Issue 76

Beam Dynamics Newsletter

3.4 FFAs at KURRI

Yoshihiro Ishi, Tomonori Uesugi, Yasutoshi Kuriyama and Yoshiharu Mori,
Institute for Integrated Radiation and Nuclear Science, Kyoto University, Japan.

3.4.1 Proton Driver for ADS

An accelerator complex at Kyoto University Research Reactor Institute (KURRI1) has been designed as a proton driver for an accelerator driven system (ADS) which is a hybrid system composed of a nuclear reactor facility and an accelerator facility. It sustains a nuclear fission chain reaction induced by a large number of spallation neutrons obtained by irradiation of a heavy metal target using high energy proton beams generated by accelerators. The nuclear reactor plays the role of neutron booster which amplifies the neutron flux from the target.

Nowadays, especially after the severe nuclear accident in Fukushima Japan, ADS is important not only as an energy production facility, but as a technique for transmuting long-lived radiative materials such as the minor actinide (MA) to others whose lifetimes are much shorter than the original ones. In the nuclear fuel cycle, MAs can be processed in a fast breeder. But in terms of the stability of the critical operation, the fraction of the MAs in the fuel system is limited to a few percent. On the other hand, in the ADS, MA can be loaded up to some 30% because the fuel system is operated at a sub-critical level.

At the Kyoto University Research Reactor Institute (KURRI), basic experimental studies about the ADS have been running since 2009 using one of research reactors, the Kyoto University Critical Assembly (KUCA)  [1]. In these studies, the KUCA has been operated in sub-critical mode and FFA accelerators have been used as a proton driver.

1 Although the name of the institute has been changed from KURRI to KURNS, which stands for “Institute for Integrated Radiation and Nuclear Science, Kyoto University”, we use KURRI in this article.

3.4.2 FFA Accelerator Complex at KURRI

A schematic diagram of the KURRI FFA accelerator complex is shown in Fig. 1  [2]. The complex used to have three FFA rings: the ION-BETA, the BOOSTER and the MAIN RING. All three rings adopt an FFA focusing scheme. However, the original injector system composed of the ION-BETA and the BOOSTER has been replaced by the 11 MeV H\( ^- \) linac in order to increase the beam intensity. Table 1 shows the basic parameters of the complex.

The new injector system consists of three linacs: RFQ, DTL1 and DTL2. and has been adopted as the injector to the ERIT ring  [3]. The injection line is shown in Fig. 3. H\( ^- \) beams are injected into the FFA MAIN RING through a charge stripping foil made of carbon. In this injection scheme, no pulse device is used. Even orbit merging magnets are not necessary because the H\( ^- \) beams are merged inside the main magnet of the MAIN RING as shown in Fig. 4. The beam current extracted from the MAIN RING has been increased by a factor of 10 as a result of this replacement. A ring footprint of the KURRI FFA MAIN RING is shown in Fig. 5. The beta functions of this ring are shown in Fig. 6

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Figure 1: Schematic diagram of the KURRI FFA Accelerator Complex. The upper pictures shows the original configuration, the lower is the upgraded one. The injector system composed of the injector (ION-BETA) and the BOOSTER has been replaced by the H\( ^- \) linac.

Table 1: Basic Parameters of KURRI FFA Accelerator Complex

Linac
Repetition rate \( < \) 200 Hz
Peak current \( < \) 5 µA
Pulse length \( < \) 100 µs (uniform)
Energy 11 MeV
MAIN RING
Field index \( k \) 7.5
Magnetic field 1.6 T (max.)
Energy 11 - 100 or 150 MeV
Revolution frequency 1.6 - 4.3 MHz
Rf voltage 4 kV

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Figure 2: FFA Accelerator Complex at KURRI.

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Figure 3: H\( ^- \) beam transport line.

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Figure 4: H\( ^- \) beam injection using the charge stripping foil.

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Figure 5: Footprint of the KURRI FFA MAIN RING.

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Figure 6: Beta functions of the KURRI FFA MAIN RING.

3.4.3 Beam Users

The proton beams from the FFA complex are delivered to users of various experiments: ADS experiments2, irradiation experiments on materials and biological experiments with irradiation to living animals (rats) for a basic study of BNCT3.

