Investigation on a high power compact K-band transit-time oscillator with bilateral distributed extraction structure

The transit-time oscillator (TTO) is one of the most promising high power microwave sources due to its high power and simple structure.^1–13 Similar to other HPM sources, the specific value of the ratio of the TTO diameter (D) to the microwave wavelength (λ), which is defined as the overmoded ratio (D/λ), is a key factor in evaluating the power handling capacity of a TTO. In lower frequency ranges, such as the C and the X bands, TTOs with the D/λ of the order of 2–4, whose center radii are generally 4–6 cm, have generated microwaves with a power of several gigawatts successfully.^14,15 However, when scaling to the K band and above with a shorter λ, the GW level output power becomes extremely difficult to be achieved due to the narrower beam channel and cavities under the same D/λ.^16,17

The issues mainly focus on two aspects. First, the intensive relativistic electron beam (IREB) is difficult to be deeply modulated in the narrow beam channel, leading to a lower fundamental modulation current. Second, the power handling capacity of the TTO is insufficient, and the risk of RF breakdown is high due to the narrow cavities. For the first issue, one of the feasible methods is to increase the gap number of the bunching cavity to improve the fundamental modulation current. With a four-gap buncher, the maximum modulation coefficient can reach as high as 120% in Ref. 18. However, more gaps mean more electromagnetic modes in the bunching cavity, bringing about intense mode competition. Another method is using the two-stage bunching cavities to enhance the beam modulation. A three-gap and a single-gap rectangle bunchers were cascaded, and the modulation coefficient was increased to 125% as Ref. 19 described. Nevertheless, in this case, the electrical field in the second-stage buncher is strong and the power handling capacity of the single-gap rectangle cavity is insufficient in high frequencies.

To tackle the second issue, the most common solution for pursuing high power is to increase D/λ for a larger diameter of the high-frequency TTO.^18–21 In K and Ka bands, D/λ has been increased to around 10.^18,19 Furthermore, current simulation results of TTO show that with a D/λ of 8.9 at 26.2 GHz, an output power of 1.27 GW was generated with a largest electrical field of 1400 kV/cm in the output cavity.¹⁸ However, as D/λ significantly increases, electromagnetic fields in TTOs become more complex and non-operating modes become more difficult to be suppressed. In addition, larger device diameters require larger magnetic field coils, resulting in huge energy consumption.

To solve these issues and achieve high power in the K-band with a low D/λ, we proposed a three-gap buncher and a single-gap trapezoidal buncher to balance the high modulation coefficient with the high-power handling capacity. Furthermore, we investigated the use of a bilateral distributed extraction cavity to obtain the high power at 18.6 GHz. Finally, the designed TTO achieved an output power exceeding 2.0 GW, while the maximum electric field in the output cavity was controlled to 1.18 MV/cm, with a D/λ ratio of 3.7. By reducing the electron beam voltage from 500 kV to 475 kV, an output power exceeding 1.79 GW can be achieved and the field will decrease to 0.98 MV/cm, which is beneficial for achieving long-life operation of TTO.

This paper is organized as follows: in Sec. II, structure model and simulation results of the proposed K-band TTO are introduced. Channel combining structure is designed in Sec. III. Finally, conclusions are drawn in Sec. IV.

The schematic structure of the proposed K-band TTO is depicted in Fig. 1. Different from the traditional TTOs that typically employ a multi-gap buncher and a concentrated output cavity, the bunching section of the proposed TTO is composed of a three-gap rectangle cavity (buncher I) and a single-gap trapezoidal cavity (buncher II). Buncher I serves as the initial excitation point for the operating mode, where the intense relativistic electron beam (IREB) undergoes preliminary modulation. Then, the IREB is further modulated in buncher II, and the fundamental modulation current is enhanced significantly. The bilateral distributed extraction cavity is a three-gap rectangular cavity, and the coupling output holes are set in the inner side of the second gap and the outer side of the third gap, respectively. Downstream of these two output waveguides, a channel combiner is integrated to connect the waveguides and efficiently merge the extracted microwaves. The center radius of the IREB is set at 30 mm, and an operational frequency of approximately 18.6 GHz is set as target within the K-band. Therefore, D/λ of the designed TTO is 3.7, marking a notable reduction compared to those for high-frequency TTOs reported to date.

