Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEOA05

A DESIGN STUDY OF ILC ELECTRON DRIVEN POSITRON SOURCE
Masao Kuriki ∗ , Hiroki Tajino, Shun Konno, Zachary Liptak, Tohru Takahashi,
Graduate School of Advanced Science and Engineering, Hiroshima U.
Kaoru Yokoya, Junji Urakawa, Tsunehiko Omori,High Energy Accelerator Research Organization
Abstract
ILC is an electron-positron linear collider based on Superconducting linear accelerator. Linear collider is the onlysolution to realize high energy electron-positron collision
beyond the limit of synchrotron radiation energy loss by ring
colliders. Because the beam current of injector of linear
colliders is much larger than that of ring colliders since
the beam is not reusable, providing an enough amount ofparticles, especially positron is a technical issue. In thisarticle, we present a design of electron driven positron source
for ILC, especially how to accelerate stably the high current
beam by compensating the heavy beam loading to obtain abeautiful multi-bunch positron beam.

speed which is faster than speed of sound in air. To solve
this problem, the positron is generated with 20 pulses andone pulse contain 66 bunches in our scheme as shown in Fig.
2. In this case, the energy density on the target is 20 times
less and the spot of each pulse can be shifted easily with aslow rotation, 5 m/s in our design [3]. The speed is slower
than a professional marathon runner. The pulse is repeatedin 300 Hz and the system is based on the normal conducting
accelerator. It takes 63 ms to generate 1312 bunches ofpositron and the generated positron is stored in DR until theaccelerating in the main linac. The pulse structure in themain linac can be controlled by the beam extraction fromDR, which is independent from that in the positron source.
197ns

INTRODUCTION
ILC is an e+e- linear collider with center of mass energy
250 GeV - 1000 TeV [1] employing Super-conducting accelerator. One pulse contain 1312 bunches with 4.8 nC charge
including 50% margin and the pulse is repeated with 5 Hz
resulting the average beam current 21 A. This is a technicalchallenge, because the amount of positron per second is 40times larger than that in SLC [2], which was the first linear
collider. The configuration of the positron source is schematically shown in Fig. 1. The positron generated by electron
beam is captured and boosted up to 5 GeV. The drive beamenergy is 3.0 GeV electron. The generated positron is captured in RF bucket by L-band Standing Wave (SW) cavities
with 0.5 Tesla solenoid field; This is Capture Linac. The
positron is further accelerated up to 5 GeV by L-band andS-band Traveling Wave (TW) cavities (Booster) followed byECS (Energy Compression Section).

Figure 1: Configuration of E-Driven ILC positron source isschematically shown.
Generating positron in the pulse format of the main linac,
1312 bunches with 545 ns, might cause a severe damage on
the production target, since 1312 bunches are concentrated ina small spot size. To relax the energy deposition density on
the target, the target has to be rotated with 400 m/s tangential∗ mkuriki@hiroshima-u.ac.jp

197ns
80ns

33 bunches

33 bunches

474 nsFigure 2: The beam structure in the positron source. Eachmini-train contains 33 bunches.
The design was progressed improving the reality of thesimulation [3–6] and finally the beam loading and its compensation is now included. For those simulations, the peakenergy deposition density on the target is kept less than 35
J/g [7], which is considered to be a practical limit of thesafety operation. To obtain uniform intensity positrons overthe pulse, the transient variation of the acceleration field by
the beam loading has to be compensated so that positrons
are accelerated uniformly. Compensation for the transient
beam loading by Phase Modulation (PM) on the input RF
was proposed by Urakawa [8,9]. The detail study of the compensation is discussed in Ref. [10, 11]. In this article, we
present the electron driven ILC positron source accounting
this effect.

ELECTRON DRIVER

3 GeV electron driver is composed from 2600 MHz (Sband) normal conducting TW cavity. The cavity is originallydesigned for ATF(Accelerator Test Facility) at KEK [12] in2856 MHz and the parameters are scaled to 2600 MHz. Asa basic unit, 4 cavities are driven by two klystrons with 80
MW peak power. Accounting 10 % power loss in RF wave
guide, the input power to one cavity is 36 MW. The shunt
impedance is 57.2 M/m with L=3.228 m and the attenuation
𝜏 is 0.57 resulting 0.91 s filling time.

