Modular Integration of a Compact Ku-Band Relativistic Triaxial Klystron Amplifier Packaged With Permanent Magnets for High-Power Microwave Generation

To achieve modular integration of relativistic triaxial klystron amplifier (TKA) devices and reduce the energy consumption of the whole high-power microwave (HPM) system, a compact Ku-band TKA packaged with permanent magnets is proposed and investigated in this paper. By optimizing the electromagnetic structure and utilizing TEM mode energy coupling, the length of the uniform magnetic field area required for the Ku-band TKA is reduced from 32 cm to 19.6 cm, with a reduction rate of 39%. By utilizing the NdFeB-N50M mainly magnetized in the ${R}$ direction, a permanent magnet guiding system weighing 90 kg is proposed. Besides, the length of the uniform zone is 20 cm with a longitudinal magnetic field of 0.5 T. Verified by the PIC simulation software CHPIC, an HPM with power of 430 MW and frequency of 14.25 GHz is generated when the diode voltage, current, and the injected microwave power are 340 kV, 4.2 kA, and 15 kW, respectively. The phase jitter of the output microwave is controlled within ${\pm } 5{^\circ }$ , which is beneficial to the coherent power combination of modular integrated TKA devices

SECTION I. Introduction

Relativistic triaxial klystron amplifier (TKA), with the advantages of high output power, stable frequency and controllable phase, is one of the most promising high-power microwave (HPM) generators for coherent power combination [1], [2]. For an HPM system with ${N}$ modules of TKA devices, the equivalent peak output power density is approximately ${N}$ ² that of a single TKA module. Consequently, the equivalent output power density of HPM systems can be rapidly improved by increasing the number of TKA modules. The HPM system of a single TKA module nowadays [3]–​[6], however, is quite bulky due to the fact that electron modulation and bunching are separated in different regions, and extremely long structures, compared with HPM oscillators [7]–​[9], are needed for TKA devices. Besides, the electron beam in TKA devices is constrained by external electromagnetic solenoids. These solenoids and their affiliated power supply systems and water-cooling systems further increase the volume of a single TKA module. What’s more, the energy consumption of the magnetic field generation system is more than ten times higher than the average power required by the TKA device itself [10], [11], which reduces the operation efficiency of the whole HPM system to less than 5%.

Replacing electromagnet solenoids with permanent magnets can eliminate the need of affiliated power supply systems and water-cooling systems for solenoids, which not only reduces the size of a single TKA module significantly, but also brings down the energy consumption of the whole HPM system dramatically. The employment of permanent magnets has been achieved experimentally for relativistic backward wave oscillators (RBWO) [11], [12] and relativistic magnetrons (RM) [10]. However, so far, there are no related experimental reports about TKA packaged with permanent magnets, and the chief constraint is that the TKA are much longer than the RBWO and the RM. As the length of HPM generators increases, the size and weight of permanent magnets required to produce the same guiding magnetic field increase exponentially. In a word, minimizing the length of TKA modules is practical and necessary for the packaging of permanent magnets.

To achieve modular integration of TKA devices, a compact Ku-band TKA packaged with permanent magnets is proposed and investigated in this paper. The total weight of the permanent magnets is approximately 90 kg, and the length of the uniform zone is 20 cm with a longitudinal magnetic field ($B_{z}$ ) of 0.5 T. With the proposed Ku-band TKA device, a frequency-locking and phase-locking HPM with power of 430 MW is generated. This paper is organized as follows: in Section II, the operation principle of TKA devices is briefly introduced. In Section III, the methods employed to compact the structure of a single TKA module are investigated systematically, and a compact Ku-band TKA is proposed. Then, the permanent magnets guiding system is designed in Section IV. The operation characteristics of the proposed TKA device packaged with permanent magnets are displayed in Section V. Finally, conclusions are drawn in Section VI.

