Study on G-band traveling wave tube based on piece-wise sine waveguide and sheet electron beam Open Access

THz waves, corresponding to a frequency range from 0.1 THz to 10 THz, offer several advantages over microwaves:¹ (1) They provide significantly greater bandwidth, aligning with the technical requirements of future communication technologies such as 6 G. (2) THz waves produce minimal ionization and their penetration is influenced by tissue density, making them particularly beneficial for medical imaging. (3) Due to their very high frequency, THz waves enhance radar resolution, positioning them as a key technology in recent advancements in microwave systems. Currently, the traveling wave tube (TWT), a linear vacuum electronic device operating in the traveling wave mode, offers advantages such as broad bandwidth, high output power, low noise, and ease of tuning compared to other electron devices. It is considered one of the most promising sources of THz waves and has been extensively studied. For instance, Baig et al.² at the University of California developed a G-band sheet electron beam TWT using Nano-CNC technology, achieving a gain of 30 dB. Additionally, Kimura et al.³ reported a 200 GHz sheet electron beam TWT created by UC Davis, which delivers an output power of 107 W and a bandwidth exceeding 30 GHz. Recent advancements in G-band TWTs within China include the following: Zhang et al.⁴ developed a G-band phase-velocity-taper TWT using the quasi-flat-roofed sine waveguide (QFRSWG) with a peak power of 205-W and a 3 dB bandwidth of 10 GHz in University of Electronic Science and Technology of China (UESTC); Feng et al.,⁵ Beijing Institute of Vacuum Electronics Technology (BVERI), designed a G-band wideband low-gain fluctuation folded waveguide (FWG) TWT with an output power of 18-W and a bandwidth of 30 GHz; Zhang et al.⁶ at UESTC developed a ridge-loaded sine waveguide (RLSWG) for G-band TWT, achieving 52 W output power and a 25 GHz bandwidth. In addition, Zhang et al.⁷ from the Chinese Academy of Engineering Physics (CAEP) developed a wideband 220 GHz traveling wave tube based on slotted segmented sinusoidal waveguides with an output power of 28.6 W and a bandwidth of 15 GHz. These results are summarized in Table I.

As the frequency band reaches the THz range, conventional circular beams encounter significant obstacles due to their high charge density, which greatly restricts their application in this range. In contrast, the sheet electron beam effectively overcomes this challenge, markedly improving the situation and boosting the output power. Additionally, certain slow-wave structures, such as the sine waveguide slow-wave and the staggered double gate, naturally incorporate strip-beam channels.⁸ Nevertheless, sheet electron beams struggle to maintain stable transmission over extended distances because of their uneven structure, and the diocotron mode often emerges after a specific transmission distance, complicating the focusing process with a uniform magnetic field.⁹ At present, the open-periodic-permanent-magnet (OPPM) system is considered a viable solution to focus the sheet electron beam and suppress its instability.¹⁰ For instance, Zhang et al.¹¹ designed an electron-optical system for a G-band sheet electron beam TWT utilizing an OPPM system coupled with an elliptical electron gun. With a cathode voltage of −25 kV, a transfer efficiency of 81% was achieved at 37.5 mm. The total and collector currents were measured at 125 and 102 mA, respectively. The instability in subsequent transmissions impedes the advancement of sheet-beam TWT toward higher currents and increased power.

In this study, we propose an open periodic permanent magnet configuration with transverse-interleaving piece-wise pole boots to transmit the sheet electron beam in G-band TWT. Simultaneously, to extend the cathode's life, we utilized a cathode with low emission density equipped with an elliptical focusing electrode that has a high compression ratio. This configuration ensures that the sheet electron beam is transmitted consistently over extended distances, achieves a high compression ratio, prevents edge curling, and enhances beam stability.¹² Compared to the gate waveguide,¹³ the sine waveguide provides a natural strip beam path and offers advantages such as wide operating bandwidth, reduced transmission loss, low reflection, and simple manufacturing, although it has a relatively low coupling impedance.^2,14 To overcome this, the paper presents a piece-wise sine structure, where phase velocity adjustments are made by altering the length of the parallel grid. These modifications facilitate beam-wave re-synchronization and improve interaction. Unlike the traditional method of changing the entire period length, this method maintains the continuity of the sine waveguide and avoids additional reflections that could cause unstable oscillations.

