Introduction

In an electron linac, the standard bunching system is composed of a standing-wave (SW) pre-buncher (PB), a travelling-wave (TW) buncher and a standard accelerating structure [1]. In the industrial area, the bunching system is usually simplified to reduce the cost by eliminating the PB and integrating the B and the standard accelerating structure together to form the \(\beta \)-varied accelerating structure. The bunching performance for this kind of system is relatively worse than that for the standard one. To keep the beam performance of the simplified bunching system similar to that of the standard one and reduce the cost as much as possible, the hybrid accelerating structure (HAS) was proposed by integrating the PB, the B and the standard TW accelerating structure together.

Fig. 1
figure 1

Schematic layout of the HAS

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Table 1 Basic design requirement of the HAS
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Recently, an S-band (2856 MHz) HAS prototype is being built at Institute of High Energy Physics (IHEP); the radio-frequency (RF) design is presented here. The 2D code SUPERFISH [2] was used to obtain the dimensions of the SW and TW cells, while the 3D code HFSS [3] was used to design the input and output couplers. Finally, the on-axis field distribution of the whole HAS prototype was investigated by HFSS, which is consistent with the beam dynamics requirement [4]. The HAS can be widely applied in the industrial area to enhance the beam performance but not increase the cost.

Beam dynamics requirement

In the NSC KIPT (National Science Centre, Kharkov Institute of Physics and Technology, Ukraine), a 100-MeV electron linac is being constructed by IHEP [5]. For that linac, a standard bunching system was adopted. The PB, the B and the accelerating structure can be tuned independently to get the appropriate beam phase and energy spectrums at the bunching system exit, so that a clean bunch without any satellite electrons in each RF period downstream the Chicane system can be obtained [5]. With 120 kV / 0.85 A electron beam emitted from the gun, a beam with 600 mA pulsed current, 2.7 \(\upmu \hbox {s}\) pulse length and \(<\pm \,4\%\) peak-to-peak energy spread can be acquired at the linac exit [5]. To make the bunching system more compact but not fairly deteriorate the beam performance, the studies by using the HAS with the schematic layout shown in Fig. 1 to replace the PB, the B and the accelerating structure were carried out [4]. By a great deal of beam dynamics calculations with PARMELA [6], the basic design requirement of the HAS can be obtained and is listed in Table 1.

The HAS consists of two SW cells, 40 TW cells and two coupler cells; the apertures of the irises for the TW cells are generally same as the 1.3-m-long TW structures for the KIPT linac [7]. In the HAS, both the SW and the TW electromagnetic fields exist. The two SW cells operate at \(\uppi /2\) mode, while the 40 TW cells operate at \(2\uppi /3\) mode. The demanded ratio of the maximum electric field amplitude in the SW1 to that in the input coupler cell is \(\sim 0.44\) [4].

2D RF design

The 2D RF design for the SW and the TW sections of the HAS were performed separately in SUPERFISH by setting the appropriate boundary conditions.

SW section design

The SW section of the HAS is generally the same as the hybrid buncher (HB) [8], while the iris apertures between the SW cells and the input coupler cell need to be tuned carefully to obtain the correct field distribution determined by the beam dynamics.

Fig. 2
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The SUPERFISH model for the SW section

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Fig. 3
figure 3

Optimized on-axis electric field amplitude distribution along the SW section

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It is well known that half of the coupler cell in the TW accelerating structure operates at the SW mode, and thus, the SW section of the HAS can be designed and optimized by using the 2D SUPERFISH model shown in Fig. 2. The left two cells are the two SW cells, while the right half-cell corresponds to half of the input coupler cell. By changing the values of a1 and a2 but keeping the resonate frequency to be 2856 MHz by adjusting rsw, r2 and r3, the on-axis electric field amplitude distribution along the SW section can be varied. Figure 3 shows the optimized results. The ratio of the field value for the first peak to that for the second peak is \(\sim 0.439\), which is \(\sim 0.3\%\) smaller than the demanded value of \(\sim 0.44\). Due to the existence of the simulation errors, this small deviation can be accepted.

