the electron beam in the SuperKEKB injector linac wasstudied by Ref. [3–5]. A charged beam with an oﬀset froma center of cavity is aﬀected by the wakeﬁeld depending on∗ This work is supported by JSPS KAKENHI Grant Number 16K17545.
† yuji.seimiya@kek.jp

Phase 2Phase 3

H/V Emittance

ChargeEnergy Spread

150/150 μm
40/20 μm

1 nC
4 nC

0.1%
0.07%

both the oﬀset size in the cavity and longitudinal particle position in the beam. The wakeﬁeld causes emittance growth.
This growth can be 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 in the reference [6].
Transported beam to MR must be stable to the extent
that the beam can be injected inside MR acceptance. SuperKEKB requirement must be satisﬁed for emittance including beam phase space jitter, called as eﬀective emittance.
We evaluate the emittance growth by beam phase space jitterand investigate the jitter source.

Figure 1: Schematic layout of the SuperKEKB injector linac.

EFFECTIVE EMITTANCE AND JITTEREMITTANCETo evaluate the emittance growth by beam phase space
jitter, we introduce following eﬀective emittance,
(1)e f f = < X 2 >< X 2 > − < X X  >2 .
γ0 β − 2α0 α + β0 γ
= 02 +  j2 + 20  j(2)2= 02 +  j2 + 20  j Bmag .
(3)
X = x + Δx, X  = x  + Δx ,0 = < x 2 >< x 2 > − < x x  >2, j = < Δx 2 >< Δx 2 > − < ΔxΔx  >2,(4)(5)(6)

where 0 and  j are nominal emittance and emittance converted beam phase space jitter (jitter emittance), respectively.
Bmag shows mismatch between measured Twiss parameterand that of design. The value equal to or larger than 1. If
Bmag = 1, there is not mismatch and eﬀective emittanceequal just nominal emittance plus jitter emittance. Bmag

is about 1 ∼ 2 in usual linac operation, which is measured
by wire scanner. Assuming that beam position and transfer
matrix between two BPMs are identiﬁed, beam angle canbe derived. Jitter emittance can be derived from the beam
position jitter and beam angle jitter.

RESULTSWe measured beam position jitter at BPM (beam positionmonitor) in the linac. Figure 2 shows measured beam position jitter and jitter emittance in the linac. Horizontal axis
shows beam line position (m) from after the electron gun.
Position jitter is standard deviation of measured beam position. Around the 140 m point of the ﬁgure, there is J-ARC
section. Though the section is dispersive, beam energy jitteris converted to beam position jitter in this section. Dispersion was 0.8 m and position jitter was about 360 μm at thecenter of this section, then energy jitter was about 0.045%.
After the J-ARC and positron generation target placed inabout 290 m point, beam position jitter and jitter emittancewas enlarged. At the end of linac, horizontal/vertical jitter
emittance was about 27/7 μm. Though target value of thehorizontal/vertical emittance in phase 3 is 40/20 μm, the effect of jitter emittance on eﬀective emittance was very large.
Figure 3 shows beam phase space jitter at before, after thetarget, and linac end. After the target, jitter emittance wasclearly increased.

Figure 3: Beam phase space jitter at before, after the target,
and linac end.
and jitter emittance were reduced. Horizontal/vertical jitter
emittance at the end of linac was 1.8/0.9 μm. Under 1 nC
beam operation, eﬀect of the jitter emittance on eﬀective
emittance is small.

Figure 4: Dispersion measurement before the dispersionsuppression.

Figure 2: Measured beam position jitter and jitter emittancein the linac. The electron beam was 1 nC and generated byRF gun.
Figure 4 shows dispersion measurement result. Very large
dispersion leak was measured. Quadrupole magnets in theJ-ARC section was tuned to suppress the dispersion. Afterthe dispersion suppression tuning, dispersion leak became
small as shown Fig. 5. Measured beam position jitter andjitter emittance after dispersion suppression is shown asFig. 6. By dispersion suppression, beam position jitter

Figure 5: Dispersion measurement after the dispersion suppression.
Though jitter emittance become small by dispersion suppression, enhancement of the jitter emittance still remain at
before and after the target. Enhancement factor, which is theratio of beam position jitter after to before the target, is notchanged remarkably by dispersion suppression. Around theFigure 7: Transverse wake potential induced by positron
generation target. Color variation shows beam position fromthe center of the target hole, 0.1 mm, 0.2 mm, ..., 0.9 mm.

Figure 6: Measured beam position jitter in the linac after
dispersion suppression. The electron beam was 1 nC andgenerated by RF gun.
target, there are some components which may inﬂuence thejitter; ﬂux concentrator, solenoid, bridge coil, pulsed magnet, and chicane. We turned oﬀ the all of the components
and measured the jitter, however there was no noticeable
diﬀerences. Electron beam for LER hits the target, whileelectron beam for HER pass through the target hole (φ2mm).
In case of positron after the target, there is not enhancementof the jitter. Then, the target hole was suspected as the jittersource.
Simulation analysis was performed by CST studio [7].
Figures 7 and 8 show simulation result of transverse andlongitudinal wake potential induced by positron generation
target, respectively. As distance between the beam position
and the center of the target increase, transverse wake potential increase nonlinearly. While, longitudinal wake isindependent of beam position from the center of the target
hole. Even beam pass through outer side of the hole, theeﬀect on the enhancement factor is too small to explain themeasurement as far as design beta function or gaussian beam
is assumed.

Figure 8: Longitudinal wake potential induced by positron
generation target. Color variation shows beam position fromthe center of the target hole, 0.1 mm, 0.2 mm, ..., 0.9 mm.
Though the target hole is being suspected as a beam jittersource, simulation result suggest that the wake ﬁeld eﬀect
is small as far as design beta function or gaussian beam isassumed. We will check beta function and beam proﬁlearound the positron generation target.

REFERENCES

CONCLUSION[1] KEKB Design Report, KEK Report 95-7, KEK, Aug. 1995.

Beam phase space jitter is reduced by dispersion suppression after J-ARC section. Under 1 nC operation, the eﬀect
to eﬀective emittance is small. However jitter emittance isstill enhanced after the target. In phase 3, 4 nC high-charged
low emittance electron beam will be required for HER (HighEnergy Ring). Therefore, we have to investigate the sourceof the beam phase space jitter continuously to reduce therisk of emittance growth.
Enhancement factor, which is the ratio of beam position
jitter after to before the target, is not signiﬁcantly changed bydispersion suppression. Dependence on ﬂux concentrator,solenoid, bridge coil, pulsed magnet, and chicane is small.

[2] Y. Ohnishi et al., presented at IPAC18, Vancouver, Canada,
Apr. 2018, paper MOXGB1, this conference.
[3] L. Zang et al., in Proc. IPAC’11, San Sebastian, Spain, 2011,
paper MOPS058.
[4] H. Sugimoto et al., in Proc. IPAC’12, New Orleans Louisiana,USA, 2012, paper TUPPC021.
[5] S. Kazama et al., in Proc. IPAC’15, Richmond, VA, USA,2015, paper MOPWA053.
[6] Y. Seimiya et al., in Proc. IPAC’17, Copenhagen, Denmark,2017, paper TUPAB005.
[7] CST home page, https://www.cst.com