To achieve a strong electron beam modulation while reducing the risk of RF breakdown in the bunching cavity, the bunching structure of the proposed TTO is designed as the combination of a triple-gap rectangular cavity and a single-gap trapezoidal cavity. Compared to commonly used four-gap cavities, there are fewer electromagnetic field modes with a larger frequency interval in the triple-gap cavity, which is beneficial for the mode control. By exciting the triple-gap cavity with a current source in electromagnetic simulation software, the resonant curve has been obtained and drawn in Fig. 2. It can be seen that only TM₀₁₁ mode at 18.03 GHz, TM₀₁₂ mode at 18.65 GHz, and TM₀₁₃ mode at 19.38 GHz are excited and their frequency intervals are 620 and 730 MHz, respectively. Additionally, the normalized electron beam conductance has been calculated and is listed in Fig. 3. From the calculation results, it can be found that with β_e, the longitudinal propagation constant of 0.39–0.53 mm⁻¹, corresponding to the voltage region between 450 and 520 kV, only the beam conductance of TM₀₁₂ mode is negative. It means the IREB losing energy during transmission and TM₀₁₂ mode can be excited in the cavity.

The models of the diode and buncher I are established in particle-in-cell simulation. When the beam voltage and current are 500 kV and 10 kA, respectively, the excited fundamental modulation current reaches about 5 kA at the end of the triple-gap cavity and reaches the maximum value of 11.4 kA through a 15 mm drift tube as depicted in Fig. 4. Therefore, 15 mm downstream, the rectangular cavity is the best position where buncher II can be loaded. In this case, the electric field is distributed as TM₀₁₂ mode in the cavity as shown in Fig. 5. The maximum value is 640 kV/cm, which is below the RF breakdown threshold. From the above-mentioned analysis, it can be concluded that the designed triple-gap cavity can reduce the risk of mode competition and the field intensity in the cavity.

It is observed from Eq. (1) that the normalized electrostatic field E_dc gradually increases as θ decreases, for the constant values of Vb r₁ and r₂. The electrostatic field is more near the trapezoidal cavity compared to the rectangular cavity, which tends to decrease the RF field around the surface of the trapezoidal cavity that causes breakdown and pulse shortening. This feature of trapezoidal cavity increases its power-handling capability.²² 

The trapezoidal cavity is designed to operate in coaxial TM₀₁ mode at 18.60 GHz as shown in Fig. 7. It can be seen from Fig. 8 that in the PIC simulation, the maximum fundamental current is boosted to as high as 13.8 kA (modulation depth 138%) after traversing a 10 mm drift tube as shown in Fig. 8.

In this case, the maximum E-field is contained within 700 kV/cm in the trapezoidal cavity as Fig. 9 shows the fundamental modulation current exceeding 10 kA in the cavity. This indicates the excellent performance of trapezoidal cavity in improving power handling capacity. According to the simulation results, it can be concluded that using the combination of a triple-gap rectangular cavity and a single-gap trapezoidal cavity can achieve a higher modulation coefficient while ensuring a sufficient power handling capacity in the bunching area.

The IREB, which is deeply modulated by bunchers, enters the multi-gap extraction cavity, and the beam kinetic energy is gradually converted into microwave. For commonly used centralized extraction structures, the coupling output hole is typically located at the end of the last gap. The microwave generated from each gap must transmit to the last one before being extracted, which results in the enhancement of the electric field. Therefore, the risk of RF breakdown increases especially at high frequencies with a smaller cavity size. In the bilateral distributed extraction structure, there are two coupling holes as Fig. 1 shows. Hole I is set in the outer side of gap III, while hole II is in the inner side of gap II. The microwave generated from the first and second extraction gaps mainly transmits to the coupling hole I, while that from the third gap transmits to the coupling hole II. In addition, the dimensions of the three extraction cavities are redistributed to adjust the proportion of output powers of two holes and further lower the electric field on the surface of the second extraction cavity. The output microwave power is measured at the outer and inner waveguide ports, as drawn in Fig. 10. The results are 0.52 GW (P₁) and 1.49 GW (P₂), respectively. Therefore, the total output power (P) of the designed TTO is about 2.0 GW, and the efficiency is 40%. The E-field distribution is drawn in Fig. 11, indicating that the maximum E-field value is 1.18 MV/cm, which can be acceptable in short-pulse operation of TTO. Furthermore, to satisfy the general electric breakdown limit of 1 MV/cm, the beam voltage is declined from 500 kV to 475 kV and the length of coupling hole I is adjusted slightly (from 1.5 mm to 2.5 mm). The corresponding output power is 0.42 GW (P₁) and 1.37 GW (P₂) as drawn in Fig. 12. The total output power (P) is about 1.79 GW, and the efficiency remains at 39.7%. The output power is still superior to the reported high-frequency HPM sources^18,19 especially considering its smaller overmoded ratio. At this case, the maximum E-field value is 0.98 MV/cm as shown in Fig. 13, which is beneficial for the long-pulse operation of the TTO.

