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

PASJ2023 THP01

BEAM DYNAMICS STUDY OF THE HIGH-POWER ELECTRON BEAM
IRRADIATOR USING SUPERCONDUCTING CAVITY
O. A. Tanaka∗ , Y. Honda, M. Yamamoto, T. Yamada and H. Sakai,High Energy Accelerator Research Organization (KEK), 305-0801 Tsukuba, Japan
Abstract
At KEK, a compact 10 MeV, 50 mA accelerator design
was proposed for irradiation purposes. The current design includes a 100 kV DC thermionic electron gun with an RF grid,a 1-cell normal-conducting buncher cavity, and a Nb3Sn
superconducting cavity that accelerates the beam to final
energies of 10 MeV. The goal of this beam dynamics study
is to suppress the beam loss (to the ppm level) in order toreduce the thermal load due to the beam hitting the cavity.
Especially, the initial electron energy (100 keV) is low andthe space charge effect is large. The main challenges are to
optimize the beam shape without beam losses and to simultaneously control and transport multiple parameters of theaccelerator components. Here, we present a method for optimizing beam transport and report the results of optimizing
beam transport using this accelerator design.

INTRODUCTION
At the Compact Energy Recovery Linac (cERL) at KEK[1], an irradiation beam line was constructed and successfully commissioned [2]. Following the recent trend in accelerator science to design a compact high-current irradiationtype accelerators [3], [4] and based on the results of irradiation experiments at the cERL [5], we aim to develop a 50
mA electron beam irradiation facility working at the total
beam energy of 10 MeV.
High-current beam acceleration can be achieved by using
a superconducting cavities (SCs). In recent years, niobiumtin (Nb3 Sn) accelerating cavities have attracted attention as
next-generation accelerating cavities to replace Nb accelerating cavities. A higher transition temperature (18.3 K) of
Nb3 Sn makes it possible to operate the beam using only asimple small refrigerator instead of the conventional large
He refrigerator. That allows to design a compact facility.
The conceptual design of the proposed machine with special
emphasize on the Nb3 Sn SCs implementation is given in [6].
The overall design of the machine assumes the electron beam to be of 10 MeV and 50 mA. Figure 1 showsa schematic of the entire system. It includes: an injector partwith an electron gun of specific design, superconducting
cryomodule, and an irradiation part, so that the machine
can irradiate a large current beam. In order to evaluate theacceleration acceptance of an electron beam irradiation facility, we performed a three-dimensional particle tracking
including the space-charge effect with the acceleration cavity
system consisted of a buncher, two 1-cell SCs, and five 2-cell
SCs. We found solutions to mitigate the beam loss applying
a multi objective optimization. In the present study the beam
∗ olga@post.kek.jp

dynamics issues associated with the irradiator design are
discussed in details.

Figure 1: Conceptual design of 10 MeV, 50 mA accelerator
using Nb3 Sn superconducting cavity.

SYSTEM OVERVIEW
The electron gun is a 100 kV thermionic DC gun with an
RF grid [7] that produces a repetitive longitudinally packed
pulsed electron beam at 650 MHz. After that, we assumed tocompress the pulsed beam in the beam direction in a 1-cellnormal-conducting buncher cavity, and then accelerate it to
10 MeV using two 1-cell SCs (𝛽 = 0.8)1 [8] and five 2-cell
SCs. The RF frequency of all SCs is 1.3 GHz. The buncher
cavity operates at 650 MHz. Two solenoids were installed
before and after the buncher to provide transverse focusing.
In the irradiation section there are two quadrupoles placed
1 m downstream the cryomodule to adjust the beam size.
Then the beam is bent downward by the dipole and reaches
the extraction window (See Fig. 2).
Originally we used a 1.3 GHz buncher cavity identical tothose at cERL. The beam velocity-modulated in the buncher
cavity compresses the bunch length to about 30 ps at the first
SC position (Z 2.4 m). This corresponds to a phase widthof about ±14 degrees for an acceleration frequency of 1.3
GHz. Bunch compression is seen at 1.3 GHz with RF phasenonlinear components and can also be a source of loss. It
is possible to reduce these losses with a collimator, but it
is difficult to compress the 100 ps bunch length with 1.3
GHz cERL buncher. Therefore, we redesign and apply thebuncher cavity based on 650 MHz to increase the RF phaserange and effectively perform bunch compression.
The beam energy is accelerated up to 10 MeV by approximately 2 MV per cavity with five 2-cell cavities, which isfeasible with Nb3 Sn. When accelerating in the 2-cell SC
cavity after passing through the buncher, the acceleration
does not occur immediately. This is because the energy ofthe beam (100 keV) is in the non-relativistic region, and the
speed of the beam is not close to the speed of light. The
2-cell cavity does not accelerate properly due to the mismatch of the cavity cells, resulting in loss of energy. In
1 Low-𝛽 resonators are just cavities that accelerate efficiently particles withvelocity 𝛽 < 1.

