2.1 Requirements of BNCT

Beryllium or lithium is chosen as the target material of AB-BNCT neutron source in most cases. Although beryllium targets achieve a better thermal performance and mechanical properties, we chose to use lithium target because it requires a lower output energy for the accelerator. The reaction ⁷Li(p,n)⁷Be was selected to produce neutrons for BNCT because of its high neutron yield and relatively soft neutron energy spectrum, which can be used in BNCT clinical treatment with no significant slowing down. More considerations are involved in the design of lithium targets, which are not the focus of this paper and are not be discussed here.

According to the requirements of the International Atomic Energy Agency (IAEA) for clinical BNCT, the desirable minimum flux of epithermal neutrons (0.5 eV to 10 keV) is 10⁹ n/cm²/s [8]. The ⁷Li(p,n)⁷Be reaction has a threshold energy of 1.88 MeV and a remarkable resonance peak at 2.25 MeV for proton. It has a relatively low output energy for the RFQ, which makes it easier to design an RFQ and reduce the cost.

Considering the requirements of the IAEA and the characteristics of the reaction, Peking University has conducted a simulation showing that a 2.5 MeV proton beam with a current of 15 mA can fully meet the requirements for cancer treatment [9, 10]. Thus, a beam current of 20 mA was chosen with a final energy of 2.5 MeV.

2.2 Beam dynamics parameters

The main parameters of the BNCT-RFQ are listed in Table 1. As indicated in Sect. 2.1, the particles to be accelerated, as well as the beam current and output energy, were determined. In addition, the frequency choice directly affects the size of the RFQ cavity, which is related to the cost of the construction. To reduce the occupied area and the construction cost of the RFQ to suit a hospital environment, the frequency is decided to be relatively higher, i.e., 200 MHz. The inter-vane voltage, which is related to the beam transmission efficiency and focusing effect, was determined to be 91.65 kV. Although the inter-vane voltage is relatively high, this parameter is considered reasonable. There are RFQs operating at higher inter-vane voltages. The LEDA RFQ in LANL has an inter-vane voltage ranging from 67 to 117 kV [11]. The IFMIF-EVEDA RFQ in LNL has a minimum voltage of 79 kV and a maximum voltage of 132 kV [12]. Meanwhile, the voltage ramp of the FRIB RFQ at Michigan State University ranges from 60 to 112 kV [13]. Portions of their operating inter-vane voltages are higher than 90 kV, which indicates that our design is reliable. A lower vane-gap voltage can improve the stability of the RFQ operation, but the length of the cavity, construction cost, and occupied area will increase. The other parameters listed in the table were determined through dynamics simulation.

2.3 Beam dynamics design

In this study, a dynamics transmission simulation was conducted using the software RFQGen [14]. Los Alamos National Laboratory (LANL) developed RFQGen based on the four-stage theory proposed by Stokes and Crandall [15], which allows the design of accelerating cells of the RFQ, including radial matching sections at both ends of the structure. The code can adjust the two-term potential functions by changing the vane geometry, thus generating both the accelerating force and the focusing force. Figure 1 shows the main parameters of the designed beam dynamics. When considering the shortest length and high transmission efficiency as the design goals, the length of this RFQ (acceleration proton beam of up to 2.5 MeV with an operating frequency of 200 MHz) is 3.2 m. Other similar RFQ accelerators are much longer, including the ADS-RFQ [16] in the Institute of Modern Physics in China (which operates at a frequency of 162.5 MHz and accelerates the proton beam from 35 keV to 2.1 MeV), which is 4.2 m, and the BNCT-RFQ [10] at Peking University (which operates at 162.5 MHz and provides acceleration of a 20-mA proton beam at up to 2.5 MeV), which is 5.2 m. The following figures show the simulation results for the beam dynamics. In Fig. 2, the transmission efficiency reaches 98.7% when 10000 particles are simulated. In addition, Fig. 3 and Fig. 4 shows the phase-space distribution and beam distribution at the entrance and exit of the RFQ.

Fig. 1.Full-screen View

(Color online) RFQ beam dynamics main parameters vary with accelerating cells.

Fig. 2.Full-screen View

(Color online) RFQ beam transmission process. There are beam envelope of the X axis and the Y axis, the difference between particle phase and synchronous phase and energy spread, respectively.

