2.1 H-bend

The H-bend in Fig. 1(a) changes the direction of the connection between two rectangular waveguide ports. The simulation results are shown in Fig. 1(b). The reflection is less than −60 dB, which means the structure is well matched.

Fig. 1Full-screen View

(a) H-bend and (b) simulation results: transmission is −0.01 dB and reflection is −64.47 dB

2.2 Impedance combiner

The impedance combiner is utilized to reassign the impedances. It is a three-port RF structure. The three ports are identical. Each port sees the combined RF impedance of the other two. Figs. 2(a) and (b) show the design and its S-parameters. S₁₁ is approximately 0.33 while both S₂₁ and S₃₁ are 0.67, which agrees with the goals well. It is a broad bandwidth structure.

Fig. 2.Full-screen View

(a) Impedance combiner; (b) simulation results and machining-error analysis-(c) for width and (d) for height of protuberance: through (c) and (d), the machining error should be controlled within ±10 μm

The width and height of the protuberance mainly determine the performance of this impedance combiner. For the width, the machining error must be controlled within ±70 μm and the height within ±10 μm according to the simulation results in Figs. 2(c) and (d).

2.3 Polarizer

A five-port RF structure was created by cascading three impedance combiners, as shown in Figs. 3(a) and (b). In this structure, if Port-4 and Port-5 are short-circuited, as illustrated in Fig. 3(a), the output power on Port-2 and Port-3 would be changed by moving the position of the short-circuited plane.

Fig. 3.Full-screen View

(a) Illustration of the five-port structure and (b) its RF design

To simplify the system in Fig. 3, an RF polarizer [7–11] was introduced, as shown in Figs. 4(a) and (b). The polarizer combines the two rectangular waveguide ports into one, converting the rectangular waveguide TE mode, TE₁₀^□, into the circular waveguide mode TE₁₁^○ to the circular waveguide with no power leaking to the other rectangular waveguide port, as shown in Fig. 4(b). The polarizer is a perfect symmetrical structure, which means that, for the power that comes from the other rectangular waveguide port, Port-2, all the converted power is transmitted to the circular waveguide port. The two rectangular waveguide ports are isolated; therefore, if power comes from its two rectangular waveguide ports, the converted power becomes two degenerated TE₁₁^○ modes in the circular waveguide with orthogonal polarization. Compared with the CERN X-band polarizer, this design removes the cylinder on the opposite side of the piston to simplify the machining. Consequently, there must be some disturbance to reduce the reflection, such as some protuberances. Simulation results of the polarizer are shown in Fig. 4(c). Both the reflection S₁₁ and transmission to the other rectangular waveguide port S₂₁ are less than −40 dB. The transmission of one TE₁₁ mode on the circular waveguide, S_3(2)1(1), is less than −50 dB, whereas, for the other TE₁₁ mode, the transmission S_3(1)1(1) is −0.04 dB.

Fig. 4.Full-screen View

(Color online) (a) Design and (b) power flow of polarizer and (c) the simulation results: S₁₁and S₂₁ are lower than −40 dB, S_3(2)1(1) is lower than −50 dB, and S_3(1)1(1) is −0.04 dB

The size and position of the protuberances affect the performance of this polarizer. Fig. 5 shows these influences. According to the simulation results, the machining error of the protuberances’ size should be controlled within ±20 μm, and the position error should be no more than ±10 μm, which are not so strict for our machine.

Fig. 5.Full-screen View

(Color online) Machining-error analyses of polarizer: analysis of (a) width of protuberances, (b) height of protuberances, (c) different positions of protuberances when the four protuberances are symmetric, and (d) when four protuberances are not symmetric-the machining error of the protuberances’ sizes should be controlled within ±20 μm, and the position error should be lower than ±10 μm

2.4 RF contact-free movable reflector

The polarizer combines two rectangular short-circuited ports into a circular one, which is connected to a movable piston. The piston is expected to reflect all the input power. However, a coaxial waveguide formed by the piston and the circular waveguide results in considerable power leaking, even though the distance between the piston and circular waveguide is minimized to the limitation of machining and assembling (approximately 0.1 mm). To reflect the two TE₁₁ modes equally and efficiently, a new RF contact-free reflector was designed, as shown in Fig. 6(a) [12]. Instead of a regular flat short-circuit plane, a choke is introduced on the reflector, collecting the vast majority of input power. The radius of the circular waveguide is expanded to 21 mm; thus, the two TE₁₁ modes are not cut off in the choke. With this choke, the power in the circular waveguide carried by two TE₁₁ modes is totally reflected to the input port, and the power leaking is minimized. The simulation results for different positions of the reflector are shown in Fig. 6(b). When the reflector moves in a relatively long range (45 mm), the transmission to the coaxial waveguide port is smaller than −60 dB all the time.

Fig. 6Full-screen View

(a) RF contact-free movable reflector and (b) its simulation results: the transmission to the coaxial waveguide port is smaller than −60 dB

The depth of the choke is not so strict. The simulation results indicate that the reflector works well when the machining error can be relaxed to 0.5 mm, which is easy to implement with our machine.

2.5 Final design

The final design combined the three components as shown in Fig. 7(a). To suppress high-order modes in the waveguide, one rectangular waveguide dimension a is reduced to 42 mm instead of 47.55 mm. However, a smaller waveguide can also cause a higher surface electrical field. In a standard C-band rectangular waveguide, the surface E-field is approximately 1.33 kV/m for 1-W input power. Therefore, the other dimension b is set to 25 mm instead of 22.15 mm to keep the same surface E-field, which is approximately 1.37 kV/m. The total size of the entire modal is approximately 250 × 250 mm². The parameters are optimized to minimize the reflection. Finally, the maximum reflection is approximately −36 dB.

Fig. 7.Full-screen View

(a) Design of C-band variable RF power splitter and (b) its E-field: the maximum surface E-field is approximately 3.4 kV for 1-W input power

This variable power splitter will be placed between the pulse compressor and the accelerators on SXFEL. According to operating experience with a C-band RF unit [13,14], the accelerators can work at 47 MV/m, corresponding to a peak E-field of 122.2 MV/m. For the RF unit of SXFEL, the output power of the klystron is 50 MW, and the average power gain of the pulse compressor is 3.2 for the SLED (SLAC Energy Doubler) [15] and 3.8 for the new spherical pulse compressor [16]. If the new spherical pulse compressor is utilized, the input power of the variable power splitter is 190 MW. As shown in Fig. 7(b), the maximum surface E-field is approximately 3.4 kV for 1-W input power. If the input power is 190 MW, the maximum surface electric field is 46.9 MV/m, which is smaller than the peak E-field of the accelerator, 122.2 MV/m. Therefore, the power splitter can work at the SXFEL facility.

Fig. 8 shows the S-parameters of this system versus piston positions. The reflection to Port-1 is less than −35 dB all the time. As the piston moves from z = 0 to 17.9 mm, the power emitted from Port-2 changes from 1 to 0 and that from Port-3 changes from 0 to 1, indicating variable power splitting.

Fig. 8Full-screen View

(Color online) S-parameters vs. piston positions. When the piston moves from 0 mm (SH_L = 73.1 mm in simulation) to 17.9 mm (SH_L = 91 mm in simulation), the power emitted from Port-2 changes from 1 to 0 and that from Port-3 changes from 0 to 1