As previously discussed, the elliptical electron gun effectively prevents the formation of curled edges, which is crucial for achieving high compression ratios and generating sheet electron beams with an extended waist. Leveraging data from the G-band TWT interaction circuit, this paper designs a high compression ratio elliptical Pierce electron gun. The gun operates at a beam voltage of 23 kV, a beam current of 230 mA, and achieves an overall area compression ratio of 18. The main configuration consists of an elliptical cathode measuring 2.1 mm by 0.9 mm and an elliptical focus electrode, as illustrated in Fig. 1.

Additional structural parameters for the electron gun, including the focusing electrode semi-axis (L_focus), the cathode radius (r_c), the anode radius (r_a), cathode-to-anode gap (Z_ac), beam injection plane location (Z_w), the perveance coefficient (uP), and sheet electron beam radius on the surface of anode (r_g) on the surface of the anode, can be efficiently determined using the Pierce method. Following an optimized iteration, these parameters are detailed in Table II.

Based on the calculations, described electron gun ultimately produces a standard elliptical beam, achieving a beam waist dimension of 1.05 mm by 0.81 mm at 15 mm from the cathode. Specifically, the sheet electron beam is reduced from 2.1 mm by 0.9 mm to 1.1 mm by 0.1 mm, achieving an area compression ratio of 18. In the twist of sheet electron beam, the ratio of horizontal to vertical dimensions is 11, the range of the gun is 14.7 mm, and the current density is approximately 300 A/cm². Following 10 iterations, the final emission current reaches 230-mA and the longitudinal velocity at the beam waist measures 8.67 × 10⁷ m/s, with a transverse velocity dispersion below 0.7%. These results are depicted in Fig. 2.

Furthermore, the asymmetric compression characteristics of the electron gun reveal significant transverse dynamics: the compression ratio on the wider side of the electron gun is 2, noticeably less than the 8 on narrower side. Throughout the formation process, sheet electron beam cross section evolves in the following manner: from a flat ellipse to a rectangular shape. The electron distribution remains relatively stable, and the laminar flow is effectively preserved. This results in sheet electron beam having an optimal velocity distribution upon entering the subsequent magnetic field, facilitating the PPM system's ability to focus on it. These findings are shown in Fig. 3.

In the above equations, B₀ represents the maximum remanence of the permanent magnet, p denotes the period of the magnetic system, while x_m indicates the width of the tunnel, and y_m is the vertical separation between the magnets. Other parameters include y_b, the thickness of the beam; x_b, the width of the beam; ω_p, the plasma frequency of the beam; and V₀, the electron velocity.

Using results obtained from the electron gun, we establish initial design parameters for the periodic permanent magnet system: the magnetic field strength B₀ is measured at 0.46 T, and the corresponding period p is 4.8 mm. Based on these results, we designed an open periodic permanent magnet system featuring a piece-wise pole shoe with lateral migration, as illustrated in Fig. 4.

The magnetic confinement system exhibits optimized geometric parameters with a total beam transport length of 100 mm, with the channel's cross-sectional dimensions being 0.86 mm × 0.146 mm. The transverse-interleaved pole configuration employs dual-stage magnetic shimming: Part I (0–40 mm) implements 0.20 mm pole displacement for wide-edge beam containment, while Part II (40–100 mm) utilizes 0.50 mm displacement to further suppress beam ripple. This configuration aims to restrict the wider edge of sheet electron beam, enhanced by the abrupt change in magnetic field. In the axial direction, a five-section permanent magnet gradient is employed to reinforce the constraint on narrow edge and prevent tearing of the sheet electron beam.

Simulation results of the magnetic system yield the following findings: The B_z axial distribution is optimal, with the peak field Bz_max reaching approximately 0.46 T, roughly double the Brillouin field B_bri; the first stage of B_y measures about 10-Gs, while the maximum field B_ymax of the second stage is approximately 40-Gs. The subsequent variation of B_y is note-worthy at 18-Gs, which could potentially influence the focusing effect of the broader edge. The period of the magnetic system is approximately 4.2-mm, closely aligning with the theoretical prediction of p_theory = 4.82 mm. The peak magnetization of the periodic magnetic system reaches 1.01 T, with a magnetization conversion rate of 45%, providing advantages over another permanent magnet configurations. These results are illustrated in Fig. 5.

