Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP23DESIGN OF THE LOW ENERGY BEAM TRANSPORT LINE FOR THE
JAEA-ADS LINAC
B. Yee-Rendon∗ , Y. Kondo, J. Tamura, F. Maekawa and S. Meigo
Japan Atomic Energy Agency (JAEA), Tokai, Japan
Abstract
The Japan Atomic Energy Agency (JAEA) is proposing a30-MW proton linear accelerator (linac) for the applicationof accelerator-driven subcritical system (ADS) technology
to achieve nuclear waste transmutation. A major challenge
for the JAEA-ADS linac is the efficient transport of a 35 keVproton beam from the ion source to the radio-frequency
quadrupole. In order to achieve this goal, we have optimized a magnetostatic low energy beam transport (LEBT)
consisting of two solenoids to reduce the transmission ofhigh-charge ions generated by the source and minimize thegrowth of proton emittance, while taking into account different values of space-charge compensation along the LEBT.
In this report, we present the optical design and discuss themultiparticle tracking results of the JAEA-ADS LEBT.

INTRODUCTION
The Japan Atomic Energy Agency (JAEA) is designingan accelerator-driven subcritical system (ADS) for transmuting minor actinides [1]. The JAEA-ADS proposal uses
a 30-MW proton beam to produce spallation neutrons foran 800-MWth thermal power subcritical reactor. JAEAADS accelerator team has completed most of the linac design [2–5]. This work focuses on the design of the low
energy beam transport (LEBT) that carries a 25 mA proton
beam from the ion source to the RFQ.

Figure 1: Schematic view of the JAEA-ADS LEBT design.
The schematic design of the JAEA-ADS LEBT is depicted
in Fig. 1, the design is composed by two solenoids, chopper,
conical collimator, and beam diagnostics. Table 1 offers asummary of the major parameters and their corresponding requirements for the JAEA-ADS LEBT. The design of LEBT
was formulated for steady-state operation, i.e., without achopper, in order to use constant space-charge compensation. Additionally, the the model employed 3D-EM solenoid
fields to consider the effect of non-linear magnetic fields.
The current solenoid scans were applied to establish appropriate configurations that were subsequently employed as
input for the RFQ models to verify their compatibility. The
manuscript outlines the criteria, simulations, and results for
the JAEA-ADS LEBT.
∗ byee@post.j-parc.jp

Table 1: Main Parameters for the JAEA-ADS LEBT. The
Requirements for the Two Developed RFQ Models: Reference [3] and Equipartioned (EP) [4] are Presented.
Parameter
Particle
ProtonBeam current (mA)
25
Beam energy (keV)
35
𝜀𝑟𝑚𝑠,𝑛𝑜𝑟𝑚,𝑡𝑟𝑎𝑛𝑠 (𝜋 mm mrad)≤ 0.2
Length (m)≤2
RFQ models
Reference EP𝛼1.29
2.9
𝛽 (mm/𝜋mrad)
0.06
0.12

OPTICS DESIGN
At low energy, high-intensity beams experience significant self-generated repulsion between charged particles,
known as space-charge. This leads to irreversible emittance
growth, resulting in increased beam size and ultimately lossof the beam. However, in regions where the beam propagatesin the presence of residual gas, the gas molecules become
ionized by the beam. The ionized secondary particles thatcarry an opposite charge to the beam are trapped and accumulated in the beam potential until reaching an equilibrium.
The net effect is a reduction of the self-repulsion of the beam
particles, the so-called space-charge compensation [6].
In this work, we focus on designing the LEBT for steadystate operation, where space-charge compensation reaches
equilibrium. The compensation depends on residual gas
pressure and EM field, e.g., ionized secondary particles are
not easily accumulated inside the beam in the presence ofelectrostatic fields. Therefore, the space-charge compensation usually changes along the LEBT.
In our case, we assumed a constant space-charge compensation by section. This was done to assumed a more reasonable model. To this end, we used the space-charge compensation degree (𝜂) different in each part, where 𝜂=100%
means that the beam is fully space-charge compensated and0%, the beam experience the full space-charge effects.
Figure 2 presents the space-charge model used in thisstudy. 𝜂 starts with a small value and increases towards
the first solenoid. Then, 𝜂 reaches a large value (usuallyassuming > 85% ). Finally, 𝜂 decreased at the entrance of
the RFQ. The values used are more conservative than theemployed by other LEBTs [7, 8] in order to achieve a morerobust design [9].
LEBT design should also avoid non-linear magnetic fields
to reduce beam loss and limit emittance growth. Addition-- 545 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP23