For the ADS experiments, the beam is transported from the accelerator facility to the sub-critical fuel system located at one of the cores in the KUCA called “A-core” (Fig. 7). Two kinds of measurement are performed in the KUCA: dynamic characteristics measurements detecting prompt and delayed neutrons, and static measurements of neutron energy spectrum or reaction rate distributions using radio-activation of the indium (In). The result of dynamic measurements from the first experiment in the world is shown in Fig. 8. There are two components in the neutron counting rate: the fast component decaying exponentially and the slow component caused by delayed neutrons almost constant in time. The presence of the delayed neutrons indicates that neutrons are generated through the nuclear fission chain reaction inside the fuel system. This series of ADS experiments has been ongoing since 2009 with changing experimental conditions such as the material of the neutron production target, configuration of the fuel system and beam intensity. The results from these experiments can be seen in articles  [4]- [8].

Reacently, on 14th and 15th February 2019, the first nuclear transmutation of minor actinides (\( ^{237} \)Np and \( ^{241} \)Am) by the ADS process was successfully demonstrated  [9] in a subcritical core at KUCA using FFA, as shown in Figs. 9-11.

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Figure 7: Connection between the FFA accelerator complex and KUCA.

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Figure 8: Measured prompt and delayed neutron behaviors obtained from different configurations of detec- tors.

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Figure 9: Measured pulsed heights of \( ^{237} \)Np and \( ^{235} \)U fission reaction rates at subcritical state.

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Figure 10: Measured pulsed heights of \( ^{241} \)Am and \( ^{235} \)U fission reaction rates at subcritical state.

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Figure 11: Measured γ-ray spectrum of \( ^{237} \)Np capture reaction rates at subcritical state

2 This work was supported by MEXT(the Ministry of Education, Culture, Sports, Science and Technology) of Japan as part of a task entitled ”Research and Development for an Accelerator-Driven Sub-critical System Using an FFAG Accelerator”.

3 Boron Neutron Capture Therapy.

3.4.4 Acceleration performance of the MAIN RING

Table 2: Parameters of FFA MAIN RING and injector

Parameter Value
Particle Proton
Kinetic energy 11 – 150 MeV
Revolution frequency 1.58 – 3.85 MHz
Twiss \( (\beta _x,\beta _y) \) (2.9 m, 2.5 m) at foil
Dispersion 24 mm/MeV
Acceleration speed 1.4 keV/turn

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Figure 12: Energy loss on passage of the carbon foil (simulated with GEANT4).

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Figure 13: Scattering angle on passage of the carbon foil ( simulated with GEANT4 ).

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Figure 14: Stripping foil and its holder.

MAIN RING Acceleration

The KURRI FFA synchrotron accelerates proton beams of 11 MeV up to 100 MeV or 150 MeV in ordinary operation. This machine is of the so-called radial sector scaling FFA type, where the field strength is designed such that \( B(r) \) along a radius is proportional to \( r^k \). The dispersion function is therefore \( (k+1)r \), where \( r \) is the closed orbit radius. In reality, because of the scaling field imperfection, the field index \( k \) gradually shifts from 7.0 at the injection orbit to 7.7 at the extraction energy orbit, while the designed value was 7.5. The orbit shift due to the acceleration is 24 mm/MeV at the injection energy. The betatron tunes at the injection energy were measured to be \( (3.63,1.39) \)  [10].

The emittance is typically assumed to be 5 \( \pi \) mm-mrad in both transverse phase planes, which corresponds to 20 mm in real space. The measured dispersion of the beam line at the injection point was \( -0.54 \) m, while the dispersion function of the ring is \( +0.59 \) m. Injected beams are captured and accelerated by a moving rf bucket. The rf amplitude is fixed at 4 kV and the accelerating phase is 20 deg over the acceleration cycle. Thus the energy gain is 1.4 keV/turn and the orbit shift by the acceleration corresponds to 1 mm/30 turns, or, 50 mm/ms.