SECTION II. The Operation Principle of TKA Devices

The schematic configuration of a TKA device is presented in Fig. 1(a) [13]. It is composed of a diode, an input cavity, some bunching cavities, an output cavity and some coaxial resonant reflectors. Firstly, a seed microwave signal at the operation frequency is injected into the input cavity and a TM₀₁ mode is established in the cavity gap. Then, a high voltage pulse is loaded onto the diode, and the graphite cathode generates an annular electron beam which will be guided by an external magnetic field to propagate longitudinally. The annular electron beam is pre-modulated when it passes through the input cavity gap. The cascaded bunching cavities are used to boost the amplitude of the fundamental harmonic current modulation [14]. The subsequent cavity is loaded at the position of the maximum modulation current of the previous cavity to obtain the maximum fundamental current modulation depth. When the intensely bunched electron beam passes through the output cavity, the energy of the electron beam will be converted into the energy of the microwave field and then exported through a coaxial waveguide. According to the operation principle of klystron amplifiers, there should be no electromagnetic coupling between adjacent beam-wave interaction cavities. Thus, some reflectors are employed to suppress the TEM energy coupling between the adjacent cavities and ensure stable operation of the device.

FIGURE 1.

Comparison schematic of two Ku-band TKA devices: (a) the initial structure; (b) the compact structure; (1) graphite cathode, (2) input cavity, (3) bunching cavity I, (4) bunching cavity II, (5) output cavity, (6) drift tube, (7) electron beam path, (8) reflector I, (9) reflector II, (10) reflector III, and (11) the uniform magnetic field area required for the operation of TKA devices.

SECTION III. Compactness of TKA Modules

For an HPM modular integration system of TKA devices, the equivalent output power density can be improved by increasing the number of TKA modules, which means that the output power for a single TKA module does not need to be very high. The power-handling capacity of TKA devices at a certain frequency, meanwhile, is proportional to the central radius of the electron beam. In order to realize miniaturization of TKA modules and maintain a certain power-handling capacity, the central radius of the proposed Ku-band TKA device is chosen to be 2.5 cm. An initial Ku-band TKA device has been systemically studied in our lab and its schematic is presented in Fig. 1(a). With the initial structure, an HPM with power of 660 MW is generated [13], when the diode voltage, diode current, and magnetic field are 494 kV, 4 kA and 0.5 T, respectively. However, the length of the uniform magnetic field area required for the operation of the TKA device is as long as 32 cm, and the outer radius of the device is 5.2 cm. Considering the large size of this device, it is not cost-effective to install permanent magnets package [12], [15], as its permanent magnets guiding system weighing more than 400 kg [16].

To realize the miniaturized permanent magnets package of Ku-band TKA devices, an improved compact Ku-band TKA is proposed and its schematic is shown in Fig. 1(b). The length of the uniform magnetic field area required for the operation of the TKA device [13] is reduced to 19.6 cm and the outer radius of the improved structure is only 4 cm. The methods employed to compact the structure of a single TKA module are discussed in detail as follows.

A. Optimizing the Diode and Magnetic Field Intensity

As is known, when coaxial permanent magnets are employed to package a certain TKA device, permanent magnets with larger radii produce less magnetic field intensity than those with smaller radii [17], [18]. It is obvious that, to produce a magnetic field of certain intensity, the weight of permanent magnets will decrease sharply with the diminution of the device’s outer radius.

Considering that the outer radius of the initial structure is a little large, we attempt to optimize the diode of the initial structure to a smaller bulk. However, as the size of the diode decreases, the risk of strong electric field breakdown on the side of the diode, under certain electron beam power, increases rapidly. In order to ensure stable operation of the device, the total power of the electron beam is also reduced. As can be seen in Fig. 1(b), the outer radius of the improved structure is reduced to 4 cm, and its diode voltage and diode current are 340 kV and 4.2 kA, respectively. The electron beam power is reduced from 1.98 GW to 1.43 GW. The radial electric field intensity on the side of the cathode is an important parameter to measure the breakdown of the diode and the radial electric field distributions of the improved diode are shown in Fig. 2. The amplitude of the radial electric field is 28 MV/m, which is lower than the breakdown threshold of stainless steel (30 MV/m) [19], demonstrating that there is little risk of diode breakdown.

FIGURE 2.

Distributions of radial electric field within the diode region.

Simultaneously, the magnetic field intensity needed to guide the electron beam is investigated, and electron profiles at different longitudinal magnetic fields are presented in Fig. 3. It is obvious that the electron beam will bombard the drift tube when the longitudinal magnetic field strength is 0.4 T. Fortunately, when the strength of the longitudinal magnetic field exceeds 0.45 T, the electron beam can transmit freely in the drift tube. To ensure stable operation of the device and to control the weight of the needed permanent magnets, the longitudinal magnetic field strength is set to 0.5 T.