where 𝐵𝜌 is the beam rigidity.
In addition, Durandeau [11] derived an expression for
the B𝑝𝑒𝑎𝑘 as a function of the number of turns, current, andgeometry of the solenoid:
𝐵𝑝𝑒𝑎𝑘 ≈Figure 2: Steady-state JAEA-ADS LEBT envelope design.
The model assumed a constant space-charge section by sections.

𝜇0 𝑁𝐼,𝑎/0.485(5)where 𝜇0 is the vacuum permeability and 𝑁𝐼 is the productof the number of coils turns and the coil current.
After substituting Eqs. (3), (4), and (5) into Eq. (1) andperforming algebraic operations, the following expression isobtained:

𝜖𝑡𝑟𝑎𝑛𝑠
0.06 𝜇 𝑁𝐼
𝑅4≈ √1 + 𝑘( 3 ( 0 )2)2 ,𝜖𝑡𝑟𝑎𝑛𝑠,0𝐵𝜌
𝜖𝑎𝑡𝑟𝑎𝑛𝑠,0ally, the solenoids must be tuned to achieve the required
Twiss parameters, i.e., produce a properly converged beam.
Solenoid 1 must keep and adequate beam size until Solenoid
2. Then, Solenoid 2 should smoothly produce a convergence
beam at the end of the LEBT. The chopper was not usedin this analysis since the beam steady-state condition wassimulated.

(6)

SOLENOID MODEL
Design and tuning of the solenoids play a major role inachieving a robust and efficient LEBT. Thus, we developed amodel that uses analytic calculation and 3D-EM simulations
for the solenoid design. 3D-EM fields allow us to consider
non-linear effects that are presented in real solenoids. Additionally, this tool assists in achieving solenoid design witha proper spherical aberration to obtain an acceptable beamemittance growth.
The emittance growth due to spherical aberrations in thesolenoid is estimated as [10]:𝜖𝑡𝑟𝑎𝑛𝑠 /𝜖𝑡𝑟𝑎𝑛𝑠,0 = √1 + 𝑘(𝐶𝛼 𝑅4 2) ,𝑓 𝜖𝑡𝑟𝑎𝑛𝑠,0(1)where 𝜖𝑡𝑟𝑎𝑛𝑠 is four-times the unnormalized emittance, 𝑘 is acoefficient that depends on the beam distribution (𝑘 = 0.11 foruniform beam distribution), 𝐶𝛼 is the spherical aberration,
𝑅 is the maximum transverse size inside the solenoid, and 𝑓is the focusing length of the solenoid.
Assuming that the solenoid field is described by:𝐵𝑧 (𝑧) =𝐵𝑝𝑒𝑎𝑘,
1 + (𝑧/𝑎)6(2)where 𝐵𝑝𝑒𝑎𝑘 is the peak of field and 𝑎 is the half of the halfwidth to full width; thus, 𝐶𝛼 and 𝑓 can be approximated to:1 ∫ 𝐵𝑧′2 (𝑧)𝑑𝑧
7≈,
2 ∫ 𝐵𝑧2 (𝑧)𝑑𝑧
12𝑎2(3)(2𝐵𝜌)29 (2𝐵𝜌)2≈,2∫ 𝐵𝑧2 (𝑧)𝑑𝑧 5𝜋𝑎 𝐵𝑝𝑒𝑎𝑘(4)𝐶𝛼 =and𝑓 =Figure 3: Unnormalized emittance growth map as a functionof the parameter 𝑎 and the products of the number of turns
in the coils per current (𝑁𝐼) . The target area (ellipse) andthe 3D model (star) are indicated.
Figure 3 shows an unnormalized emittance growth map
as a function of the parameter 𝑎 and 𝑁𝐼 for the JAEA-ADSLEBT using Eq. (6). For this scan, 𝜖𝑡𝑟𝑎𝑛𝑠,0 = 46.33 𝜋 mm
mrad is used according to ion source simulations [5], 𝐵𝜌
is 0.027 Tm for a proton beam with an energy of 35 keV.
Additionally, it was assumed a 𝑅= 30 mm, and an uniform
beam distribution, 𝑘 = 0.11. A target area was indicated𝜖𝑡𝑟𝑎𝑛𝑠based on preliminary results to achieve a 𝜖𝑡𝑟𝑎𝑛𝑠,0< 1.4.
As a result, the suitable parameters for 𝑎 are between 120
to 150 mm and for 𝑁𝐼, from 4000 to 500 A−turns, whichcorrespond to a 𝐵𝑝𝑒𝑎𝑘 between 170 to 220 mT.
Using the CST Studio Suite program [12], a 3D model
was created based on the analytic results. The model consistsof 6 coils, a shielding yoke made of iron, and a beam pipewith radial and longitudinal mirror symmetry. The coils
use hollow cables for water cooling. Figure 4 shows the 3D
design, and the optimized Bz field, while the specifications ofthe model are provided on Table 2. There was an acceptableagreement between analytic and 3D model results.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP23