Fig. 3.Full-screen View

(Color online) Beam profiles at the entrance and exit of the RFQ.

Fig. 4.Full-screen View

(Color online) Beam distribution at the exit of the RFQ.

2.4 Dynamics design tolerance

Only the ideal states of the parameters are considered in the dynamics transmission simulation. However, a slight disturbance will occur with the parameters when the beam travels from the ion source and low-energy beam transport line (LEBT) to the entrance of the RFQ. This may affect the transmission efficiency of the RFQ; thus, it is necessary to study whether the effect of the non-ideal matching conditions on the beam transmission efficiency is acceptable. Seven parameters (disturbance of input beam energy, current, voltage factor, normalized emittance, energy spread, Twiss parameters, and spatial displacements) were considered in this study. Figure 5 shows the results (the red triangles represent the designed parameters).

Fig. 5.Full-screen View

(Color online) The effects of the (a) input energy, (b) input beam current, (c) normalized vane voltage, (d) normalized emittance, (e) energy spread, (f) Twiss parameters (α,β), and (g) spatial displacements on the transmission efficiency.

The input beam energy has an impact on the synchronous phase. Therefore, a deviation of the input energy may change the synchronous conditions, which leads to beam loss. As shown in Fig. 5(a), the beam transmission efficiency is below 90% when the input energy is greater than 33 keV or less than 27 keV. The beam current is related to the space-charge effects, which increase with the beam intensity. As shown in Fig. 5(b), the beam transmission efficiency is over 98% as long as the beam current is lower than 30 mA. Figure 5(c) shows the change in beam transmission efficiency when the normalized voltage factor varies from 0.8 to 1.1, where a voltage factor of 1.00 indicates 91.65 kV. The beam transmission efficiency is acceptable if the vane voltage is 0.93-times higher than the designed voltage. Figure 5(d) shows the relationship between the normalized emittance of the beam and beam transmission efficiency. To ensure that the beam transmission efficiency is greater than 90%, the transverse emittance of the input beam should be no greater than 0.9 mm●#x22C5;mrad. In addition, the beam transmission efficiency has sufficient margins for the beam energy spread, Twiss parameters, and beam spatial displacement, as shown in Figs. 5(e)–(g). Overall, the parameters in Fig. 5 have a good margin for the beam transmission efficiency, which can guarantee a neutron flux for BNCT treatment.

3.1 Quadrilateral cavity

A quadrilateral four-vane RFQ has a cross section similar to a square. Its right angles are replaced by arc angles to avoid point discharge and local over-temperature. Because the cross section is centrosymmetric, a quarter of the sketch is shown in Fig. 6(a), which is determined using nine parameters. The values of the parameters determine the shape of the cross-section. The values are presented in Table 2.

Fig. 6.Full-screen View

(Color online) Cross-sections of (a) quadrilateral RFQ and (b) octagonal RFQ.

3.2 Octagonal cavity

The octagonal four-vane RFQ is an RFQ with a cross section similar to an octagon. From the sketch of the cross-section, it is similar to the quadrilateral cavity except that the arc angles at the four peaks are replaced by straight lines, as shown in Fig. 6(b)). Table 2 lists the design parameters, which are similar to those of the quadrilateral cavity. Here, θ₃ is designed to have a larger value to reduce the power loss and local power density.

3.3 Comparison

To determine which type of cavity is better in terms of performance, a comparison of high-frequency parameters between the quadrilateral RFQ and octagonal RFQ is presented in Table 3, where Δf indicates the difference in frequency between the nearest quadrupole and dipole modes. The vane is made of copper and has an electrical conductivity of 5.8×10⁷ S/m. To reduce the simulation time, we use the performance of a slice of the cavity instead of the entire RFQ cavity. For a more realistic simulation, the boundaries of the cross profiles (lengthwise direction) were set as magnetic boundaries. The similar structure parameters, cavity frequency, and slice thickness of both types were designed in the same way. It is clear that the values of Δf are both above 6 MHz. It is likely that neither requires a frequency-separation structure. This is proved in the following section. From the perspective of the cavity size, H of the octagonal slice is 11.4% larger than that of the quadrilateral slice, which means that the cross-sectional area of the octagonal cavity is 13% larger than that of the quadrilateral cavity. A smaller size can reduce the costs of the construction and space. In addition, the quadrilateral slice has a higher Q value and less total RF loss. The cooling system for the quadrilateral cavity is easier to design and construct. Considering that the injector will be operated in CW mode, the quadrilateral RFQ cavity is a better choice.

