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

PASJ2022 WEP001

DESIGN AND BEAM DYNAMICS STUDIES OF AN ADS RFQ BASED ON
AN EQUIPARTITIONED BEAM SCHEME
B. Yee-Rendon∗ , Y. Kondo, J. Tamura, K. Nakano, F. Maekawa and S. Meigo
Japan Atomic Energy Agency (JAEA), Tokai, Japan
R. A. Jameson
Institut Angewandte Physik (AIP), Frankfurt, Germany
Abstract
The Japan Atomic Energy Agency (JAEA) is designing a30-MW proton linear accelerator (linac) for the acceleratordriven subcritical system (ADS) project. The radio frequency quadrupole (RFQ) is an essential component forthe performance of high-intensity linac, especially in ADS
projects where stringent reliability is demanded. The JAEAADS RFQ will capture a 20 mA proton beam and acceleratefrom the energy of 35 keV to 2.5 MeV, where the spacecharge effects are severe. The JAEA-ADS RFQ’s design
employs the equipartitioning (EP) beam scheme to control
the emittance growth and compactness. As a result, the beam
halo formation was minimized and allowed the optimizationof the superconducting linac downstream part. A remarkable feature of this RFQ is the low Kilpatrick factor of 1.2
adopted to achieve high stability by reducing the probabilityof surface sparking on the vane. This work presents anddiscusses the results of this RFQ design.

εn,r ,l σl= 1,εn,r ,t σtwhere εn,r is the normalized root-mean-square emittance, σis phase advance, and the sub-indexes t and l stand for transεn,r ,l σlverse and longitudinal, respectively. Hereinafter εn,ris, t σtrefer as EP condition.
Table 1: Specification for the JAEA-ADS RFQParameterParticle
Beam current (mA)
Frequency (MHz)Initial energy (keV)
Final energy (MeV)
RF duty factor
KP factor
Beam transmission (%)
Final n,r ,l (π mm mrad)
n,r ,l /n,r ,tParticle outside the acceleration band [6](%)
Length (m)INTRODUCTION
The Japan Atomic Energy Agency (JAEA) is developing a 30-MW cw superconducting proton linear accelerator(linac) for the accelerator-driven subcritical system (ADS)
project [1]. Figure 1 displays a simplified version of theJAEA-ADS linac.

(1)

Proton20162352.5100% (CW)
≤ 1.2
≥ 97
≤ 0.39≤ 1.5≤1≈7

However, by fulfilling EP condition, Eq. 1, the valuesof the phase advance per period (σ/L period ) are restricted.
Moreover, σl /L period is related to the accelerating gradient(Eacc ) of the cavities by the following relation:
σl /L period ∝Eacc .

(2)

Combined Eq.1 and 2, we obtain:
Eacc ∝ (Figure 1: Simplified scheme of the JAEA-ADS linac.
The linac has a normal conducting part and a superconducting one, where most of the acceleration occurs [2]. TheMain linac, superconducting part, adopted an equipartitioned (EP) beam scheme [3]. EP condition balances theinternal energy between planes, minimizing the emittanceexchange by removing free energy between transverse andlongitudinal planes that could drive parametric resonances.
Thus, it provides low emittances, tight beams, and low beamloss. The EP condition is represented as:∗ byee@post.j-parc.jp

σt /L period 2) .
εn,r ,t /εn,r ,l(3)A reference design of JAEA-ADS RFQ [4] employeda conventional RFQ design [5]. Beam transmission wasover 97%, with final εn,r s of 0.22 and 0.39 π mm mrad on
the transverse and longitudinal plane, respectively. The
reference RFQ design had an output εn,r ,l /εn,r ,t equal
to 1.77; consequently, Eacc ∝ ((σt /L period )/1.77)2 in theMain linac. By decreasing the final ratio to 1.5, Eq. 3 showsthat Eacc of the cavities of the Main linac could be increased
by 18% regarding the ratio of 1.77, which will help to reduce
the number of required cavities. Therefore, to improve thebeam quality provided by the RFQ and increase the acceleration efficiency at the Main linac, an intermediate RFQ
design based on the EP beam scheme is developed to satisfy- 499 -Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEP001

the requirements listed in Table 1. This manuscript presents
and discusses the results of the EP JAEA-ADS RFQ design.