Stripping Foil

The stripping foil is made of carbon whose thickness is 10 \( \mu \)g/cm\( ^2 \), and its dimensions are 25(H)\( \times \)30(V) mm\( ^2 \). It is fixed at a three-sided holder at the tip of the rod, which limits the vertical aperture. The energy loss and scattering angle of an 11 MeV proton were simulated by GEANT4. Figures 12 and 13 show the distribution of lost energy and scattering angle, respectively. The stripping efficiency of H\( ^- \) ion was \( >99 \)%.

Simulation Studies

Multi-particle simulations in 6-dimensional space have been carried out. The stripping foil is defined as a rectangle in \( (r,y) \), and particles are injected only when they fall inside the foil (Fig. 14). A circulating particle undergoes scattering and energy loss when it hits the foil. Any particle that exceeds the vertical aperture is lost.

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Figure 15: Horizontal (red) and vertical (blue) emittance growth caused by foil scattering. The number of surviving particles is plotted in black (full-span=100%). The dashed lines show the case with an infinitely large foil.

Emittance Growth without Acceleration

First, free emittance growth caused by the scattering was simulated without acceleration. A constant frequency rf was applied to maintain the beam energy. The results showed that the transverse emittances increased linearly at a constant rate of 70 \( \pi \) mm-mrad/ms, as in Fig. 15, and the speed was independent of the initial distribution. Significant beam loss at the vertical aperture started around 0.1 ms, which corresponds to 150 turns, and 90% of the beam was lost within 0.5 ms.

With Acceleration

With acceleration, the synchronous particle orbit is shifted at a rate of 50 mm/ms. Therefore a particle continues hitting the foil for 0.2 ms on average. This time is comparable to the emittance growth, as shown in Fig. 15. Simulation studies were carried out with acceleration, assuming the injected beam to be matched to the ring. Figure 16 shows the simulated emittance growth and beam loss. The capture efficiency was 25.7%. Each captured particle hits the foil 200 - 500 times.

The dependence on the momentum spread of the injected beam has also been studied (Fig. 18). The capture efficiency was reduced to 9% by increasing the momentum spread up to 1%.

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Figure 16: Vertical emittance growth (blue) and number of survived particles (black, full-span = 100%).

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Figure 17: Histogram of number of foil traversals by a captured particle.

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Figure 18: Capture efficiency dependence on initial momentum spread.

Summary of Acceleration performance of the MAIN RING

Simulation studies of charge-exchange multi-turn injection have been performed including effects of scattering by the foil. The simulated capture efficiency was reduced to 25.7%, compared with 35% without scattering. However the efficiency is still higher than the experimental results show. Further studies, including experiments, such as injection mismatch, are necessary to understand this discrepancy.

3.4.5 Betatron Tune Behavior During Acceleration

Generally, a scaling FFA accelerator has zero-chromatic characteristics i.e. the betatron tunes are fixed during acceleration. This nature can be realized by orbit similarity for the different energy beams and an FFA magnetic field form

(1) \begin{equation} B(r,\theta )=B_0(\theta )\left (\frac {r}{r_0}\right )^k, \end{equation}

where \( \theta \) is the azimuthal angle, \( r \) is the radius from the machine center and \( k \) is a constant number. If these scaling conditions are fulfilled, zero-chromatic operations can be carried out. However, in a practical machine, it is impossible to guarantee such a perfect zero-chromatic field configuration. One of major reasons for breaking the conditions is leakage of the magnetic field from the main body region to the straight section. If the leakage field distribution scales in the same manner as the main body field, zero chromaticity would be conserved. However, this is not the case for real machines. Since the gap of the FFA magnet becomes wider toward the inside, the influence of the leakage field becomes stronger in the inside without adjusted the field clamps.

There are two similar radial sector scaling FFA synchrotrons at KURRI: BOOSTER and MAIN RING. These rings adopt different types of magnets: one has no return yokes: the so-called ‘yoke free type’ adopted by MAIN RING, which has large tune variations causing non-negligible beam losses; the other has return yokes and field clamps adopted by BOOSTER, which has smaller tune variations compared with MAIN RING. We report the tune measurements and calculations based on 3-d magnetic field calculations for these two types of ring and discuss the scaling conditions in FFA accelerators  [11].