The accelerating structure fabrication is always accompanied by geometrical tolerances. The most important dimensions for the SW section are the cell radius and iris radius. Table 2 shows the parameter sensitivity of the SW section. In the HAS prototype fabrication, \(5\upmu \hbox {m}\) manufacturing tolerance was selected.

Table 2 Parameter sensitivity of the SW section
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TW section design

SUPERFISH is well established to calculate the RF properties of the SW disc-loaded accelerating structure. However, by carefully analysing the similarities and differences between the SW and TW field, the SUPERFISH calculation results for the same structure operating at the SW mode can be converted to that operating at the TW mode. The rules for the conversion are as follows:

  1. 1.

    For the same mode pattern, the resonating frequency f and the quality factor Q for both the TW and the SW are same, while the stored energy W for the TW is half of that for the SW.

  2. 2.

    Except the 0 and \(\uppi \) modes, the effective shunt impedance per unit length \(r_{0}\) for the TW is twice of that for the SW [9].

  3. 3.

    The group velocity for the TM01 mode of the disc-loaded structure can be given by S

    $$\begin{aligned} v_g =\frac{P}{W_\mathrm{TW} }=\frac{\frac{1}{2}\int {E_r \cdot H_\phi \mathrm{d}s} }{\left( {\int \frac{\varepsilon E^{2}}{2}\mathrm{d}V+\int {\frac{\mu H^{2}}{2}\mathrm{d}V} } \right) _{\mathrm{unit\,length}}} \end{aligned}$$
    (1)

    P is the power flow through the surface, which is parallel to the direction of the group velocity \(v_\mathrm{g}\) for the TW. \(W_\mathrm{TW}\) is the energy stored per unit length, which is half of \(W_\mathrm{SW}\). \(E_{r}\) and \(H_{\varPhi }\) are the transversal components of the TW field.

Fig. 4
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The SUPERFISH model for the TW cell

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Table 3 Main specifications of the TW section
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The TW section for the HAS is the traditional disc-loaded type waveguide structure, which operates at the \(\hbox {TM}_{01,2\uppi /3}\) mode. By using the SUPERFISH model under the Neumann boundaries shown in Fig. 4, \(E_\mathrm{r}\) and \(H_{\varPhi }\) for the TW can be derived from that for the SW by using the following relations [10].

$$\begin{aligned} \hbox {Z}= & {} \frac{d}{2},\;E_\mathrm{{r,TW}} =E_{{r,sw}} \left( {\frac{d}{2}} \right) /\sqrt{3},\;H_{\phi ,\mathrm{TW}} =H_{\phi ,\mathrm{SW}} \left( {\frac{d}{2}} \right) \nonumber \\ \end{aligned}$$
(2)
$$\begin{aligned} \hbox {Z}= & {} d\;,\;E_{r,TW} =E_{r,sw} \left( d \right) \;\;/\sqrt{3},\;H_{\phi ,TW} =H_{\phi ,SW} \left( d \right) \nonumber \\ \end{aligned}$$
(3)

The parameters for each cell in the TW section can be calculated cell by cell. Finally, the main parameters for the TW section can be obtained and are listed in Table 3.

The filling time \(T_\mathrm{F}\) for the TW section is the spent time of the RF power flowing from the input coupler cell to the output coupler cell, which can be calculated by

$$\begin{aligned} T_\mathrm{F} =\sum _1^n {\frac{D_\mathrm{n} }{v_\mathrm{g,n} }\approx \frac{2Q_\mathrm{average} \tau }{\omega }} \end{aligned}$$
(4)

\(D_\mathrm{n}\) and \(v_\mathrm{{g,n}}\) are the cell length and group velocity for the \(\hbox {n}^{\mathrm{th}}\) cell, respectively. \(Q_\mathrm{average}\) is the averaged value of the quality factor Q for all the cells. \(\omega \) is the angular frequency corresponding to the resonating frequency f.

Since there are 40 cells in the TW section, the parameter sensitivity of each cell is generally similar; Table 4 shows that of the cell TW6 as an example. Same as the SW section, \(5\,\upmu \hbox {m}\) manufacturing tolerance was selected.

Table 4 Parameter sensitivity of the TW section
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3D RF design

The 2D RF design of the HAS is the foundation of the 3D design. Due to the non-asymmetrical feature, the input and output RF couplers must be designed in 3D. Here 3D code HFSS was used.