RFQ DESIGN STRATEGY
The design and the beam dynamics studies were donein the LINACS framework developed by Jameson [7],LINACSrfqDES and LINACSrfqSIM provide full control ofall RFQ design and simulations parameters, including beamdriven design, fully 3D simulation using correct quadrupolar symmetry and carefully connected Poisson solution for
external and space charge fields, and extensive analysis techniques. In LINACS, the RFQ parameter adjusting is doneby solving beam equations or by specifying rules for theevolution of the beam parameters. The RFQ parameters aretuned to provide the required external fields that allow thespecific beam target characteristics.
EP JAEA-ADS RFQ adopted a similar procedure as otherEP RFQs [8, 9]. The RFQ is divided into three sections: radial matching, Shaper, and Main RFQ. The radial matchingcomprises a few cells, usually four, that accept the beamfrom the upstream part. Shaper is where the beam begins tobunch and where the beam is brought to the EP condition.
Main RFQ is where the beam is finally bunched and accelerated to its target energy. The design strategy consisted ofadjusting the RFQ parameters to satisfy the two matchingequations along the RFQ and the EP equation from the endof the Shaper until the end of the RFQ. The end of the Shaper
is a key point for the RFQ design because there the beam isclose to the design size; thus, it is a robust and convenient
location to bring the beam to the EP condition. Furthermore,
the bunching process starts at the Shaper; therefore, it has a
crucial role in the longitudinal beam emittance. The transverse and longitudinal sizes are used to satisfy the matchingequation, and the vane modulation (m) is tuned to achieve
the EP condition. Thus, the rest of the variables were adjusted according to the rules to achieve the required beam
performance.

BEAM DYNAMICS STUDIESThe optimization of the RFQ was carried out using beam
dynamics analysis, which comprised the tracking of 100,000
macroparticles using the LINACSrfqSIM program. As anexample of the optimization process for the RFQ parameters,
we discussed the selection of the synchronous phase (φs )at the end of the Shaper. Figures 2 and 3 summarize theimportant results of this scan. For φs target values close to−90 deg, the beam bunching becomes adiabatic; thus, thelongitudinal emittance growth is reduced but increases theRFQ length, see Fig. 3(c).
Figures 2(a) and (b) show that the five models stay close to
the EP condition and are below the limit of the εn,r ,l /εn,r ,t ,respectively. Figure 2(c) presents a spike in the longitudinalemittance after the Shaper, which position is slightly different for each model, where some particles escaped from thelongitudinal acceptance and eventually lost, thus reducing
the emittance. At the entrance of the Main RFQ section,

Figure 2: EP condition (a), longitudinal to transverse emittance ration (b), and the longitudinal (c) and transverse (d)normalized rms emittance along the RFQ for different φs target at the end of the Shaper. The magenta dotted line shows
an EP condition value of 1 for subplot (a) and an emittanceratio of 1.5 for subplot (b).

the beam characteristics for each model were different: the−84 deg φs target model was almost unaffected by resonances
resulting in a smooth beam envelope, but -85 and −86 deg
cases suffered from harmful resonances, ending in a significant transverse emittance growth, as shown in Fig. 2(d).
−84 deg φs target case provides the best performance interms of emittance growth and shortest length, but Fig. 3(b)reveals that it has a fraction of out energy particles beyond
the acceptable limit presented in Table 1. −88 deg φs target
model has the higher transmission and the smallest beam
fraction of out energy particles, as shown in Figs. 3(a) and- 500 -Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan
October 18 - 21, 2022, Online (Kyushu University)

PASJ2022 WEP001(b). The emittance growth control, and the EP and emittanceratios are acceptable, but it has the longest length. However, the length still fulfills the specification; furthermore,
the length could be reduced by applying other parameter
optimizations. Thus, we chose the −88 deg as the φs target
at the end of the Shaper.

Figure 4: Vane parameter for the EP JAEA-ADS RFQ.
Table 2: Design parameter of the EP JAEA-ADS RFQParameter
Inter-vane voltage (V)ρt /r0mmax
amin (mm)r0 (mm)φs,max (deg)
Bmax
Number of cells
Length (m)Figure 3: Transmission (a), out energy particles (b), andRFQ length (c) as a function of the φs target at the end ofthe Shaper.
Figure 4 shows the cell parameters for the optimized RFQ
design, where a is the minimum radius of the electrode tip,
r0 is the average bore radius, B is the dimensionless focusingparameter, Ws is the design energy, and V is the inter-vanevoltage. One distinct feature of this RFQ is its long Shaper
section, essentially the first 1.3 m of the RFQ. 80% of theShaper is composed of a "porch" section, i.e., a fraction of
the length where the φs remains −90 deg, which helps toachieve a smooth bunching process. Table 2 summarizes theprincipal parameters of the design.
Figure 5 shows the evolution of the EP condition,
εn,r ,l /εn,r ,t , and the normalized rms emittance along theRFQ. The EP condition, red dashed line in Fig. 5 (a), approaches one at the end of the Shaper, then increases over one