Design parameters of the main magnets

The lattice structures of BOOSTER and MAIN RING are almost the same in that they are both DFD triplets. However, the basic design concepts of the main magnets are totally different. For MAIN RING, the different energy beam extraction is realized by changing the position of the extraction kicker and septum magnets. In this scheme, the beams with different energies are extracted through different trajectories. Therefore, we needed to expand the extraction channel which is located at the space for the return yoke. It is difficult to provide a wide channel inside the return yoke iron, eradicating the leakage field inside the channel. A novel idea to get around this difficulty is to get rid of return yokes. The input model of the main magnet in MAIN RING for the magnetic field calculation by TOSCA is shown in Fig. 19. Flux generated by the coil of the F-pole returns through the D-poles, making the use of field clamps impractical. At the cost of an increase in leakage field in the straight section, we found a solution to the variable energy beam extraction. As shown in Fig. 20, there is leakage magnetic field more than a few 100 gauss at the center of the straight section.

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Figure 19: The input model of the main magnet in MAIN RING for the magnetic field calculation by TOSCA. Return yokes are not installed to make energy variable beam extractions easy. No field clamps are adopted.

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Figure 20: \( B_z \) vs \( \theta \) along different radii for the unit cell in MAIN RING. Red, green and blue lines correspond to radii of 4.4 m, 4.9 m and 5.3 m, respectively.

Figure 21 shows the TOSCA input model of the BOOSTER main magnet, which has return yokes and field clamps to minimize the leakage field at the straight sections. As seen in Fig. 22, the leakage field at the center of the straight section is almost zero. In addition, the shape of \( B_z(\theta ) \) including leakage field scales with radius, which is desirable for zero chromaticity.

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Figure 21: The input model of the main magnet in BOOSTER for the magnetic field calculation by TOSCA. Return yokes and field clamps are adopted.

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Figure 22: \( B_z \) vs \( \theta \) along different radii for the unit cell in BOOSTER. Red, green and blue lines correspond to radius of 1.2 m, 1.4 m and 1.6 m, respectively.

Tune spread, resonance crossing and beam losses

Betatron tunes for different energies have been measured in MAIN RING and BOOSTER. The measurements were performed at the flat top after acceleration for different energies. The tune footprint during acceleration in MAIN RING is shown in Fig. 23. Tunes from the simulations based on 3-d magnetic field maps are also shown in this figure. These are calculated from the transfer matrix determined in a small segment along the scalloped closed orbit,which is obtained by using a 4th order Runge-Kutta solver. A simulation code named EARLIETIMES  [12] has been used to calculate closed orbits, tunes and other features.

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Figure 23: MAIN RING betatron tune footprints. Blue and brown squares indicate measurements and simulations, respectively.

The tune spread during acceleration in MAIN RING is too large to avoid crossing resonance lines. Figure 24 shows the output signal from the bunch monitor. One can see some non-negligible beam losses around 1.0 ms, 2.7 ms, 4.3 ms and 20.1 ms from the start of acceleration. These loss timings could be related to the same timings as resonance crossing indicated in Fig. 23. In this case, the harmful resonance seems to be \( Q_x-2Q_y=1 \).

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Figure 24: The output signal from the bunch monitor. There are some notable beam losses during acceler- ation.

The tune footprint during acceleration in BOOSTER is shown in Fig. 25. The tune spread is small compared with MAIN RING, small enough to avoid crossing the resonances. In this case we need only be concerned with \( Q_x+2Q_y=5 \), but no obvious beam loss can be seen, as shown in Fig. 26.

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Figure 25: BOOSTER betatron tune footprints. Blue and brown squares indicate measurements and sim- ulations, respectively.

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Figure 26: Output signal from the bunch monitor indicated by a blue line. There is no obvious beam loss during acceleration.

Summary of Betatron Tune Behavior During Acceleration

As with the BOOSTER at KURNS, a scaling FFA accelerator, with magnets adopting flux return yokes and field clamps to suppress the leakage magnetic field at the straight section, considerably reduces the tune excursion during acceleration. In other words, it is scaled.

3.4.6 Upgrade Plans

In order to make the facility multi-capable, we are investigating two upgrade possibilities: (1) increasing the beam current up to the order of µA by increasing the repetition rate to the order of 100 Hz; (2) upgrading the energy by adding a new ring outside the MAIN RING.