FIGURE 3.

Electron profiles at different longitudinal magnetic fields.

B. Axial Flipping of the Input Cavity

After reducing the radial size of the device, we explore how to shorten the axial length of the device. The injected microwave signal of TKA devices is usually provided by high-power klystrons, which are named as seed sources. Generally, the output microwave signal of a seed source is fed into the TKA input cavity through a rectangular waveguide and the output mode is the TE₁₀ mode. However, the operation mode of the TKA input cavity is the coaxial TM₀₁ mode. It is quite difficult to directly convert the TE₁₀ mode in rectangular waveguide into the TM₀₁ mode in the coaxial input cavity, thus a mode converter is employed to connect the seed source and the input cavity. The mode converter firstly converts the TE₁₀ mode in the rectangular waveguide into TEM mode in the coaxial waveguide, which can be easily converted into the TM₀₁ mode in the input cavity, as these two modes are both angular symmetry modes. Due to the fact that the mode converter plays such a complex role, it will inevitably take up some axial space. The mode converter is usually placed between the diode and the input cavity [4], [20], [21], and we attempted to place it between the input cavity and bunching cavity I to reduce some axial length of the device.

The structure model of the input cavity in the initial Ku-band TKA device is shown in Fig. 4, and it contains three microwave ports, namely Port I, Port II and Port III. Among them, Port I is the input port, and Port II and Port III are the drift tube coupling ports. For the initial structure, Port II is connected to the diode, and Port III is connected to bunching cavity I. For the compact structure, the connection is reversed. In general, the input cavity of the compact structure has an axial flip relative to the initial structure. The S₂₁ curve and S₃₁ curve of the input cavity are shown in Fig. 5. It is obviously that both of these curves have a resonant frequency at around 14.25 GHz, and their S parameters at this resonant frequency are nearly the same, meaning the resonant characteristics of the input cavity almost remains unchanged after being axially flipped.

FIGURE 4.

The structure model of the input cavity in the initial Ku-band TKA device.

FIGURE 5.

S parametric curve of the input cavity in the initial Ku-band TKA device.

For a TKA input cavity, the injected microwave absorption efficiency and fundamental harmonic current modulation capability are the most important parameters for describing its operation performance [22]. In order to test the operation performance of the axially flipped input cavity, it is connected to the diode and a 10-kW seed microwave is injected into the input cavity. The time evolution of the microwave power absorbed by the axially flipped input cavity is shown in Fig. 6. The irregular fluctuation of the absorption power curve is caused by the dynamic energy exchange between the electron beam and the input cavity electric field. The peak microwave absorption power of the input cavity is 9.6 kW, corresponding to a microwave absorption efficiency of 96%. The fundamental harmonic current distribution after the axially flipped input cavity is shown in Fig. 7. The peak value of the fundamental harmonic current is 133 A, and the corresponding modulation depth is 3.2%. As the fundamental harmonic current modulation depth gets such a high value, the axially flipped input cavity could operate very well.

FIGURE 6.

Time evolution of the microwave power absorbed by the axially flipped input cavity.

FIGURE 7.

Fundamental harmonic current distribution after the axially flipped input cavity.

C. Utilizing TEM Mode Energy Coupling

In general, TEM mode energy coupling between different beam-wave interaction cavities in TKA devices has adverse effects on the stable operation state of the devices [13], [23]–​[25]. However, a detailed analysis of the causes of the TEM mode in TKA devices shows that the TEM mode in the drift tube is derived from the operation mode (TM₀₁ mode) of the bunching cavities, which gradually transforms into TEM mode for propagation at the discontinuous structure between the cavities and the drift tube. Considering the other way round, it can be affirmed that the TEM mode in the drift tube can also be converted to the corresponding TM₀₁ mode in the bunching cavities. The core reason is that the resonant frequencies of the two modes are exactly the same. This means that there will be two TM₀₁ modes in the upstream cavity. One is the TM₀₁ mode electromagnetic field converted by TEM mode leaking from the downstream cavity. The other is the TM₀₁ mode electromagnetic field existing in the upstream cavity itself. Under certain conditions, when the phase difference of the two TM₀₁ modes is $2{n} {\pi }$ ($n = 1, 2, 3 {\dots }$ ), the two electromagnetic fields can be stably superimposed and achieve positive feedback coupling [26]. To sum up, the electromagnetic field in the upstream cavity is enhanced in a direct proportion, which is equivalent to indirectly enhance the fundamental current modulation ability of the upstream cavity. The enhancement of the modulation ability of the upstream cavity is helpful to shorten the drift tube between adjacent beam-wave interaction cavities, and realize the compact design of the device.

