Figure 1 (a) shows the PSRWG SWS that evolves from the rectangular waveguide with wide side length *a* and narrow side length *b*, in which its two E-planes are simultaneously oscillated up and down along the longitudinal direction with an amplitude *h* and a period *p*. Meanwhile, the oscillating amplitude should not exceed half of the narrow side length of the rectangular waveguide. Under these conditions, the cross section of the PSRWG SWS can be kept uniform and a rectangular electron channel with the cross-sectional area of *a* × *h**b* can just be formed. As can be seen from Figure 1 (b), the oscillating curve in H-plane is a piecewise sine curve formed by inserting line segments into peaks and troughs of the sine curve. The length of line segment is *w* and the period of sine curve is *p**0*, respectively.

The Eigen-mode solver in 3D electromagnetic simulation software Ansoft HFSS is used to analyze the slow-wave characteristics of the PWSWG SWS [20]. In order to obtain broad matching in the frequency range of 210-240GHz, the dimensional parameters of PWSWG SWS are partly optimized through calculations and given as follows: *a*=770*µm*, *p*=460*µm*, *h*=180*µm*, *h**b*=140*µm*. For the PWSWG SWS, the length of line segment *w* is key structural parameter that affects its slow wave characteristics. And the influence of the line segment length on dispersion properties and interaction impedances have been analyzed by the simulation method, as shown in Fig. 2. Fig. 2 (a) shows that the normalized phase velocity decreases and the cold bandwidth becomes narrow as the line segment length *w* increases from 30 to 130*µm*. At the same time, it can be seen from Fig. 2 (b) that the interaction impedance values increases gradually with the increase of line segment length *w*. Considering the balance between bandwidth and output power of TWT, a compromise is made between dispersion characteristics and interaction impedance values in our design. So, the optimized value of the line segment length *w* is 80*µm*.

Using the structural parameters obtained from the above optimization, the Brillouin curve of the PWSWG SWS has been depicted in Fig. 3. In order to ensure the best synchronization around 220GHz, the electron beam voltage is selected to be 20.9kV. It can be noted from Fig. 3 that this SSRWG SWS has a main competitive mode (Mode-2) that can cause back-wave wave oscillation. Although the interaction impedance at the cross point is about 0.15ohm, this oscillation risk must be considered during the actual device design [21].

Then, the slow wave characteristics of the PWSWG SWS between the PWSWG SWS, the SWG SWS and the FRSWG SWS have been compared as shown in Fig. 4. Three SWSs have almost the same structural parameters, as given in Table 1. It should be pointed that to obtain the maximum interaction impedance in the comparison, the flattened height *h**c* is optimized to be a quarter of the beam tunnel height *h**b* [22]. From Fig. 4, we find that PWSWG SWS has the flatter dispersion curve and the lower normalized phase velocity compared to the other two SWSs. According to the synchronization conditions, we can infer that PWSWG SWS has wider bandwidth and lower synchronization voltage [21]. At the same time, the interaction impedances of PWSWG SWS are significantly larger than those of the other two SWSs in the frequency range of 210-240GHz. In detail, the interaction impedance of the PWSWG SWS at 220GHz is about 46.7% and 16.6% larger than the SWG SWS and the FRSWG SWS, respectively.

Table 1

Structural parameters of the PWSWG SWS, the SWG SWS and the FRSWG SWS

Parameter | PWSWG SWS | SWG SWS | FRSWG SWS |

**Wide side length** a | 770*µm* | 770*µm* | 770*µm* |

**Oscillating amplitude** h | 180*µm* | 180*µm* | *1*80*µm* |

**Oscillating period** p | 460*µm* | 460*µm* | 460*µm* |

**Beam tunnel height** hb | 140*µm* | 140*µm* | 140*µm* |

**Line segment length** d | 80*µm* | *-* | *-* |

**Flattened height** hc | *-* | *-* | 35*µm* |

To understand the physical mechanism of interaction impedance growth, we can analyze it by interaction impedance *K**c* expression (1). Here, *P**w* represents the transmission power flow on the axis, *E**zn* and β*n* represents the amplitude of the longitudinal electrical field and the phase constant of nth spatial harmonic. For the three SWSs, the TWT operates on the first positive space harmonic (*n* = +1).

$${K_c}=\frac{{|{E_{zn}}{|^2}}}{{2{\beta _n}^{2}{P_w}}}$$

1

The longitudinal electrical fields *E**z* of three SWSs at the typical frequency of 220GHz have been calculated, as shown in Fig. 5. For the PWSWG SWS, the longitudinal electric field distribution can be improved effectively by adjusting the line segment length. Apparently, the longitudinal electrical field amplitude of the PWSWG SWS is much larger than the other two SWSs in the beam wave interaction region. This is the most important factor for the improvement of interaction impedance. The interaction impedance growth in SWS means that the coupling strength between electromagnetic wave and electron beam will become stronger. As a result, we can speculate that the TWT based on PWSWG SWS may have higher interaction efficiency and better amplification performance.