The beam transport characteristics under the optimized PPM field are quantified in Fig. 6 through 3D particle tracking simulations: Long-distance circulation remains effective, achieving an efficiency of 105 mm at 100%, resulting in a final collecting electrode current of 230-mA with minimal electron interception. In terms of envelope morphology, as the beam advances, the overall fluctuation of the X-direction envelope increases, changing from (0.5 ± 0.1 mm) to (0.6 ± 0.2 mm). With the progression of the beam, the pulsation diminishes, and the overall distribution of the Y envelope ranges from (0.06 mm, 0.14 mm), with a slight deterioration near the outlet. The average filling rate of the electron beam within the channel is 39%, peaking at 73% near the exit, where the average filling rate in the Y/X direction is 64%, 61%, respectively.

Throughout the beam transmission process, the electron beam maintains stability without notable disturbances, exhibiting laminar flow with minimal disruptions at the broader edge. The electron beam achieves an ideal configuration at 69 mm, with acceptable configurations also observed at 22, 26, 42, 50, and 69 mm, while configurations at 34, 59, and 93 mm are less than ideal. The size range of the envelope in the high-frequency area fluctuates between 0.4 × 0.06 mm² and 0.8 × 0.14 mm². These findings are illustrated in Fig. 7.

Finally, the tolerance analysis of the EOS is carried out, the results are shown in Fig. 8. We can see: the transverse displacement of the polarized boot of the periodic magnetic system has a great influence on the flow, which affects sheet electron beam current mainly by influencing B_y. Among them, the offset of the polar bot has the most significant influence on circulation. When Offset_polebot deviates from the design value of 0.1 mm, the circulation can be reduced by 40%; the shape of pole bot pin also has a great influence on the flow effect, when it deviates from the optimal shape 0.1 mm, the flow decreases by 10% at most; in addition, the influence of the transverse assembly deviation of the electron gun body on the flow cannot be ignored, and the assembly deviation of 0.3 mm can cause the flow to decrease by 20%.

Overall, the influence of most structural parameters on circulation is less than 10%, and the flow remains effective. In general, the complete EOS delivers a beam power up to 5500 W for the G-band TWT, ensuring conditions suitable for producing more than 300 W of RF output. Furthermore, across a long flow distance of 100 mm, sheet electron beam maintains 100% transmission, preserving the laminar flow and structural integrity of the electron beam throughout the process without any signs of unstable modes. Additionally, the tolerance analysis for the PPM system indicates that the EOS exhibits robust stability and is not prone to errors from assembly, presenting considerable practical value.

Optimization of the sine structure was performed to align the forward wave of the fundamental mode with sheet electron beam. After optimization, the achieved structural dimensions are: the width of the side $(a=0.86 mm)$⁠, the channel height $(hTunnel=0.146 mm)$⁠, the gate height $(hvane=0.40 mm)$⁠, and the parallel segment length $(Wparall=0.101 mm)$⁠. Figure 9(b) presents the calculated dispersion and coupling impedance values for the slow-wave cell. The results indicate that the interaction frequency of the cell is approximately 200 GHz, with a coupling impedance of $1.66 Ω$ and a normalized phase velocity of 0.288c. This phase velocity is slightly below the 23 kV sheet electron beam velocity, enhancing beam-wave interaction. Moreover, the operating bandwidth of the slow-wave unit spans 47 GHz, covering frequencies from 185 GHz to 232 GHz. Within this range, phase velocities vary between $(0.290c,0.285c)$⁠, and the coupling impedance approaches $1 Ω$⁠.

To further investigate the dispersion-coupling characteristics of piece-wise sine cells, we analyze the influence of gate height and parallel segment length on these characteristics. The findings are as follows: with an increase in gate height, the phase velocity curve shifts downward within the high-frequency range, resulting in a rapid narrowing of the interaction frequency band toward the low-frequency range, as depicted in Fig. 10(a). Additionally, a slight increase in coupling impedance is observed within the low-frequency region, while a slight decrease occurs in the high-frequency range, as shown in Fig. 10(b).