To utilize the positive feedback coupling of the TEM mode, reflector I before the bunching cavity I is eliminated. The reasons for eliminating the reflector I instead of the other one or more reflectors are as follows.

1. In a typical TKA device, the energy stored in the downstream cavity is almost a thousand times more than that in the upstream cavity [25]. Since the input cavity is the first cavity in a TKA device, the energy stored in it is the lowest among all the cavities. This implies that the input cavity has the lowest fundamental harmonic current modulation ability, and the distance required for electron beams to be sufficiently clustered behind it is also the longest [3], [5], [27]. Based on the above analysis, enhancing the fundamental harmonic current modulation ability of the input cavity by utilizing the positive feedback coupling of the TEM mode can significantly reduce the axial length of the drift tube after the input cavity.

2. Since the input cavity has the lowest energy storage capacity, the TEM mode energy coupling strength between the input cavity and the bunching cavity I can be easily controlled. If we eliminate another reflector or more than one reflector, the excessive energy coupling could interfere or even impede the stable operation of TKA devices.

In order to realize positive feedback energy coupling of the TEM mode between the input cavity and the bunching cavity I, the fundamental harmonic current modulation ability of the two-stage cascade bunching cavity without the reflector I is tested by PIC simulation software CHPIC [28], and the investigation model is shown in Fig. 8. Since the phase difference between the two TM₀₁ modes is directly proportional to the distance between the input cavity and the bunching cavity I [26], the drift distance is optimized detailly to achieve positive feedback energy coupling. The optimization methods are outlined in [26] Since the positive feedback phase has a period of $2{\pi }$ , the optimal drift distance between the input cavity and the bunching cavity I is also periodic. The positive feedback energy coupling can be realized over a series of periodic distances, but the fundamental harmonic current modulation ability differs a lot [29]. There is an optimal drift distance that allows the fundamental harmonic current of the composite cavity to reach saturation. When the drift distance is shorter than the optimal length, the fundamental harmonic current cannot reach the maximum value because the electron beams cannot be clustered sufficiently. When the drift distance is longer than the optimal length, the fundamental modulation current will not continue to increase. To obtain the largest fundamental harmonic current modulation depth and to shorten the axial length of the device as much as possible, we tried to make the device operate at this saturation point. After optimization, the best drift distance between the input cavity and the bunching cavity I was found to be 5.2 cm.

FIGURE 8.

TEM mode energy coupling model of two-stage cascade bunching cavities.

In order to illustrate the enhancement effect of the TEM mode positive feedback energy coupling, we compared and tested the fundamental current modulation ability of the cascade bunching cavities under the best coupling distance with and without reflector I (That is, whether the TEM mode energy coupling is established).

The gap integral voltage of the bunching cavity I under positive feedback (without reflector I) and no feedback (with reflector I) conditions are shown in Fig. 9. It can be observed that the gap integral voltage of bunching cavity I under both positive feedback and no feedback conditions is relatively stable, and the peak value of the gap integral voltage under the positive feedback condition is almost twice that of the no feedback condition, demonstrating that TEM mode positive feedback energy coupling is feasible. The fundamental harmonic current distribution under positive feedback and no feedback conditions are shown in Fig. 10. On the one hand, the peak value of the fundamental harmonic modulated current (5.08 kA) in the two-stage cascade bunching cavities under the positive feedback condition is obviously larger than that under the no feedback condition (4.19 kA). On the other hand, under the condition of positive feedback, the position of the peak value of the fundamental harmonic current of the two-stage cascade bunching cavities is obviously advanced, which is beneficial to further reduce the axial length of the device.

FIGURE 9.

The gap integral voltage of the bunching cavity I under positive feedback and no feedback conditions.

FIGURE 10.

The fundamental harmonic current distribution under positive feedback and no feedback conditions.