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Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEOA05

Energy fluctuation by the transient beam loading is compensated by amplitude modulation (AM) on the input RF[11]. A perfect compensation is possible with two components AM, a step pulse and a trapezoidal pulse. In this case,a high peak power is required at the vertex of the trapezoidal
modulation and the acceleration field becomes less. In thisdesign study, we employ one component AM with a step
pulse to revive the average acceleration field allowing forsome variation. 𝐸0 is the initial cavity field, and 𝐸1 is theamplitude of AM. 𝐸1 is determined as
𝐸1 =𝑟𝐼 ⎛ −𝜔/𝑄𝑡𝑝 𝑒−2𝜏
⎜
⎟,
+ 1⎞
2 ⎝ 1 − 𝑒−𝜔/𝑄𝑡𝑝⎠(1)

where 𝑡𝑝 is the pulse length setting the same cavity voltage
at 𝑡 = 𝑡𝑓 and 𝑡 = 𝑡𝑓 + 𝑡𝑝 . The initial field 𝐸0 is determined as𝑃𝑚𝑎𝑥 =𝐿(𝐸 + 𝐸1 )2𝑟(1 − 𝑒−2𝜏 ) 0(2)where 𝑃𝑚𝑎𝑥 is the maximum input RF power.
Figure 3 shows the temporal evolution of the cavity
voltage with AM. The acceleration voltage per cavity is
31.9 ± 0.4 MV with 0.65 A beam loading current 𝐼𝐵 with 36
MW input power. The error is the variation in RMS by thetransient beam loading. The first two cavities are driven by
two klystrons, so that the input power per cavity is 72 MW
resulting 43.5 ± 0.6 MV with the same 𝐼𝐵 . The electron
driver is composed from two cavities as the injector and100 cavities as the normal section. The total beam energy is
3.3 GeV which has 10% margin. The lattice of the electron
driver is summarized in Table 1.
7060

V (MV)

5040

Table 1: The lattice configuration of the electron driver. Theenergy and the gain is in MeV. G, Q, and S stand for RF Gun,quadrupole magnet, and S-band cavity.
SectionPre injector
Injector #1
Injector #2
Injector #3
Linac #4-#7
Linac #8-#25

LatticeG + 2S + 3Q
4(2Q + S)
2(2Q + 2S)
2(Q + 2S)
4(Q + 4S)
18(Q + 4S)

Energy gain
92.0
127.6
127.6
127.6
510.4
2296.8Energy
92.0
219.6
347.2
474.8
985.2
3282.0speed. At the down stream of the target, a flux concentrator
as a magnetic focusing to suppress the transverse momentumis placed. The detail of those arrangements is presented inRef. [6]. The loading on the target is evaluated by PEDD
(Peak Energy Deposition Density in J/g); the W-Re destruction limit is 76 J/g [13], and the safe operating threshold isconsidered to be 35 J/g [6]. The positron production yieldis 1.17 as evaluated in , the electron bunch charge is 4.1 nC.
PEDD for 4.8 nC electron bunch is 33.6 J/g [6], giving 28.7
J/g for 4.1 nC. This is even lower the threshold.

CAPTURE LINAC

The capture linac is composed from 36 APS (Alternate
Periodic Structure) 𝜋/2 mode SW cavity. The structureis 1.3 m long with 21 cells. The shunt impedance is 31.5
M/m. The purpose of the capture linac is to confine thegenerated positrons in a RF bucket. An effective way for thecapturing is the deceleration capture method where positrons
are placed on the deceleration phase [14]. The positron ismoving to the acceleration phase by phase slipping graduallyand the positron is captured at the acceleration phase. Figure
4 shows the captured positron distribution in the longitudinal
phase space 𝑧 and 𝛿 = (𝛾− 𝛾)/̄ 𝛾̄ where 𝛾 and 𝛾̄ are Lorentz
factor and the average. The positrons after acceleration aredistributed along the RF curvature.

30

20

10000.5

11.5

2μsFigure 3: Accelerating voltage evolution of the 3m S-band
cavity with the one-component AM with 0.65 A beam loading current. The red solid line shows the beam duration.
The solid line, dotted line, and dashed line show the cavity voltage, the RF voltage, and the beam loading voltage,
respectively.

TARGET AND MAGNETIC FOCUSING

Figure 4: Longitudinal phase space (𝑧 − 𝛿) distribution ofpositron at the end of the capture linac.

