To achieve coherent power combination of Ka-band high-power microwave (HPM), a phase-locked klystron-type coaxial relativistic Cherenkov generator (PKC-RCG), which combines the advantageous characteristics of weak dimensional sensitivity of RCG and low input power ratio of relativistic triaxial klystron amplifier (TKA), is proposed and investigated in this paper. The PKC-RCG is composed of two parts: a pre-modulation region adapted from TKA and an energy exchange region adapted from RCG. The pre-modulation region is used for initial speed modulation of intense relativistic electron beams (IREB), ensuring that the output frequency is consistent with the input frequency. The energy exchange region is used for deep clustering of the IREB and achieving efficient beam–wave energy conversion. Phase locking of the output HPM is accomplished through phase delivery of the modulated IREB. Specially designed reflectors and cascaded single-gap bunching cavities with active suppression of asymmetric TM mode are employed in the pre-modulation region to suppress energy coupling and achieve a lower input power ratio. Disk-loaded slow-wave structure with smooth inner conductor is employed in the energy exchange region to further decrease the dimensional sensitivity of RCG. By the proposed Ka-band PKC-RCG, an HPM with a power of 550 MW and a frequency of 29.0 GHz is obtained with ohmic loss being taken into account. Moreover, the input power ratio and phase-locking bandwidth of the proposed Ka-band PKC-RCG are −51.4 dB and 30 MHz, respectively.
I. INTRODUCTION
High-power microwave (HPM) technology, with its broad potential applications in the fields of particle accelerators, plasma heating, space propulsion, etc., has garnered significant interest globally.1–4 The pursuit of higher output power remains a perpetual focus in HPM fields. Coherent power combination is recognized as one of the most promising measures to enhance the effective output power of HPM systems.1,5 For a coherent power combination of multiple HPM generators, their output frequencies and phases must be closely matched.6–8 Relativistic triaxial klystron amplifier (TKA), characterized by the advantages of low input power ratio, stable frequency, and controllable phase,8–10 emerges as a leading candidate for coherent power combination. Phase-locking TKAs have been experimentally confirmed in X-band and Ku-band, and typical results are 10.0 GHz/−45.2 dB (frequency/input power ratio) for X-band11 and 14.25 GHz/−48.1 dB for Ku-band.12 However, the development of TKA, when scaling to higher frequency bands,13 is constrained by power-handling capacity, machining and assembly errors, etc. For instance, a Ka-band TKA was studied in Ref. 13, and an HPM with power of GW level was obtained in simulation, while only hundreds of kW was achieved in experiments. The smaller geometry and greater dimensional sensitivity in high-frequency bands are considered the main causes.14
Another promising HPM generator for coherent power combination is the phase-locked relativistic Cherenkov generator (RCG), recognized for its high power capacity and weak dimensional sensitivity. Phase-locked RCG has been experimentally validated in X-band and Ku-band, and the typical experimental results are 9.3 GHz/−35.4 dB15 and 9.26 GHz/−42.2 dB, respectively.16 The input power ratio of phase-locked RCG reported thus far is obviously inferior to TKA. In addition, lossy materials, which confront the risk of RF breakdown and gas release, must be applied to suppress energy coupling and achieve suppression of parasitic modes,16,17 which has affected the development of this configuration. Furthermore, when scaled to higher frequency bands, overmoded structures are required to maintain their power-handling capacity, which will further bring about modes competition and other problems, and no pertinent results have been reported.
To achieve coherent power combination of Ka-band HPM, a phase-locked klystron-type coaxial relativistic Cherenkov generator (PKC-RCG), which combines the advantageous characteristics of weak dimensional sensitivity of RCG and low input power ratio of TKA, is proposed and investigated through simulations in this paper. The PKC-RCG can be regarded as a combination of the current modulation part of TKA and the energy exchange part of RCG. Specially designed reflectors18 and cascaded single-gap bunching cavities with active suppression of asymmetric TM modes19 are employed to suppress the energy coupling and achieve a lower input power ratio, and no lossy materials are needed. Disk-loaded slow wave structure (SWS) with smooth inner conductor20 is employed to further decrease the dimensional sensitivity of RCG. Finally, an HPM with a power of 550 MW and a frequency of 29.0 GHz is produced, considering the ohmic loss of high-frequency microwaves. In addition, three-dimensional PIC simulation results are consistent with those of two-dimensional simulation, and no self-excitation of asymmetric modes is observed in the Ka-band PKC-RCG. Furthermore, the input power ratio and phase-locking bandwidth of the proposed Ka-band PKC-RCG are −51.4 dB and 30 MHz, respectively. The remainder of this paper is structured as follows: in Sec. II, the structure model and operation principle of the proposed Ka-band PKC-RCG are briefly introduced. Simulation results of the PKC-RCG are displayed in Sec. III, and conclusions are drawn in Sec. IV.