What’s more, to improve the beam energy conversion efficiency of the device, a new double-gap output cavity with higher extraction efficiency is employed to replace the original single-gap output cavity.

D. PIC Simulation Results

Finally, the compact structure of the Ku-band TKA device is shown in Fig. 1(b). Compared with the initial structure shown in Fig. 1(a), the length of the uniform magnetic field area required for the compact structure is reduced from 32 cm to 19.6 cm, with a reduction rate of 39%. Besides, its outer radius is also reduced from 5.2 cm to 4 cm, with a reduction rate of 23%. The size of the optimized device is thus significantly reduced, meaning that the compact structure is more conducive for modular integration and permanent magnets packaging.

The envelope curve of the output power of the compact Ku-band TKA device is shown in Fig. 11, and indicates that an HPM with power of 400 MW is generated. The frequency and power of the injected seed microwave are 14.25 GHz and 15 kW, respectively. The negative flowing power in the compact Ku-band TKA device is shown in Fig. 12, and its values at the downstream of the input cavity and bunching cavity I are 105 kW and 48 kW, respectively. The negative flowing power at the end of the input cavity is 105 kW, which is about 7 times more than that of the injected seed microwave (15 kW), indicating that energy coupling between the input cavity and the bunching cavity I is very strong. Furthermore, this also demonstrates that the TEM mode energy coupling between the input cavity and the bunching cavity I is well established.

FIGURE 11.

Envelope curve of the output power of the compact Ku-band TKA device.

FIGURE 12.

Negative flowing power of the compact Ku-band TKA device.

SECTION IV. Scheme of the Permanent Magnets Guiding System

After completing the compact design of the Ku-band TKA device, we begin to study the design of the permanent magnets guiding system. To minimize the volume and weight of the permanent magnets, NdFeB-N50M with excellent (BH)$_{max}$ is selected. Its characteristic parameters are as follows [30]: $B_{r}$ > 1.39 T, $H_{cj}$ > 1114 kA/m, $H_{cb}$ > 1035 kA/m, (BH)$_{max}$ > 373 kJ/m³, and density of 7.55 g/cm³.

Given the fact that the magnetic leakage factor of permanent magnets magnetized in the ${Z}$ direction is quite large [17], [18], the permanent magnets guiding system proposed in this paper is mainly magnetized in the ${R}$ direction and its longitudinal section diagram is presented in Fig. 13. It has an inner radius of 4.5 cm, an outer radius of 15 cm, an axis length of 39 cm and total weight of about 90 kg. The red vector arrow represents the direction of magnetization of the permanent magnet steel. The small magnetic block magnetized in the ${Z}$ direction is used to compensate the $B_{z}$ generated by the permanent magnets magnetized in the ${R}$ direction. Finally, the distribution map of the magnetic field line is shown in Fig. 14.

FIGURE 13.

Longitudinal Section diagram of the permanent magnets guiding system.

FIGURE 14.

Distribution map of the magnetic field line of the permanent magnets guiding system.

The magnetic field distribution curve of the permanent magnets guiding system on the electron beam line is shown in Fig. 15. The length of the uniform zone of the axial magnetic field intensity ($B_{z}$ ) is about 20 cm ($- 10{\sim }10$ cm), which is a little longer than the optimal length (19.6 cm) of the uniform magnetic field area required for the operation of the compact Ku-band TKA device. Besides, $B_{z}$ in this zone is about 0.5 T, with a minimum value of more than 0.494 T, corresponding to a non-uniformity of less than 1.2%. In addition, the radial magnetic field intensity ($B_{r}$ ) in this zone is no more than 0.02 T, which effectively ensures the efficient transmission of the electron beam without radial divergence.

FIGURE 15.

Magnetic field distribution curve of the permanent magnets guiding system on the electron beam line.

SECTION V. Operation Characteristics With Permanent Magnets Packaged

After completing the design of permanent magnets guiding system, the operation characteristics of the proposed compact Ku-band TKA device packaged with permanent magnets are investigated, and the results are as follows.

A. Combined Simulation Results

The magnetic field distribution curve on the path of the electron beam line, when the permanent magnets field is introduced, is shown in Fig. 16. The $B_{z}$ is larger than 0.494 T and the $B_{r}$ is less than 0.02 T. In order to further prove the validity of this permanent magnets field, we observed the electron beam transmission trajectory in the output cavity region, and its envelope diagram is shown in Fig. 17(a). As can be seen, almost all electrons pass through the output cavity, demonstrating that the permanent magnets field can support high efficiency transmission of the electron beam.