The impact of sine structure length on dispersion is relatively minor compared to that of gate height. For instance, at the center frequency (200 GHz), changing the length from 0.37 mm to 0.33 mm results in a decrease in phase velocity of 0.015c, from 0.289c to 0.2875c. Conversely, increasing the vane height from 0.40 mm to 0.45 mm leads to a phase velocity decrease in 0.03c (from 0.289c to 0.286c) at this frequency point, as shown in Fig. 11(a). Additionally, as illustrated in Fig. 11(b), reducing the length of the sine structure can slightly enhance coupling impedance across the entire frequency spectrum; for example, when the length decreases from 0.37 mm to 0.36 mm, the coupling impedance increases from 1.9  $Ω$ to 2.3  $Ω$ at 194 GHz.

To further demonstrate the superiority of the piece-wise sine slow wave cell, a normal slow-wave unit was designed here for comparison with the new structure. The comparison results of the coupling impedance are shown in Fig. 12. At the operating frequency of 195 GHz, the coupling impedance of the new unit is 35% higher (0.57  $Ω$⁠) than that of the classic unit. All in all, when the gate height is set at 0.40 mm, the entire slow-wave unit exhibits flat dispersion characteristics, yielding a large operating bandwidth of up to 47 GHz. Similarly, with a sine structure length of 0.37 mm, the unit achieves a coupling impedance of 1.6  $Ω$ near the center frequency while maintaining this wide operating bandwidth. This design offers significant advantages over traditional sine structures by effectively combining large coupling impedance with a broad bandwidth.

In this section, a ribbed waveguide is employed to design the input coupler. The slow-wave sections are interconnected through two ring attenuators in three parts, where the first and second slow waves consist of 30 units each, and the third slow wave comprises 69 units, resulting in a total of 129 units. This structure is illustrated in Fig. 13(a). To enhance interaction efficiency, a phase velocity jump design has been incorporated at the third slow-wave position, specifically at 7/10. A five-stage phase velocity jump is implemented, with jump lengths for the parallel sections of the sine units being −5 μm, −10 μm, −15 μm, and −20 μm, respectively. In total, there are 20 jump units, with each jump segment consisting of 5 units. The entire phase velocity jump region accounts for 16% of the total number of slow-wave units. The remaining key structural parameters are summarized in Table III.

The system utilizes lossy copper as the background material, characterized by a conductivity of 3 × 10⁷ S/m. The transmission characteristics of the high-frequency system have been calculated, with the results presented in Fig. 13(b). It is observed that the −15 dB return loss bandwidth of the system spans 31 GHz, covering the range from 194 GHz to 225 GHz. Within the interaction band of 206–218 GHz, the return loss remains below –20 dB, making it less prone to backward-wave oscillation (BWO) and ensuring stable operation of the TWT. During this period, the in-band transmission loss exceeds −60 dB, and the ring attenuator effectively attenuates the back-wave signal over a short length, further preventing self-excitation of the TWT.

Finally, the third slow wave of the wave tube was processed, and cold test was carried out. The results showed that the reflection characteristics of the measured slow wave were in good agreement with the design results, but there was only a slight deviation from the design value in the insertion loss. The preliminary analysis may be caused by the slight assembly deviation of the final assembly of the cold test parts. The above results are illustrated in the Fig. 14(b).

A particle-in-cell (PIC) simulation was conducted on the designed piece-wise sine high-frequency system, with the results illustrated in Fig. 15(a). The simulation reveals that the system achieved a stable output power of 410 W at 195 GHz, powered by a sheet electron beam operating at 23 kV and 230 mA, with dimensions of 0.6 × 0.11 mm², as associated with the previously mentioned OPPM EOS. At this point, an input RF power of 100 mW, yielding a gain of 36.2 dB. Sheet electron beam delivers an input power of 5300 W, with an interaction efficiency of approximately 8%. No significant backward-wave oscillation (BWO) was observed throughout the output signal diagram, ensuring the stable operation of the wave tube. Additionally, spectral analysis indicates that power output is predominantly concentrated around 195 GHz, exhibiting a remarkably clean spectrum, as shown in Fig. 15(b).