II. STRUCTURE MODEL AND OPERATION PRINCIPLES
The schematic configuration of the Ka-band phase-locked klystron-type coaxial relativistic Cherenkov generator (PKC-RCG) is depicted in Fig. 1. It comprises two parts: a pre-modulation region adapted from TKA and an energy exchange region adapted from RCG. The pre-modulation region is used to generate high gain and the energy exchange region with disk-loaded SWSs and low Q-factor is mainly used to extend bandwidth. Structure design and optimization of the Ka-band PKC-RCG are conducted using particle-in-cell (PIC) simulation software CHPIC.21 The diode voltage, current, magnetic field, and the injected RF microwave power are 440 kV, 5.35 kA, 1 T, and 4 kW, respectively. The pre-modulation region consists of an input cavity, two reflectors (reflector I and reflector II), and two bunchers (buncher I and buncher II). The energy exchange region consists of a reflector (reflector III) and two sections of SWS (SWS I and SWS II). Furthermore, real materials rather than perfect electrical conductor (PEC), as shown in Fig. 1, are incorporated in the simulation of the Ka-band PKC-RCG, as the ohmic loss of the Ka-band electromagnetic wave is significant in metal conductors.22 Considering the RF breakdown threshold and ohmic loss of metal materials, the main structure of the Ka-band PKC-RCG is fabricated from stainless steel, while the input cavity is made of aluminum.23
Schematic configuration of the Ka-band PKC-RCG: (1) input cavity, (2) reflector I, (3) buncher I, (4) reflector II, (5) buncher II, (6) reflector III, (7) SWS I, (8) SWS II, and (9) electron beam path.
Schematic configuration of the Ka-band PKC-RCG: (1) input cavity, (2) reflector I, (3) buncher I, (4) reflector II, (5) buncher II, (6) reflector III, (7) SWS I, (8) SWS II, and (9) electron beam path.
A. Resonance characteristics of beam–wave interaction cavities
The pre-modulation region consists of a series of discrete cavities with gap width and resonant characteristics detailed in Table I. As given in Table I, the optimized resonant frequency of the three sets of beam–wave interaction cavities is similar to the operating frequency (29.0 GHz) of the device, which ensures that the IREB can steadily acquire a pre-modulated frequency consistent with the injected microwave frequency. The three sets of beam–wave interaction cavities are all single-gap structures, which feature excellent active suppression effect of asymmetric TM modes.19 Their operational modes are TM021 mode, TM011 mode, and TM011 mode. Notably, the input cavity employs a single-gap high-order mode structure, contrasting with the reentrant fundamental-mode structure employed in the traditional X-band and Ku-band.12,24 The rationale for this choice is the short wavelength of the Ka-band microwave, which results in a small size and high machining and assembly tolerances for the reentrant fundamental mode input cavity, making it unsuitable for Ka-band HPM sources.13
Gap width and resonant characteristics of the pre-modulation region of the Ka-band PHPMA.
. | Gap width/mm . | Operation mode . | Frequency/GHz . | Quality factor . |
---|---|---|---|---|
Input cavity | 2 | TM021 | 28.993 | 838 |
Buncher I | 1.5 | TM011 | 28.980 | 775 |
Buncher II | 1.2 | TM011 | 29.018 | 623 |
. | Gap width/mm . | Operation mode . | Frequency/GHz . | Quality factor . |
---|---|---|---|---|
Input cavity | 2 | TM021 | 28.993 | 838 |
Buncher I | 1.5 | TM011 | 28.980 | 775 |
Buncher II | 1.2 | TM011 | 29.018 | 623 |
The energy exchange region comprises two sections of disk-loaded SWS. Disk-loaded SWS are utilized for two primary reasons: (1) The power capacity of outer corrugated walls is significantly higher than that of inner one or bilateral one.25 (2) The inner conductor of the outer corrugated SWS is a uniform and smooth structure, affording a higher tolerance for decentration and dislocation between the inner and outer conductors. The dispersion characteristics and axial electric field distribution of the SWS II are depicted in Fig. 2. The inner radius (Ri), outer radius (Ro), period length (L), gap width (d), and corrugated depth (h) of SWS II are 63.4, 72.5, 3.5, 1.7, and 1.5 mm, respectively. As shown in Fig. 2(a), the beam line corresponding to 440 kV intersects with the quasi-TEM mode synchronously, and the synchronous frequency is 28.883 GHz. Figure 2(b) indicates that the working point is 6π/7 mode of the quasi-TEM mode. In addition, the period length, gap width, corrugated depth, and synchronous frequency of the SWS I are 3.0 mm, 1.7 mm, 1.5 mm, and 28.889 GHz, respectively. Furthermore, the Q-factor at the working point of the SWS I and the SWS II are 57.5 and 56.3, respectively.