Solenoid current scans were implemented to determined
the suitable values for the LEBT operations. Figure 5 shows
the proton transmission obtained by thoses scans. The range
was restricted between 45 to 75 A because it provides anappropriate setting region for a high proton beam transmission and a current density operation lower than 3.2 A/mm2 ,which is well below the current limit for water-cooled coilsof 10 A/mm2 .

Figure 4: 3D Solenoid model: (a)-subplot presents geometry details of the model and (b)-subplot shows the longitudinal B-field at the center of beam pipe.
Table 2: 3D Solenoid Parameters
Parameter
Length (mm)External diameter (mm)Aperture diameter (mm)Total number of coil turns
Nominal coil current (A)Nominal B𝑝𝑒𝑎𝑘 (mT)𝑎 (mm)

Figure 5: Proton transmission from the solenoid scans. The
equivalents B𝑝𝑒𝑎𝑘 fields are also given.
Configurations with high solenoid currents result in higher
proton transmission due to a larger magnetic field, resulting
in a more compact beam. For settings with I𝑐𝑜𝑖𝑙1 higher than
60 A and I𝑐𝑜𝑖𝑙2 values larger than 55 A, larger transmission
is registered. Notably, for configurations with I𝑐𝑜𝑖𝑙2 around
55 A, high transmission is obtained for almost any valueof I𝑐𝑜𝑖𝑙1 , which pointing out the importance of the proper
focusing of the last solenoid.

300460
160
782
60217
130

Table 4: Cases with more than 90% of Proton Transmission

BEAM DYNAMIC STUDIESThe beam dynamic studies used the output parameters ofthe extraction system for the JAEA-ADS linac [5] as input
parameters. Actual proton sources not only produce proton
beams but also other high-charge ions. Therefore, in thiswork, proton and H2 + were simulated. Table 3 presents
the input parameters for the LEBT simulations. The beam
dynamic studies were done using the TraceWin code [13].
Table 3: Input Parameters for the LEBT Simulations
ParameterProtonH2 +Beam energy (keV)
𝛼𝛽 (mm/𝜋mrad)
Distribution type
Beam current (mA)𝜀𝑟𝑚𝑠,𝑛𝑜𝑟𝑚,𝑡𝑟𝑎𝑛𝑠 (𝜋 mm mrad)
Number of macroparticles

35-1.73
0.16
Uniform
25.06
2.980.090.10
1× 105 1.2× 104

CaseI𝑐𝑜𝑖𝑙1 (A)I𝑐𝑜𝑖𝑙2 (A)123456789101112131415455055606065
6570707075
7575757555555555
6055
6055
6065
55
60
65
7075

Table 4 shows cases with transmission over 90%. The
beam performance of these cases was analyzed and com-- 547 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP23

pared to identify suitable candidates for RFQ models (yellowareas), as shown in Fig. 6. Proton transmission is increased
by increasing solenoid current but causes high-charge ionstransmission too. We are interested in the region with highproton transmission but low high-charge ions transmission.
In addition, high-current solenoids will keep the beam small,thus reducing the emittance growth by no-linear fields. The
requirements more restricted were a convergence beam (positive 𝛼) and a small beam size (small 𝛽), see Table 1.