The spatial distribution of the electron phase is depicted in Fig. 16(a). Most electrons reside in the deceleration field, with power amplification concentrated mainly in the latter half of the second slow wave. Consequently, electrons transferring energy at the high-frequency end exhibit uneven clustering. In the absence of a phase velocity jump, the electron energy reaches a minimum value of $2.1×104eV$ at 60 mm, resulting in no effective beam-wave interaction. The introduction of a phase velocity jump reduces the electron energy to approximately $1.8×104eV$ at the end of the high-frequency system, effectively enhancing the interaction efficiency. Additionally, as shown in Fig. 16(b), the clustering in the middle of sheet electron beam is prominent, while the edges remain relatively weak, consistent with the electric field distribution characteristics of the sine waveguide.

Figure 17 illustrates the variations in axial power within the TWT. Initially, the first and second slow waves boost the input signal by 16 dB, resulting in a power output of approximately 4 W. The primary amplification occurs in the third slow wave, leading to an increase in about 30 dB. Without a phase-velocity jump, saturation is reached at an axial length of 68 mm. With the implementation of phase velocity jump technology, the saturation point is extended to 73 mm. Ultimately, power is extracted from the interaction zone via the output coupler, with the maximum axial power reaching approximately 506 W at the end of the second slow wave circuit.

The beam-wave interaction of the tube is calculated frequency by frequency. As shown in Fig. 18, the tube exhibits maximum gain and output at 187 GHz, corresponding to an output power of 580 W and a gain of 37.6 dB. However, this frequency also shows a more pronounced occurrence of self-excited oscillation, rendering it unsuitable for operational use. Ultimately, the TWT demonstrates high output power and excellent stability at 195 GHz, with an output power of 410 W. Furthermore, the bandwidth for 300 W spans approximately 11 GHz, covering the range from 190 GHz to 201 GHz. Currently, the TWT has a 14 GHz 3 dB bandwidth, which extends from 190 GHz to 204 GHz.

Finally, as the input power increases, the TWT reaches a saturation state, and gain decreases. The peak gain is observed at an input power of 10 mW, with the TWT exhibiting a peak gain of 42.0 dB and an output power of 160 W. However, the output power can continue to increase with higher input power, remaining below saturation. At this point, when the microwave input power is 100 mW, the output power can reach up to 410 W at 195 GHz, as illustrated in Fig. 19. In addition, considering the deviations in actual processing, a tolerance analysis was conducted on the most critical parameter, the period length. The results indicated that a processing error of 3-μm⁶ could lead to a 10% reduction in power, with the worst case being approximately 390 W.

In this study, we introduce a novel sine waveguide that incorporates a piece-wise transverse-interleaving open-periodic-permanent-magnet (STI-OPPM) focusing system to develop a G-band high power sheet-beam TWT. This TWT delivers a maximum stable output power of 410 W at 195 GHz, powered by a 23 kV, 230 mA sheet electron beam, achieving an electronic efficiency of approximately 8%. It also has a gain of around 36.2 dB and a 3 dB bandwidth of approximately 15-GHz. Compared to the normal G-band TWTs, the proposed design demonstrates a 40% improvement in power-bandwidth product, achieving 410 W output with 15 GHz bandwidth, while maintaining a compact form factor of 100 mm in length, significantly enhancing the development of compact, high-power G-band TWT.

This Work was supported by the National Natural Science Foundation of China (Grant No. 62101519) and the Innovation and Development Fund of Institute of Applied Electronics, China Academy of Engineering Physics.

The authors have no conflicts to disclose.

Youhui He: Data curation (equal); Formal analysis (equal). Guowu Ma: Conceptualization (equal); Data curation (equal). Luqi Zhang: Conceptualization (equal); Data curation (equal). Yi Jiang: Formal analysis (supporting); Funding acquisition (supporting). Wenqiang Lei: Formal analysis (supporting); Funding acquisition (supporting). Rui Song: Formal analysis (supporting); Investigation (supporting); Writing – review & editing (supporting). Dimin Sun: Formal analysis (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Xiuyuan Xu: Writing – review & editing (supporting). Junzhi Wang: Writing – review & editing (supporting). Hongbin Chen: Project administration (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.