Beam Stacking at High Energy Orbit

As a potential candidate for a high intensity proton driver of a spallation neutron source, an FFA accelerator has advantages in terms of a high repetition rate such as 100-1000 Hz. However, some users desire a low spill rate (\( \sim \)10 Hz) for their experiments e.g. neutron radiography using TOF which needs to get rid of contamination from a pulse of different timing. FFA rings can provide long interval pulses for users, while the machine operation itself is kept at a high repetition rate by using rf stacking after acceleration [13]. This scheme reduces space charge effects at the injection energy. For the machine, the charge in each bunch can be reduced by a high repetition rate. In the high energy region i.e. outer radius, accelerated beams are stacked and can continue to circulate until the necessary amount of charge is accumulated. For users, highly compressed beams with a long time interval can be delivered.

To confirm the feasibility of rf stacking at extraction energy, simulation studies have been carried out. Figure 27 shows the results from the stacking simulations. In the upper plot, the longitudinal phase space structure is shown. The vertical axis is the momentum and the abscissa is the rf phase. The red points are stacked particle coasting around the extraction orbit, the green points represent accelerated particles landing on the extraction orbit and the blue lines are separatrices. In these simulations, the acceleration goes up to 150 MeV. While the landing process is happening, some stacked particles are already slipping below the bucket in the phase space. Eventually, beams have been stacked below the extraction momentum. In the lower plot, the momentum distribution is plotted. After first acceleration, the full width of momentum spread is about 0.5%, the final momentum spread after 10 stacks is 2.5% of the full width. This is much smaller than might be suggested by a naive guess based on the intrinsic momentum spread of each stacked beam multiplied by number of stacks i.e. \( 0.5\% \times 10 \).

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Figure 27: Results of the beam stacking simulation. The upper plot shows the phase space from the stacking simulations with adiabatic landing and the lower is the momentum distribution after the beam stacking.

Although simulation studies showed that adiabatic landing, where the rf voltage is adiabatically reduced, is effective to suppress the momentum spread of the stacked beam, an experimental study is necessary.

An Additional Ring

The number of neutrons produced through the nuclear spallation process depends strongly on the beam energy of the primary protons. If the beam energy is increased from 100 MeV to 400 MeV, the number of neutrons corresponding to single primary proton is increased by a factor of 20. Therefore, an energy upgrade of the accelerator facility is an attarctive proposition to the reactor physicists.

Fortunately, there is an enough space to build an additional higher energy ring outside the MAIN RING. A basic design of the additional ring is now being carried out. The layout of the complex with a newly designed 400 MeV FFA ring is shown in Fig. 28.

Table 3: Parameters of the 400 MeV FFA Ring

Lattice 16-cell
Field index \( k \) 0.672
Energy 150 - 400 MeV
Average orbit radii 6.6 - 9.3 m
Magnetic field 1.3 T
Tune ( 1.356, 2.248 )

The basic parameters of the new ring are shown in Table 3. The ring consists of 16 cellsand the betatron functions for one cell are shown in Fig. 29.

The value of \( k \)is set to 0.672, which is rather small. This value makes serpentine acceleration  [14] possible. The longitudinal phase space structure in this acceleration scheme is shown in Fig. 30. Generally, the benefits of this scheme are follows:

  • • Since a fixed frequency is used, it is easy to get a high electric field in the acceleration cavity.

  • • Fast and continuous acceleration becomes possible.

  • • The ERIT mechanism  [3] can be applied to generate secondary particles such as pions and their decay muons.

In the ordinary ERIT system as shown in Fig. 31, the ring is operated in a storage mode. However, in the extended ERIT system, the ring will operate in an acceleration mode. In this operation mode, since the beam hits the target at the maximum energy, the production efficiency of the secondary particles becomes high compared with the case of the storage mode.

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Figure 28: Layout of the complex with a newly designed 400 MeV FFA ring, which surrounds the MAIN RING.

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Figure 29: Betatron functions for a basic cell of the 400 MeV FFA ring.

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Figure 30: Phase space structure in the longitudinal direction for the serpentine acceleration.

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Figure 31: ERIT mechanism to produce secondary particles.

References
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