4.1 tuner design

The cylindrical structures shown in Fig. 7 are the tuners of the RFQ, and Table 4 shows the design parameters of the tuners. Tuners are used to slightly tune the overall resonant frequency of the cavity to keep the operating frequency of the cavity stable at the design frequency, or to adjust the local resonant frequency or electric field distribution of the cavity to achieve flatness of the electric field distribution along the cavity.

Fig. 7.Full-screen View

Design diagram of (a) whole cavity and (b) tuners.

As shown in Fig. 7, the RFQ cavity has 64 tuners with a radius of 20 mm and a pre-insertion depth of 15 mm, uniformly distributed over the symmetrical electrodes. The effect of the tuners on the cavity frequency can be studied by adjusting the insertion depth of the tuners. According to Fig. 8, there is a linear relationship between the insertion depth and the cavity frequency, and the average sensitivity is 1 kHz/mm per tuner, that is, the tuning range of the whole cavity is -0.92 to 1.0075 MHz.

Fig. 8.Full-screen View

Effect of tuner insertion depth on cavity frequency (for all tuners).

As indicated in Sect. 3.3, there is no need for a frequency-separation structure. This is proven in Sect. 4.3 after the whole cavity simulation has been completed.

4.2 Undercut design

Another important task of an RF structure design is to tune the horizontal distribution of the electric field between electrodes along the longitudinal direction. The flat distribution of the electric field is extremely important for a frequency regulation during an operation. If the electric field is flat, when the depth of the tuner insertion or draw out is the same during the frequency regulation, the influence on the cavity voltage is also the same. The field distribution of the RFQ without undercuts is shown in Fig. 9. The electric field is low at both ends and high in the middle of the RFQ. The structure of undercuts is shown in Fig. 10, and Table 4 lists the design parameters of the undercuts. The undercut design generally adopts a triangular type, which has the advantages of high mechanical strength and convenient processing. By cutting off the conductor part and increasing the volume of the vacuum part, as shown in Fig. 9, the electric field distribution is flat along the longitudinal direction after adding the undercuts.

Fig. 9.Full-screen View

Normalized electric field distribution between electrodes with and without undercut.

Fig. 10.Full-screen View

Design diagram of undercuts.

4.3 Whole cavity simulation

Thus far, the design of the cross-section and model of the RFQ cavity has been completed. To reduce the computing time, the electromagnetic structure design and electromagnetic simulation described in this paper are all carried out using the average aperture R0 instead of the vane-tip modulation data generated by RFQGen software in the dynamics simulation, the results of which are similar. To increase the accuracy of the results and make the model more similar to a real RFQ, the electrodes were chamfered, and the modulations of RFQ were added to the model in the following whole-cavity simulation.

The RFQ cavity has 64 tuners, with a 3162.62-mm vane length and 3176.75-mm total length of the cavity and no frequency separation structure. The radial matching gap at the entrance of the RFQ (8.68 mm) and the fringe-field gap at the exit of the RFQ (5.45 mm) were added to the cavity. Both were determined using RFQGen software. CST software was used to simulate the entire cavity, and the K_p factor was found to be 1.69. The specific high-frequency parameters are listed in Table 5.

It is necessary to determine whether the dipole mode affects the normal operation mode of the RFQ because it will be excited if its frequency is close to the operation frequency. In the final whole-cavity RF simulation, as shown in Table 5, the minimum frequency interval Δf between the dipole mode and working quadrupole mode is 2.144 MHz. The Q value of the cavity was 14,361. According to references [23, 25], the effect of the dipole mode on the working quadrupole mode can be calculated through the following:

where f₀ represents the operating frequency of the cavity, which was 200 MHz in this case. Thus, the value of α is 0.32%, which means that the nearest dipole mode has little effect on the operation mode. Therefore, there is no need for a mode separation structure.