Coupler design

For the HAS prototype being built at IHEP, single-feed waveguide input and output couplers were adopted. Both the input coupler before the attachment of the SW section and the output coupler can be matched based on the matching procedure for the \(2\uppi /3\) mode proposed by Dr. R. L. Kyhl [10] and confirmed with the field transmission method. However, the attachment of the SW section changes the matching status of the input coupler; further, adjustment of the input coupler dimensions needs to be done by using the 3D model shown in Fig. 5. Table 5 lists the main dimensions. wo, bo and wi, bi are the dimensions before and after the attachment of the SW section, respectively. Figures 6 and 7 show the electric field amplitude and phase distributions along the axis of the 3D model used for the input coupler matching, respectively. Figure 8 shows the S11 curve at the input coupler port of the 3D model. For comparison, the results of the case before the attachment of the SW section are also shown.

Fig. 5
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3D model for the input coupler matching after the attachment of the SW section

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Table 5 Main dimensions of the 3D model for the input coupler matching
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Fig. 6
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On-axis electric field amplitude along the 3D model for the input coupler matching

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Fig. 7
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On-axis electric field phase along the 3D model used for the input coupler matching

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Fig. 8
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S11 curve for the input RF coupler

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Full structure calculation

By assembling the SW section, the TW section and the two RF couplers together, the 3D structure of the HAS can be constructed.

In recent years, with the development of the computer technology, simulation of the full 3D structure of the HAS becomes possible. In this situation, the full structure calculation of the HAS was also carried out in HFSS. To minimize the CPU time and the memory use, only 1/2 model of the HAS shown in Fig. 9 was created. The material chosen for the surfaces of the HAS is oxygen-free copper and a perfect magnetic boundary condition is set on the symmetry plane.

Fig. 9
figure 9

The 1/2 model of the HAS prototype

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Figure 10 shows the electric field amplitude distribution along the axis of the HAS prototype. The field distribution used in PARMELA is also shown. One can see that there are 43 peaks, first of which corresponds to the first cell in the SW section. The second and 43rd peaks correspond to the input and output couplers, respectively. The other 40 peaks correspond to the 40 TW cells. The HFSS simulation result is well consistent with the beam dynamics requirement.

Figure 11 shows the electric field phase distribution. The phase jump between the SW and the TW sections is \(180^{\circ }\), which indicates that the operating mode in the SW section is \(\uppi /2\) mode. In the TW section, the phase advance from one cell to another is \(120^{\circ }\), which is the case of the \(2\uppi /3\) mode.

Fig. 10
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Electric field phase distribution along the axis of the HAS prototype

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Method for fabrication and cold test

The engineering design of the HAS prototype is being conducted. On the outer wall of each cell, there are two non-penetrated holes distributed uniformly in the circumferential direction with \(180^{\circ }\) angular distance. For each hole, a nut will be brazed inside, and then, push-and-pull method can be used for the structure tuning.

Fig. 11
figure 11

Electric field amplitude distribution along the axis of the HAS prototype

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For the fabrication, the prototype can be generally divided into four parts: the SW section with the input coupler, the \(\beta \) varied TW section from TW1 to TW6, the \(\beta =1\) TW section from TW7 to TW40 and the output coupler. Before the final brazing of the whole prototype, the SW section, the input coupler, the \(\beta \) varied TW section and one specially designed output coupler will be assembled together for pre-tuning by specific equipment. Correspondingly, the output coupler will also be pre-tuned.

For the tuning and cold test after brazing, a field distribution measurement and tuning platform specially developed for the hybrid accelerating structure will be used [8]. Bead-pull method based on the non-resonant perturbation theory will be adopted. The final tuning result will be based on the field measurement result; several iterations between the tuning and measurement usually need to be done.

Conclusions

The RF design studies on the HAS have been conducted by SUPERFISH and HFSS. The HAS integrates all the functions of the PB, the B and the accelerating structure in the standard bunching system. The obtained electric field distribution can fully meet the beam dynamic requirement. The HAS can be widely applied in the industrial area to enhance the beam performance but not increase the construction cost. The HAS prototype is being developed, and the cold test will be conducted in the very near future.