FIGURE 16.

Magnetic field distribution curve on the electron beam line in the uniform magnetic field region required for the operation of TKA device.

FIGURE 17.

The electron beam envelope diagram at the output cavity: (a) under the permanent magnets field; (b) under the uniform magnetic field of 0.5 T.

Fig. 18 shows the envelope curve of the output power of the compact Ku-band TKA device when the permanent magnets field is introduced. The output power is 430 MW, which is 30 MW more than that obtained under a uniform magnetic field of 0.5 T. Since the simulation structure of the compact Ku-band TKA device remains the same and the only difference is the guiding magnetic field, the increment of the output power comes from the influence of the permanent magnets field on the motion of the electron beam. The electron beam transmission trajectory, under the uniform magnetic field of 0.5 T, in the output cavity region is shown in Fig. 17 (b). Compared with that under the permanent magnets field, the biggest difference is the bombardment position of the electron beam. The electron beam under the permanent magnets field bombards on the side wall of the drift tube, converting part of the potential energy of the electron beam into kinetic energy. Due to the fact that the output cavity can convert the electron beam kinetic energy into microwave energy [21], the output microwave power of the compact Ku-band TKA device attains an increment of 30 MW under the permanent magnets field. The time-frequency and time-phase curves of the output microwave are shown in Fig. 19. As can be seen, the output frequency is locked at 14.25 GHz and the phase jitter is controlled within ${\pm } 5{^\circ }$ after 28 ns.

FIGURE 18.

Envelope curve of the output power of the compact Ku-band TKA device when the permanent magnets field is introduced.

FIGURE 19.

Time-frequency and time-phase curves of the output microwave when the permanent magnets field is introduced.

It is worth mentioning that the investigation of the proposed compact Ku-band TKA device is only verified by two- dimensional computer simulations so far, and subsequent relevant experimental researches are under way. However, due to the employment of specially designed single-gap modulation cavities [27], [31], asymmetric modes competition can be effectively suppressed.

B. The Output Performance With Different Input Parameters

In the experiments, the diode voltage is supplied by a pulse power source, and the injected microwave signal is generated by a high-power klystron. Therefore, the diode voltage and the input power both have a certain adjustable range. In order to better guide the experiments and achieve high-efficiency and stable operation of the device, the operation characteristics of the compact Ku-band TKA device were investigated under the above two parameters. At the same time, we further explored its performance under different input frequencies and different magnetic field intensity.

The output powers and efficiencies of the compact Ku-band TKA device under different diode voltages is presented in Fig. 20, under the condition that the diode impedance is fixed. When the diode voltage increases from 302 kV to 378 kV, the output power grows from 200 MW to 452 MW. The power conversion efficiency increases first and then decreases, reaching a maximum 30.1% at the voltage of 340 kV. Taking into consideration of the output power and efficiency of the device, the voltage 340 kV is much beneficial. The relative phases between the injected microwave signal and the output microwave under different diode voltages are illustrated in Fig. 21. The relative phase is defined as:

$$\begin{equation*} 2\pi \int f_{out} -f_{in} dt+\Delta \varphi\tag{1}\end{equation*}$$ where, $f_{out}$ and $f_{in}$ are the frequency of the output microwave and the frequency of the injected microwave signal, respectively. As shown in Fig. 21, the phase of the output microwave is well locked and phase jitter is controlled within ${\pm } 5{^\circ }$ under a fixed diode voltage. Nevertheless, the phase differences increase as the beam voltage increases, owing to the transit time effect of the electron beam in the high frequency structure.

FIGURE 20.

Output powers and efficiencies under different diode voltages.

FIGURE 21.

Phase differences under different diode voltages.