As described in Sec. II, microwaves are extracted from two coupling holes and propagate as coaxial TEM mode in two output waveguides of the TTO. The frequency of the microwaves in two waveguides is completely consistent at 18.61 GHz as shown in Fig. 14, while the phase difference after saturation remains at around 32° as drawn in Fig. 16. In addition, the power ratio of the two ports is calculated as 0.258:0.742 according to the output power 0.52 and 1.49 GW, respectively. Consequently, it is necessary to design a high-power combiner, which satisfies the above-mentioned phase and power conditions, to achieve efficient channel combination of the microwaves. The structure of the combiner is drawn in Fig. 17. Port 2 and Port 3 are the input ports of the combiner, corresponding to the two output ports of the TTO. Port 1 is the output port of the combiner.

Therefore, the phase difference between the two waveguides can be adjusted solely by varying the length of the waveguides. To compensate for the phase difference of 32°, the length difference between the two waveguides should be set as (1.43 + n^*16.05) mm.

The simulation model of the combiner has been established and optimized in CST software. To adjust the transmission coefficients of the combiner, three adjustment blocks are introduced in the outer waveguide where the electric field is relatively weak. The phase difference red from $Δφ31−Δφ32$ is 30° at 18.61 GHz as listed in Fig. 18, which can compensate the phase difference of the output waveguides effectively. The number of mesh cells is 1 162 678 in the simulation. It has been verified that when the mesh cells increase to 1 675 656, the change of phase difference is less than 0.12°. The power ratio of the two ports, S²₂₁: S²₃₁, is calculated to be 0.254:0.746 at 18.61 GHz as drawn in Fig. 19, which satisfies the requirement. Furthermore, the sum of S²₂₁ and S²₃₁ approaches 1, while the reflect coefficient S²₁₁ is close to 0, indicating that the reflection of the combiner can be ignored and will not affect the operation of the TTO. The model of the TTO and the combiner are connected, the PIC simulation is carried out as Fig. 20 shows, and the electron momentum in the z-direction in the bunching section is plotted in Fig. 21.

After loading the combiner, the fundamental modulation current still maintains good consistency and the amplitude variation is less than 1% as drawn in Fig. 22 (from 13.8 kA to 13.67 kA). The microwave power measured from the output port of the combiner is about 2 GW as shown in Fig. 23, which is equal to the sum of the power output from the two ports of the TTO. Consequently, the simulation results convincingly validate the feasibility of the proposed scheme. The sensitivity of the B-field is simulated, and the results are shown in Fig. 24. The output power obtains the maximum value with the B-field of 0.78 T. When the magnetic field exceeds 0.78 T, although the output power undergoes a minor decrease, it consistently remains above 1.6 GW within a significant range of variation. Therefore, this TTO exhibits a certain level of stability.

To realize the high power with low D/λ at K-band, a TTO with the improved bunching and output structures is proposed and investigated in this paper. When D/λ is set to 3.7 and the operating frequency is 18.6 GHz, the bunching structure, consisting of a triple-gap rectangular and a trapezoidal cavity, is optimized to obtain a 138% modulation coefficient successfully, while the maximum value of E-field in the bunching structure can be controlled to 700 kV/cm. The output cavity with bilateral distributed extraction structure is simulated, and the microwave power of 2.02 GW is extracted with a maximum E-field of 1.18 MV/cm, which is significantly better than previously reported results in the high-frequency domain. By reducing the electron beam voltage from 500 kV to 475 kV, an output power exceeding 1.79 GW can be achieved and the field will decrease to 0.98 MV/cm, which is beneficial for achieving long-life operation of TTO. Finally, a high-power combiner is designed, and the output microwaves from the TTO are combined.

This work was supported by the National Natural Science Foundations of China under Grant No. 62101574.

The authors have no conflicts to disclose.

Wei Zhang and Hongtao Yao contributed equally to this work.

Wei Zhang: Data curation (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Hongtao Yao: Data curation (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jinchuan Ju: Conceptualization (lead); Funding acquisition (lead); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Tengfang wang: Data curation (equal); Software (equal). Yunxiao Zhou: Data curation (equal); Software (equal). Ying Li: Software (equal); Writing – review & editing (equal). Jun Zhang: Funding acquisition (equal); Project administration (equal).

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