**2. TWT Design and Simulation**

The TWT primarily contains five parts: electron gun, focusing system, radio frequency (RF) circuit, RF windows, and collector. The building blocks of the TWT are shown in Figure 1.

A Pierce's electron gun is used to produce an electron beam with a current of 20 kV and 50 mA. The type of the cathode is M-type and the cathode loading is 5 A/cm2. A focus electrode modulates the beam providing a duty cycle from 0.1% to continuous wave. The double anodes adjust the beam current and transmission. Opera 3D is used to design the electron gun, and the simulation result is shown in Figure 2. The designed beam voltage and current of the TWT are 20 kV and 50 mA with a beam radius of 0.06 mm and a beam-shot of 10 mm, respectively.

**Figure 1.** Building blocks of the G-band TWT.

**Figure 2.** Simulation result of the electron gun.

Sm2Co17 periodic permanent magnet (PPM) is used as the focusing system. The samarium cobalt magnets produce an on-axis *B*z whose peak value is 0.5 T. The system is simulated by opera 3D. Figure 3 shows the simulation model. According to the simulation results, a high beam transmission ratio of 99% through the small diameter beam tunnel in the slow wave circuit is essential.

**Figure 3.** Model of Sm2Co17 periodic permanent magnet focusing system.

A folded waveguide is employed as the slow-wave structure in the TWT. It is fabricated with CNC-machining. The material chosen was oxygen free copper. The fabricated circular is shown in Figure 4.

**Figure 4.** The fabricated circular of the folded waveguide slow-wave structure.

Figure 5 shows the dispersion curves of a traditional folded waveguide circuit. For traditional fold waveguide slow-wave structure, *n* = −1 forward branch of the dispersion curve was used for the circuit, which operated as usual.

**Figure 5.** Dispersion curves of a traditional folded waveguide circuit.

For the fully symmetric folded waveguide slow-wave structure, there is no stop band at phase shift of 540◦ in theory. However, due to the machining, the actual slow wave structure will have a certain asymmetry, which may result in a stopband at the phase shift of 540◦ [12]. This stopband may affect the matching characteristics at the frequency, which may depress the output power at this frequency. In addition, it may result in the undesired 3π oscillations. Therefore, phase shift of 540◦ is usually avoided to fall into the operating frequency band when designing the folded waveguide slow-wave structure.

According to the calculation formula of coupling impedance

$$\mathbb{K}\_c = \frac{|E\_z|^2}{2\beta P}$$

for folded waveguide slow-wave structures, the closer to the cutoff frequency, the stronger coupling impedance is. Here, *Ez* is the axial component of the electric field, *β* is the phase constant of the electromagnetic wave, and *P* is the power flowing. Therefore, in order to obtain greater power and higher interaction efficiency, the operating point is usually selected within 540◦.

However, as shown in Figure 5, the phase shift within 540◦ means that the dispersion is stronger, which directly affects the operating bandwidth of the TWT. As the dispersion intensity of the folded waveguide slow-wave structure is positively correlated with the proportion of the beam injection channel size to the waveguide, due to the limitations of the performance of the current focusing system, it is difficult to further reduce the size of the beam injection channel in the THz band.

One way to achieve broadband performance is selecting the operating point above 540◦, which is not usually used for its lower coupling impedance. The dispersion is more flat, which is more conducive to the synchronization and interaction between beam and wave. In addition, as the operating point moves away from the cutoff frequency, high frequency loss can be reduced. The saved power from high frequency loss can be stored in the beam and recovered by the deeply depressed collector with an efficiency of more than 90%.

At the same time, the decrease of electronic efficiency can inhibit the dynamic defocus of the beam, which is beneficial to improve the dynamic flow rate.

By the above design routes, the G-band broadband folded waveguide slow-wave structure is designed, and its cold characteristics are calculated by CST Microwave Studio. The simulation results are shown in Figures 6–9.

**Figure 6.** Dispersion curves of the folded waveguide circuit.

**Figure 7.** Normalized phase velocity of the folded waveguide circuit.

**Figure 8.** Coupling impedance of the folded waveguide circuit.

Considering the effects of dispersion, coupling impedance, and attenuation, the working point is selected between 540◦ to 630◦. The beam line almost coincides with all frequency points from 208 GHz to 233 GHz, which ensures excellent beam–wave synchronization in the band and allows a wideband beam–wave interaction.

According to the results of Figures 7 and 8, the difference of phase velocity is less than 1% of vpc (center) and the coupling impedance of the folded waveguide circuit is over 0.5 <sup>Ω</sup> in band. The effective conductivity of the circuit is empirically set as 2.6 × <sup>10</sup><sup>7</sup> S/m considering the surface roughness. The attenuation coefficient of the folded waveguide circuit is less than 150 dB/m, as shown in Figure 9.

The severed folded waveguide circuit consists of an input section and an output section, which ensures the stable operation while providing a high gain over 30 dB with low ripples.

The center frequency is usually selected as the reference frequency to find the operating voltage when designing TWTs. The method is applicable when designing low frequency TWTs or THz narrow band TWTs, as their variation of in-band coupling impedance is small. However, for THz wideband TWT, the in-band coupling impedance varies strongly, and the coupling impedance of which at the low frequency may be more than three times that at the high frequency end, resulting in large gain ripple.

The design scheme in this paper does not follow the traditional design scheme, and the highest frequency in band has been taken as the reference frequency to determine the operation voltage. By adjusting the dispersion strength of the slow-wave structure, the beam–wave interaction performance at the low-frequency can be adjusted, which can bridge the gain ripple caused by the change of coupling impedance.

The performance of the circuit is simulated by using a large signal beam–wave interaction software microwave tube simulator suite (MTSS). The saturation output power of the circuit is over 12 W and the saturation gain is over 27.8 dB in 208–233 GHz at the designed beam voltage and current, as shown in Figures 10 and 11.

**Figure 10.** Saturation output power of the circuit.

**Figure 11.** Saturation gains of the circuit.

In order to increase the total efficiency, a double stage depressed collector with an efficiency of over 90% is used in the TWT. The design voltage of the first stage is 17.5 kV, and the voltage of the second stage is 18.5 kV. The simulation results are shown in Figure 12 and Table 2. According to the results, the total efficiency of the TWT can be over 8% in band.

**Figure 12.** Electron distribution in the double stages depressed collector.

**Table 2.** The simulation results of different frequency.


Diamond is used as window disk material because of its small dielectric constant, small loss tangent, high thermal conductivity, and good broadband matching. Both the input

and output RF windows of the TWT are pillbox windows, and the waveguide standard WR-4 is selected according to the operating frequency. CST Microwave Studio was used to optimize the S-parameters of the window. The measured S21 of a typical RF window is about −1 dB and the S11 is lower than −10 dB in 200–240 GHz, as shown in Figure 13.

**Figure 13.** Measured S11 and S21 of a typical RF window employed in the TWT.