Fig. 22 shows the output powers and gains of the compact Ku-band TKA device under different input powers. When the input power is increased from 5 kW to 25 kW, the output power varies between 310 MW and 430 MW, whereas the gain decreases from 47.9 dB to 42.2 dB. To begin with, the output power increases with increase of input power, and reaches a maximum of 430 MW at the input power 15 kW. With further increase of the input power, the output power remains relatively stable. However, when the input power exceeds 20 kW, the output power drops steadily. The reason is as follows: with the increase of the input power, the modulation capability of the input cavity enhances fast, causing the optimal position of bunching cavity I to move forward. Since the structural size of the device remains unchanged, the bunching cavity I deviates from its optimal loading position, leading to a decrease of output power. The relative phases between the injected microwave signal and the output microwave under different input powers are presented in Fig. 23. The phase of the output microwave is well locked by the input microwave after 28 ns when specific power is injected and the phase differences under different input powers are controlled within ${\pm } 5{^\circ }$ , which is beneficial for power coherence combination.

FIGURE 22.

Output powers and gains under different input powers.

FIGURE 23.

Phase differences under different input powers.

Fig. 24 shows the output powers and gains of the compact Ku-band TKA device under different input frequencies. When the input frequency increases from 14.240 GHz to 14.260 GHz, both the output power and gain first increase and then decrease. When the input frequency varies between 14.248 GHz and 14.250 GHz, the output power reaches 430 MW. However, the output power of the TKA device drops sharply when the input frequency exceeds this range, because the resonant frequencies of beam-wave interaction cavities are near the design index 14.250 GHz. Therefore, the larger the frequency gap between the input frequency and the design index of 14.250 GHz, the poorer the exchange efficiency of the beam-wave interaction. The relative phase differences between the injected microwave signal and the output microwave under different input frequencies is plotted in Fig. 25. When the input frequency varies from 14.240 GHz to 14.260 GHz, the output microwave phase can be locked well, and the phase jitter of the output microwave can be controlled within ${\pm } 5{^\circ }$ . Under different input frequencies, the phase difference is locked at different values, which is caused by the different phase shift constant.

FIGURE 24.

Output powers and gains under different input frequencies.

FIGURE 25.

Phase differences under different input frequencies.

Shown as Fig. 3, the longitudinal magnetic field intensity has a great influence on the transmission of the electron beam. When the magnetic field intensity is lower than 0.45 T, the electron beam, due to transverse expansion, would be partially deposited on the drift tube wall, causing electron current losses. To explain the effect of the proximity of the electron beam with the drift tube, we further explore the output performance of the proposed compact Ku-band TKA device under different magnetic field intensity. The output power and the relative phase differences of the device, under different magnetic field intensity, are shown in Fig. 26 and Fig. 27, respectively. Compared with the transmission path of the electron beam presented in Fig. 3, it is easy to find that the electron beam deposited on the drift tube wall will cause the decrease of the output power, but the output microwave phase of the device can still remain relatively stable. However, as the decrease of magnetic field intensity, the phase jitter increases gradually, which is not conducive to coherent power combination. Therefore, it is necessary to adopt a guiding magnetic field higher than 0.45 T or introduce a focusing electrode [32] in the experiment to ensure efficient transmission of the electron beam.

FIGURE 26.

Output powers under different magnetic field intensity.

FIGURE 27.

Phase differences under different magnetic field intensity.

SECTION VI. Conclusion and Perspectives

To realize modular integration of relativistic triaxial klystron amplifier (TKA) devices, a compact Ku-band TKA packaged with permanent magnets is proposed and investigated in this paper. Firstly, the length of the uniform magnetic field area required for the TKA device is reduced from 32 cm to 19.6 cm by optimizing the electromagnetic structure and utilizing TEM mode energy coupling. With a length reduction rate of up to 39%, the miniaturization and compactness of the Ku-band TKA device can be achieved. Secondly, NdFeB-N50M with special magnetization direction and configuration is utilized to design the permanent magnets system. The total weight of the permanent magnets is approximately 90 kg, and the length of the uniform zone is 20 cm with a longitudinal magnetic field ($B_{z}$ ) of 0.5 T. Combined simulation results demonstrate that an HPM with power of 430 MW and frequency of 14.25 GHz is generated when the diode voltage, current, and the power are 340 kV, 4.2 kA, and 15 kW, respectively. Besides, the frequency and phase of the output microwave are locked well, which is beneficial to the coherent power combination of modular integrated TKA devices. This paper has realized the permanent magnets package of Ku-band TKA devices in the level of 100 kilograms for the first time, and subsequent relevant experimental researches are under way.