# Novel Dual Beam Cascaded Schemes for 346 GHz Harmonic-Enhanced TWTs
## 2 HHTWT
### SWS Design Methodology of HHTWT
#### 2.2.2 The SWS Length Determination  
The following simulation results are obtained by CST Particle Studio. The operating voltage and current are set to 18.4 kV and 10 mA in Particle in Cell (PIC) simulation, respectively. With frequency increased, transmission loss caused by skin effect becomes significantly high. The surface roughness, determined by different manufacture technology, also has significant effect on the transmission loss [21; 22]. The precision computer numerical control (CNC) lathe and electric discharge machining (EDM) are main and mature processing methods and widely applied in the fabrication of THz band and E-band SWS [22; 23]. By referencing experimental cases in [22; 23] and summarizing our engineering experience in [21], the effective conductivities of sections operating at E band and THz band are set as \(3.5\times 10^{7}\) S/m and \(1\times 10^{7}\) S/m, respectively.  
Due to low input power, the length of the modulation section should be long enough to ensure deep electron beam modulation. Hence, we construct 100 periods of modulation SWS, and determine the length of modulation section depending on the bunch state of electron beam. The frequency of input signal is 86.5 GHz, and the input power is 200 mW.  
The phase space of beam electron in the modulation section is shown in Figure 3. It shows the amplification process is at linear state before 38 mm. Hence, the length of modulation section is set as 38 mm.  
In order to determine the length of the drift tube, a series of current monitors are placed every other millimeter on the drift tube. Figure 4 plots the Fourier transform of the electron current signal at the end of the drift tube. Fundamental component and other three high harmonic components are also shown in it. However, only the fourth harmonic wave can be excited and amplified because the fundamental wave and other lower-order harmonic waves are cut off in the radiation section. In general, the length of the drift tube is controlled at the position where the fourth harmonic current is the largest. Figure 5 depicts the relative amplitude of the fourth harmonic current curve versus the length of the drift tube. The length of the drift tube is determined as 12 mm. Figure 6 shows the phase space graph of the electron beam at the end of the drift tube. It depicts that the electron  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Modulation Section** & **Radiation Section** & **Drift Tube** \\ \hline a & 2 mm & 0.5 mm & / \\ b & 0.32 mm & 0.085 mm & / \\ p & 0.64 mm & 0.17 mm & / \\ h & 0.51 mm & 0.2 mm & / \\ r & 0.08 mm & 0.08 mm & 0.08 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Structural parameters of the HHTWT.  
Figure 2: High frequency characteristics of the modulation and the radiation section. (**a**) The modulation section; (**b**) the radiation section.  
beam is modulated by EM wave and stay in the linear state. The energy is still stored in the electron beam.  
The length of the radiation section is chosen where output power reaches saturation point. Figure 7 shows the power versus the length of the HHTWT at 346 GHz. Hence, the length of the radiation section is 34 mm. The phase space graph of electron beam at the end of radiation section is shown as Figure 8.  
Figure 4: The Fourier transform of the electronic current signal.  
Figure 5: The graph of amplitude of the fourth harmonic.  
Figure 3: The phase space graph of the electron beam in the modulation section.  
Figure 8 shows the fourth harmonic is excited. Compared with Figure 6, the velocity of central cluster decreased significantly in Figure 8. It means the electron beam transfers a lot of energy to the EM wave, during the beam wave interaction in the radiation section. For convenience of reference, the parameters of HHTWT are summarized in Table 2.  
Figure 8: The phase space graph of the electron beam at the end of the radiation section.  
Figure 6: The phase space graph of electron beam at the end of drift tube.  
Figure 7: Power curve of the HHTWT at 346 GHz.