Target is a rim with 500 mm diameter and 16 mm thickness
made from tungsten-rhenium alloy. To avoid overlappingof the pulse on the target, it is rotated with 5 m/s tangential

In the capture linac, the beam phase is moving over thelinac. To compensate the voltage variation by the beamloading, phase modulation (PM) should be introduced. The- 52 -Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEOA05

detail of the beam loading compensation with PM is described in Ref [11]. We consider a combination of two input
RF signals with a constant RF amplitude for PM. The phaseof each input RF signals are modulated. If the phase modulation for the two klystrons are the same sign, the phase of thecombined RF is modulated. If the anti sign, the amplitudeof the output is modulated.
If the phase modulation to RF is instantaneous, the beamloading is compensated perfectly [11]. In reality, however,
the klystron is driven by a cavity, which has a finite time
constant; even if the phase of the RF input is modulated,the modulation of the klystron output appears with a delay.
To evaluate the effect of the delay of PM, we perform thenumerical calculation. If there is a delay with 𝜏 as the time
constant, the input RF evolution is̃𝑉𝑅𝐹=𝑉𝑅𝐹 {𝑢(𝑡) − 𝑢(𝑡 − 𝑡𝑏 )}Figure 6: Imaginary part of the cavity voltage evolution with
22.5 MW RF power with 1 A beam loading current startingat the filling time. PM with delay is applied.

𝑡−𝑡𝑏

𝑡−𝑡𝑏+𝑉𝑅𝐹 𝑢(𝑡 − 𝑡𝑏 )𝑒𝚤𝜙 (1 − 𝑒− 𝜏 ) ,(A)+𝑉𝑅𝐹 𝑒− 𝜏 𝑢(𝑡 − 𝑡𝑏 )(3)

where 𝑉𝑅𝐹 is the RF voltage amplitude, 𝑢(𝑡) is the step function, 𝑡𝑏 is time to start the beam acceleration, and 𝜙 is PM
angle. We calculate the cavity response with this modulation.
As the klystron Q value, we assume 2000. It can be compared with Q value of APS cavity, 25000. Klystron response
is 12 times faster than that of APS cavity. The time constant𝜏 is 0.24s in this case. This Q value of klystron is quite
ordinal and further optimization for a faster response is possible, but we assume this value anyway. The cavity voltage
is calculated using a coupled pendulum model developed byT. Shintake [15].

Figure 5: Real part of the cavity voltage evolution with 22.5
MW RF power with 1 A beam loading current starting at
the filling time. PM with delay is applied.
Figures 5 and 6 show the cavity voltage evolution withdelay of the klystron output according to Eq. (3). Figure 5and 6 show the real part and the imaginary part, respectively.
We start the beam acceleration at the filling time (kink in Fig.
5). The input RF power is 22.5 MW and the beam current
is 1 A. The beam angle 𝜃 is 𝜋/6. The imaginary part has asmall dip as shown in Fig. 5). The amplitude is -0.15 MV.
This value should be compared to the real part amplitude, 1621.5
10.50All− 0.5Electron
Positron−1− 1.5−2020406080100(ns)Figure 7: The beam loading current as a function of timein the capture linac. The electron, positron and sum of
the current are shown with dotted, dashed, and solid lines,
respectively.
MV. The dip of the imaginary component cause the phasefluctuation of 9.4 mrad, whose impact on the acceleration islimited.
Figure 7 shows the beam loading current as a functionof time, where the origin of time is when the positron isgenerated in the target. The electron, positron and sum ofthe current are shown with dotted, dashed, and solid lines,respectively. Initially, the beam loading current by electron
and positron are cancelled, but it rapidly increased because
they are captured at ”acceleration phase”. The acceleration
voltage by the cavity is decreased when the beam loading
current is increased as shown in Fig. 8.

CHICANE AND BOOSTER LINAC

After the capture linac, a chicane is placed to remove
electrons. As a sub-effect, the bunch length is shortened by
the momentum compaction factor. The chicane parameter isadjusted as the bunch length after the chicane is minimized
as shown in Fig. 9.
The positron booster is composed from L-band [16] andS-band [17] Traveling Wave (TW) cavities. The parameters
are summarized in Table 2.

- 53 -Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

30

V_beam
V_Cavity
V_RF30

Voltage by L-band 2m TW cavity (MV)(MV)

PASJ2022 WEOA05

20

100− 10− 202520151050020406080100(ns)

00.5

11.5

22.5

3μs

Figure 10: The voltage evolution of the L-band 2m TWcavity with 22.5 MW RF input and 0.78 A beam loading
current is shown with the same manner as those in Fig. 3.
Voltage by 2m S-band TW cavity (MV)

Figure 8: The cavity voltage (solid line), the beam loading
voltage (dashed line) and the RF voltage (dotted line) are
shown as a function of time.