60.2
0.75
2.6
4.5
4.9 - 9.3
-25.3
8.9
365
6.9

at the beginning of the Main section, and finally smoothly
converges near the EP condition. The model indicates thatthe εn,r ,l /εn,r ,t , blue dotted line in Fig. 5 (top), is mainlyaffected by the longitudinal emittance performance because
the transverse emittance remains almost constant, Fig. 5(b).
Figure 6 presents the transverse distribution (a) and the longitudinal phase space (bottom) at the end of the RFQ. The
distribution exhibits a tight beam in the transverse plane withless dense tails. The longitudinal phase space is contained± 40 deg in phase and ± 75 keV, ∆W/W0 = 3%, in energy.
Table 3 confirms that the model satisfies the specification of
the RFQ design.
Table 3: Beam dynamics results of the EP JAEA-ADS RFQ- 501 -Parameter
Initial transverse distribution
Initial n,r ,t (π mm mrad)
Initial longitudinal distribution
Final n,r ,t (π mm mrad)
Final n,r ,l (π mm mrad)
n,r ,l /n,r ,tBeam transmission (%)
Particle outside the acceleration band (%)
Length (m)water bag
0.2
uniform phase
0.22
0.32
1.45
99.7
0.85
6.9

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

PASJ2022 WEP001

beam scheme. The design applied a smooth bunching process to control the longitudinal emittance growth and reduce the number of particles outside the energy band, which
is a potential source of beam loss in the downstream sections. In addition, the model exhibits a high beam transmission with appropriate control of the transverse size. Theεn,r ,l /εn,r ,t of 1.45 raises the accessible longitudinal phase;
consequently, increasing the available accelerating gradientin cavities at the main linac of the JAEA-ADS. The design
satisfies the requirements for the JAEA-ADS linac; thus, it
is another viable choice that offers extra control over thebeam performance and high acceleration efficiency for theJAEA-ADS linac.

ACKNOWLEDGMENTS
Figure 5: EP and emittance ratios (a) and normalized rmsemittance (b) obtained from beam dynamics studies.

The authors would like to thank to the members of theJAEA-ADS group for their comments and suggestions. This
work was supported by the Subsidy for Research and Development on Nuclear Transmutation Technology.

REFERENCES[1] T. Sugawara et al., “Research and Development Activities for
Accelerator-Driven System in Jaea”, Prog. Nucl. Energy, vol.
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007[2] B. Yee-Rendon et al., “Design and beam dynamic studies of a 30-MW superconducting linac for an acceleratordriven subcritical system”, Phys. Rev. Accel. Beams., vol. 24,p. 120101, Dec. 2021. doi:10.1103/PhysRevAccelBeams.
24.120101[3] R. A. Jameson, “Beam-intensity limitations in linear accelerators”, IEE Trans. Nucl. Sci., vol. 28, p. 2408, June. 1981.
doi:10.1109/TNS.1981.4331708[4] Y. Kondo et al., “Reference design of the RFQ for JAEA-ADSlinac”, JPS. Conf. Proc, vol. 33, p. 011015, March. 2021.
doi:10.7566/JPSCP.33.011015[5] K. R. Crandall et al., “RF quadrupole beam dynamics designstudies”, in Proc. of the 1979 Linac Conf.,New York, USA,Sept. 1979, paper S4-1, pp. 205-216.

Figure 6: Transverse distribution (a) and longitudinal phasespace (b) at the end of the RFQ.

[6] Particles outside the energy band are particles that are transmitted through the RFQ, but they are not in the longitudinal
acceptance of the beam. These particles will not be properly
accelerated and transmitted by the downstream structures; thus,
they are eventually lost. It is necessary to reduce them to guarantee hands-on maintenance and operate with high reliability
in the accelerator.
[7] R. A. Jameson, LINACS, open source, full Poisson since 2012.

CONCLUSIONSAn alternative RFQ design based on the equipartitioned
beam scheme has been developed for the JAEA-ADS linac.
The EP JAEA-ADS RFQ design was optimized by adjusting its parameters to provide the required external fields toachieve the desired beam performance. In particular, thevane modulation was tuned to achieve an equipartitioned[8] R. A. Jameson, “RFQ design and beam-loss distribution forIFMIF”, ORNL, Oak Ridge, USA, Rep. ORNL/TM-2007/001,January, 2007.
[9] Y. Kondo et al., “Development of a radio frequency
quadrupole linac implemented with the equipartitioning beam
dynamics scheme”, Phys. Rev. Accel. Beams., vol. 22, p.
120101, Dec. 2019. doi:10.1103/PhysRevAccelBeams.
22.120101- 502 -