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

PASJ2023 THP01

Figure 2: Layout of accelerator components.
order to eliminate cavity mismatch, each cell of the 2-cellcavities is made independent and the beam is slightly preaccelerated by two 1-cell (𝛽 = 0.8) cavities. As the graphsof the minimum speed of transportation (see Fig. 3) read, if
the minimum velocity is less than zero, the beam will run
in the opposite direction, and it will be impossible to use it
as an accelerator. If the amplitude of the cavity is increased
too much, it will enter a region where the beam cannot be
accelerated properly. The region that satisfies the condition
that the energy finally rises without reverse run is wider forthe 𝛽 = 0.8 cavity.

Figure 3: Minimum speed of transportation for 𝛽 = 1 1-cellcavity (top) and 𝛽 = 0.8 1-cell cavity (bottom).

BEAM DYNAMICS
Simulation Setup
To study the beam dynamics in the compact Nb3 Sn accelerator, the injector part and the superconducting cryomodule
were introduced into simulation. The electron gun distribution was included in this calculation, and the beam transport
calculation was performed with the layout shown in Fig.
4. We started the calculation by giving the particle distribution of the 100 keV beam at the cathode of the electron
source. For the electron gun, solenoids, buncher and 2-cellcavities simulation the 1D field distributions of those fromcERL were used. For the 1-cell cavity, the gap length of
the TESLA cavity was reduced 𝛽 = 0.8, and the 1D field

distribution was used. General Particle Tracer [9] was used
for the calculation. For the initial beam parameters pleaserefer to Table 1.
Table 1: Initial Parameters of Electron Beam
Parameter
Bunch charge
Number of particles
Electron gun energy
Cathode size
Initial bunch length

Value
77 pC (50 mA at 650 MHz)106 in tracking,2000 in optimization
100 keV
5.73 mm (uniform)
100 ps (Gaussian ±4𝜎)

The motivation of the simulation study was the following.
Assuming an initial beam, optimization was performed bya simulation including the space charge effect of a multiparticle beam, so that the beam parameters at the exit of theaccelerator were confirmed.
The electron emission surface of the hot cathode is approximately 10 mm, and the mean transverse energy (MTE)
is 0.5 eV is used to generate a beam. The beam diameterat the electron gun exit is approximately 8 mm at its maximum. To control the space charge effect solenoid focusing
is introduces into the design. Thus, the first solenoid focuses
the beam, so that the beam diameter becomes 10 mm orless at the collimator position. Then the beam expandingon passing through the buncher cavity is focused again by
the second solenoid. The beam size reaches the maximum
diameter of 28 mm at the second solenoid, which is smaller
than the beam pipe diameter of 60 mm. Therefore, it canbe inferred that the beam loss at this location can be sufficiently suppressed. Another point is that the essential beam
size relaxation at the second solenoid location allows in thefollowing effectively shrink the transverse beam size in the
cryomodule.

Optimization Strategy
The optimization strategy was: for given layout of theaccelerator, it was necessary to adjust the amplitudes andphases of cavities, and strengths of the solenoids to find the
optimum conditions. Namely, to reach the target energy (10MeV), the energy width of the emitted beam was required
to be narrow, so that there was no loss during transportation.
For low velocity beams the parameters are intricately corre-- 662 -

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

PASJ2023 THP01

Figure 4: Layout of the injector and the superconducting cryomodule.
lated. In addition, the influence of the space charge effectis also large. For this reason, simultaneous optimization ofmultiple parameters was necessary.
Optimization targets were the following: (1) to minimize
final bunch l ength; (2) to minimize maximum beam size
during transportation; (3) minimize final energy spread; (4)minimize maximum amplitudes of the cavities; (5) final energy should be reached. Then the distribution of 1,000,000
particles was set up, and the magnetic field of the solenoids
on the transport of the beam, the acceleration voltages andthe phases of the buncher and SCs were set as free parameters. The beam energy is accelerated up to 10 MeV byapproximately 2 MV per cavity with five 2-cell cavities. The
acceleration gradient is below 10 MV/m. Bayesian optimization toolbox [10] and solver based on multidimensional
Newton-Raphson algorithm [11] were used independently
for the optimization to reach a reliable model of the accelerator. Their results converged. Then the acceleration voltages
and phases of the buncher and SCs were confirmed. Together
with it, the solenoids suppressed beam divergence due to thelarge initial space charge effect. As the final result of the
optimizations, it was possible to transport the beam without
hitting the 70 mm beam pipe.