Based on the analysis, cases 3 and 4 were chosen as inputs for the RFQ models since they had the most suitableperformance. Table 5 displays the beam performance for theaccepted cases. For the Reference RFQ, only a performancecomparison with Case 3 is presented in Fig. 7 since the results indicate that Case 3 is acceptable. In the case of EP
RFQ, the two cases resulted in an RFQ transmission of over93%, but there was a considerable increase in longitudinalemittance, as shown in Fig. 8 (b).
Table 5: Beam Parameters for the Cases 3 and 4Figure 6: Beam performance for the interested cases:(a) Proton and H2 + transmission, (b) Twiss 𝛽, (c)𝜖𝑟𝑚𝑠,𝑛𝑜𝑟𝑚,𝑡𝑟𝑎𝑛𝑠 , and (d) Twiss 𝛼. The yellow areas indicate
the suitable performance required for the RFQ models. In
addition, the trending for models with second coil current of
55 A (red-dashed line) and 60 A (blue-dashed-dot line) areplotting on the subplots (b) and (c).

Parameter

Case 3

Case 4

Particle
Beam current (mA)
Beam energy (keV)𝜀𝑟𝑚𝑠,𝑛𝑜𝑟𝑚,𝑡𝑟𝑎𝑛𝑠,𝑓 𝑖𝑛𝑎𝑙 (𝜋 mm mrad)
𝛼𝛽 (mm/𝜋mrad)

Proton
2035
0.17
0.12
1.1
1.6
0.05
0.11

Figure 7: Emittance comparisons for the Reference RFQ
model using the baseline (ideal) input parameters and theobtained for the Case 3.

CONCLUSIONSThis work reports the first studies for the LEBT design for
the JAEA-ADS linac. The JAEA-ADS LEBT adopted a magnetostatic model using two solenoids to transport the beam- 548 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP23

bata, Hidetomo 0guri, and the members of the JAEA-ADS
group for their comments and suggestions.

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Figure 8: Emittance comparisons for the EP RFQ modelusing the baseline (ideal) input parameters and the obtainedfor the cases 3 and 4.

[6] N. Chauvin et al., “Source and Injector Design for IntenseLight Ion Beams Including Space Charge Neutralisation”, inProc. of the LINAC2010, Tsukuba, Japan, Sept. 2010, TH302,pp. 740-744.

from the ion source to the RFQ. First, a systematic procedure
integrating analytical calculations and 3D-EM simulations
was developed to design and optimize the JAEA-ADS LEBT
solenoid to reduce emittance growth produced by the aberrations. Then, the LEBT design was optimized for the steadystate case, i.e., without chopper operation. The simulation
studies considered different values of space-charge compensation along the LEBT length. Solenoid current scans wereapplied to determine optimum values. The analysis foundseveral configurations that provide high proton transmission.
Among those cases, Case 3 (I𝑐𝑜𝑖𝑙1 = 55 A and I𝑐𝑜𝑖𝑙2 = 55 A)
and Case 4 (I𝑐𝑜𝑖𝑙1 = 60 A and I𝑐𝑜𝑖𝑙2 = 55 A) were used as
input for the two RFQ designs for JAEA-ADS: the Reference
and EP. The results showed that Case 3 is suitable for the Reference RFQ model. High beam transmission was achievedin cases 3 and 4 for EP RFQ, but further optimizations areneeded due to extra emittance growth.
Our next step is to develop a better LEBT design using
the WARP code [14], which will help us accurately estimate
space-charge compensation and study beam transients.

[7] L. Bella, “Beam Dynamics Characterization of theIFMIF/EVEDA RFQ Input Beam”, Ph.D. thesis, Physics andAstronomy Dept. Univesita degli Studi di Padova, Padova,Italy, 2017.

ACKNOWLEDGMENTS
The authors would like to thank to Nicolas Chauvin,Lorenzo Neri, Cristhian Valerio, Kai Masuda, Takanori Shi-

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