(a) Dispersion characteristics and (b) axial electric field distribution of SWS II.
(a) Dispersion characteristics and (b) axial electric field distribution of SWS II.
B. Operation principle
The operation principle of the Ka-band PKC-RCG is described as follows: Initially, an RF signal with operation frequency is injected into the input cavity and a TM021 mode is established in the cavity. Subsequently, a high voltage pulse is loaded onto the diode, and the graphite cathode generates an annular intense relativistic electron beam (IREB) by explosive emission of cold cathode.26,27 The IREB is then guided by an external magnetic field to propagate longitudinally. The IREB is pre-modulated when it passes through the input cavity. Upon passing through the series of bunchers (buncher I and buncher II), these cavities’ resonant frequencies, which are close to the pre-modulated frequency of the IREB, are excited. Furthermore, the excited modes modulate IREB in return and boost the amplitude of the fundamental harmonic current. When the pre-modulated IREB enters the energy exchange region, an electromagnetic field of the same frequency will be excited in the two sections of SWS, as the synchronous frequency (28.9 GHz, as depicted in Fig. 2) of the electron beam line with the dispersion curve of the quasi-TEM mode is close to the pre-modulated frequency (29.0 GHz). The electromagnetic field will further modulate the IREB to achieve a fundamental harmonic current modulation depth of no less than 120%. Concurrently, when the IREB passes through the energy exchange region, the energy of the electron beam will be converted into the energy of the microwave field. Then, the generated HPM pulse will be radiated through a horn antenna into free space. Reflector I and reflector II are utilized to suppress the TEM energy coupling in the pre-modulation region and ensure that the IREB steadily acquires a pre-modulation frequency consistent with the injection frequency of the RF signal.18 Reflector III is utilized to suppress the TEM energy coupling between the pre-modulation region and the energy exchange region, ensuring the stable and independent operation of each part, and helping to obtain phase-locked HPM output. It is noteworthy that the structure of the PKC-RCG proposed in this paper is analogous to that of a Twystron.28,29 However, the Twystron functions as a microwave amplifier, while the PKC-RCG presented here is designed as an HPM oscillator, as shown in Fig. 3.
(a) Envelope curves of the output power. (b) Spectrum of the output microwave without RF signal injected.
(a) Envelope curves of the output power. (b) Spectrum of the output microwave without RF signal injected.
In general, the pre-modulation region is used for the initial speed modulation of the IREB, ensuring that the frequency of the output HPM is consistent with that of the RF signal. The energy exchange region is used for deep clustering of IREB and achieving efficient beam–wave energy conversion. The composite structure of the pre-modulation region and the energy exchange region can achieve phase-locked HPM output with a low input power ratio.
III. SIMULATION RESULTS
The schematic configuration of the Ka-band PKC-RCG is shown in Fig. 1, and it can be regarded as a combination of the current modulation part of TKA and the energy exchange part of RCG. The output power and frequency of the Ka-band PKC-RCG are adjustable and can be controlled via the RF signal, with specific adjustments detailed as follows.
A. Free-running state without RF signal injected
Initially, in the absence of injected RF signal, the device operates in a free-running state and the envelope curves of output power and frequency are displayed in Fig. 3. The output power is 523 MW with a saturation time of 32 ns, and the free-running frequency is stabilized at 29.007 GHz, which demonstrates that the PKC-RCG is not an amplifier but a phase-locking HPM oscillator. Although the free-running RCG exhibits stable output frequency, its arbitrary initial phase precludes its use for coherent power combination.15
The fundamental harmonic current distribution of the free-running state is presented in Fig. 4(a). The fundamental harmonic current modulation depth increases rapidly in SWS I and the first half of SWS II, and then declusters rapidly in the second half of the energy exchange region. The beam–wave energy exchange is accomplished within a longitudinal length of 5 cm, which demonstrates the compact advantage of RCG. In addition, the fundamental harmonic current at the front end of the energy exchange region is about 50 A. The peak current of the pre-modulation region is two orders of magnitude lower than that of the energy exchange region (6.88 kA), which means the energy coupling between the pre-modulation region and the energy exchange region is well suppressed.