Results and Discussion
The final results of the optimization procedure are summarized in Table 2. The evolution of the beam parameters
is shown in Fig. 5.
Table 2: Optimized Parameters
Cavity name

Amplitude
MV/cav.

Crest 𝜙deg.

𝜙 off.
deg.

Buncher
INJ1 (1-cell)
INJ2 (1-cell)
INJ3 (2-cell)
INJ3 (2-cell)
INJ3 (2-cell)
INJ3 (2-cell)
INJ3 (2-cell)

0.0024
0.36
0.35
1.19
1.88
1.89
1.90
1.91

-58.8
-62.8
-127.9145.4-42.2-174.5
56.4
133.6

-90.0
1.0
0.0
-85.9
4.2
0.0
0.0
0.0

Solenoid nameCurrent (A)

SL1
SL2

2.75
1.24

Let’s discuss the major knobs that could be used to control
and to tune the beam. To control the bunch length effectively
a combination of the buncher phase and the first 2-cell cavity
phase offset is used in the model. Buncher cavity involves
so-called "zero-cross bunching" to compress the bunch andto leave its phase space linear. Then the bunching processlaunched at the buncher is stopped using a velocity bunching
technique in the first 2-cell cavity (phase offset added to thecrest phase). The bunch length behaviour is given in Fig.5
on top. Target compression achieved (see Table 3).
A key knob to control the transverse beam size (Fig.5
in the middle) is solenoid focusing. As it was mentioned
above, the relaxation of the beam size at the location of thesecond solenoid (after the buncher cavity) is crucial for theminimization of the beam size in the presence of the strong
space charge force. The cavity focusing effect turned tomake a small impact into overall beam size minimization.
Nevertheless, the beam size at the exit of the cryomodule
is good (5.41 mm). Additional tuning available through 2
quadruples at the irradiation section.
Since the main acceleration occurs in five 2-cell cavities,
energy tuning knobs are naturally amplitudes of those cavities. One should keep in mind, that the first 2-cell cavity
is responsible for the velocity bunching. Therefore the fineenergy tuning should be done via rest four 2-cell cavities.
Let us remind that 1-cell cavities are indispensable for theslight acceleration of the 100 keV beam coming from theelectron source. This stage is of a great importance to reachthe final energy of 10 MeV with a cryomodule. Anotherpoint is on the energy spread behaviour. It increases after
accelerating in two 1-cell cavities since those oppose a considerable fringe field effect on the beam as reads the energy
graph in Fig.5 in the bottom.

SUMMARY
Assuming an initial beam distribution, we performed
three-dimensional beam tracking including the space charge
effect. As a result of optimization by two independent methods mentioned above, the result of transportation with noloss was obtained. Based on the above calculation results andon the design of the injection section, Nb3 Sn cryomodule,
and irradiation section [6], we designed the entire irradiator.
By using the Nb3 Sn cavities, it is possible to accelerate 10
MeV and 50 mA without loss, and a very compact irradiation
accelerator can be achieved.

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

PASJ2023 THP01

ing Research Program / Innovative quantum beam technology development for highly efficient nanocellulose production".

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Figure 5: Time evolution of the beam parameters through thetransportation line: rms bunch length (top); rms transverse
beam size (middle); energy and energy spread bottom).
Table 3: Beam Parameters at the Exit of the Cryomodule
Parameter
Total energy
Rms bunch length
Rms transverse beam size
Energy spread

Value[6] H. Sakai, “Conceptual design of the high-power electron
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10.09 MeV
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SheffieldML/GPyOpt

ACKNOWLEDGMENTS
This work is supported by the "NEDO Leading Research
Program / Energy and Environment New Technology Lead-[11] A. Gil, J. Segura, and N.M. Temme, ”Numerical Methods
for Special Functions,” Society for Industrial and Applied
Mathematics (SIAM), Philadelphia, PA, 2007. ISBN:
978-0-898716-34-4.

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