504540
3530
25
20
15
10
5
00

0.2

0.4

0.6

0.8

1

1.2

1.4μs

Figure 9: Longitudinal phase space (𝑧 − 𝛿) distribution of
positron after the chicane.
By assuming 4.8 nC bunch charge, the beam loading current in the booster is 0.78 A. Figure 10 and 11 show thevoltage evolution of the L-band and S-band cavities with thebeam loading, respectively. The beam loading compensation
scheme is identical to that of the S-band TW cavity in theelectron driver. The voltage are 16.5 ± 0.1 MV for L-bandcavity and 29.2 ± 0.6 MV for S-band cavity. Those voltages
are evaluated with 𝑃𝑚𝑎𝑥 is 22.5 MW for L-band and 36 MWfor S-band including 10% power loss by wave guide. Table 3
summarizes the lattice configuration of the booster based on
the design in Ref. [4]. As the energy at the booster entrance,
250 MeV is assumed.
Table 2: Parameters of L-band and S-band TW Cavities inthe Booster
Parameter
Shunt impedance
LengthAperture (2a)Attenuation 𝜏
Filling time 𝑡𝑓

L-band46.5
2.00
35.0 39.4
0.261
1.28

S-band55.1
1.96
24.3-20.3
0.333
0.55

unit
M/mmmmFigure 11: The voltage evolution of the S-band 2m TW
cavity with 36 MW RF input and 0.78 A beam loading
current is shown with the same manner as those in Fig. 3.

ECS AND POSITRON YIELDThe purpose of ECS is to compress the energy spreadof positron after the booster, down to ±0.75%, within DR(damping ring) acceptance. ECS is composed from threechicane (18.6m, 55.8 m in total) and 4 L-band 3m TW cavities (4Q+4L lattice, 22.4 m) driven by 4 klystrons. Other twoL-band 3m TW cavities (2L, 6.4 m) driven by two klystrons
are set for the beam loading compensation.
The positron yield is defined as the number of positronsobtained in DR dynamic aperture (acceptance) per electrons
Table 3: Lattice configuration of the booster. In addition tothe abbreviation in Table 1, L stands for L-band TW cavity.
The gain is the acceleration energy in the section and Energy
is the beam energy at the end of the section in MeV.
Lattice
4Q+1L
4Q+2L
4Q+4L
4Q+4S

s- 54 -unit #3151825# of cavity
1260
72
100

Energy gain
198
990
1188
2860

Energy
448
1438
2626
5486

Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEOA05REFERENCES[1] “ILC Technical Design Report”, Rep. KEK-Report, 2013.
[2] “SLC Design Report”, Rep. SLAC-R-714, 1984.
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52, 2012. doi:10.1016/j.nima.2011.12.032[4] Y. Seimiya et al., “Positron capture simulation for the ILC
electron-driven positron source”, Prog. Theor. Exp. Phys.,vol. 2015, no. 10, Oct. 2015. doi:10.1093/ptep/ptv136[5] M. Kuriki et al., “Electron Driven ILC Positron Source witha Low Gradient Capture Linac”, in Proc. LINAC’16, East
Lansing, MI, USA, Sep. 2016, pp. 430–433. doi:10.18429/
JACoW-LINAC2016-TUPRC008

Figure 12: Longitudinal phase space (𝑧 − 𝛿) distribution ofpositrons after ECS section. 𝑅56 of ECS is -1.04. The solid
circle shows DR acceptance.

[6] H. Nagoshi, M. Kuriki et al., “A design of an electron driven
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Figure 13: Positron yield as a function of 𝑅65 of ECS. 𝑅56
is optimized for each 𝑅65 .
on the production target. The DR acceptance is [1](𝛾𝐴𝑥 + 𝛾𝐴𝑦<0.07 m,(4)22𝑧𝛿) +()0.035
0.0075<1.0.

(5)Figure 12 shows the longitudinal phase space distribution
after ECS with DR acceptance (solid circle). Figure 13
shows positron yield as a function of 𝑅65 of ECS. 𝑅56 is
optimized for each 𝑅65 . Yield is 1.17 and uniform in regionof −1.2 < 𝑅65 < −1.

SUMMARY

According to detail studies of the beam loading compensation for SW and TW cavities, the acceleration field isdetermined. Based on those parameters, the number of RF
units and the lattice are fixed and the ILC E-Driven positronsource design is established. The evaluated positron yield
was 1.17 giving the electron intensity on the target satisfying
the safety condition.

ACKNOWLEDGEMENTS

This work is partly supported by Grant-in-Aid for Scientific Research (B) and US-Japan Science and TechnologyCooperation Program in High Energy Physics.

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[10] M. Kuriki, “Energy Spread Compensation in Arbitrary Format Multi-Bunch Acceleration With Standing Wave andTraveling Wave Accelerators”, in Proc. IPAC’18, Vancouver, Canada, Apr.-May 2018, pp. 307–310. doi:10.18429/
JACoW-IPAC2018-MOPMF076[11] M. Kuriki et al., “Beam Loading Compensation of Standing
Wave Linac with Off-Crest Acceleration”, in Proc. IPAC’22,
Bangkok, Thailand, Jun. 2022, pp. 1893–1896.
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