(a) Fundamental harmonic current distribution and (b) negative flow power distribution of the free-running state.
(a) Fundamental harmonic current distribution and (b) negative flow power distribution of the free-running state.
The negative flow power distribution of the free-running state is displayed in Fig. 4(b), and its electromagnetic energy is mainly stored in the energy exchange region. The peak electromagnetic energy of the buncher II is about 4.2 MW, three orders of magnitude lower than that of the energy exchange region (2.9 GW), which demonstrates that the energy coupling between the two regions is well controlled from another side. In summary, the pre-modulation region of the PKC-RCG hardly works in the free-running state, and the device can be regarded as a self-excited RCG in this state.
B. Frequency locking state with RF signal injected
When the RF signal is injected, the output power and frequency vs time curve of the proposed Ka-band PKC-RCG are depicted in Fig. 5. An HPM with power of 550 MW and frequency of 29.0 GHz is generated, when the power and frequency of the injected RF signal are 4 kW and 29.0 GHz, respectively. The frequency of the output HPM corresponds to that of the injected RF signal, demonstrating that the Ka-band PKC-RCG can realize the amplification of the injected signal. As shown in Fig. 5(a), the output power of the device increases rapidly after 16 ns and reaches saturation at 20 ns under the traction of the injected RF signal. The saturation time with the RF signal injection is 12 ns faster than that without injection, indicating that the loading of the RF signal is conducive to accelerating the building up of electromagnetic oscillation in the device. In addition, the phase vs time curve is displayed as the orange line in Fig. 5(b), and the phase of the output microwave is well-locked after the output power becomes saturated. The phase jitter of the output microwave is maintained within ±5°, which is beneficial to the coherent power combination of the proposed Ka-band PKC-RCG. Furthermore, the output power of the frequency-locking state is larger than that of the free-running state, and this is related to more efficient beam–wave energy conversion. The remainder of this paper only investigates the situation with RF signal injection.
(a) Envelope curve of the output power. (b) Frequency and phase vs time with RF signal injected.
(a) Envelope curve of the output power. (b) Frequency and phase vs time with RF signal injected.
The longitudinal distributions of the fundamental harmonic current and electron beam power are illustrated in Fig. 6(a). The fundamental harmonic current modulation depth gradually intensifies in the pre-modulation region, and rapidly increases and reaches saturation after entering the energy exchange region. The peak value of the fundamental harmonic current appears at the second period of SWS II with an amplitude of 6.80 kA, corresponding to a modulation depth of 127.1%. As shown by the green line in Fig. 6(a), the IREB barely loses any energy in the pre-modulation region, and the beam–wave energy conversion is conducted in the energy exchange region. The positive and negative flow power distributions of the Ka-band PKC-RCG are displayed in Fig. 6(b). Consistent with the green line in Fig. 6(a), the electromagnetic energy of the PKC-RCG is predominantly stored in the energy exchange region.
(a) Fundamental harmonic current distribution and electron beam power. (b) Positive and negative flow power distributions of the frequency locking state.
(a) Fundamental harmonic current distribution and electron beam power. (b) Positive and negative flow power distributions of the frequency locking state.
C. Suppression of asymmetric modes self-excitation
The self-oscillation of asymmetric modes is a difficulty for HPM devices, which will lead to output pulse shortening, and even worse, destroy the operation of HPM devices.10,16,30,31 For the Ka-band PKC-RCG proposed in this paper, the suppression of asymmetric modes self-excitation is achieved through the following three aspects: (1) Single-gap bunching cavities are employed to reduce the risk of self-excitation of asymmetric TM modes in the pre-modulation region.19 (2) Specially designed reflectors are employed to suppress energy coupling of the TEM mode and asymmetric modes.18 (3) The operation mode of the energy exchange region is induced by pre-modulated IREB and has obvious advantages in the process of mode competition, which can restrain the development of asymmetric modes.32
Three-dimensional (3D) PIC simulations were conducted to verify the suppression effect of asymmetric modes. The envelope curve of the output power and spectrum of the output microwave in 3D simulation are displayed in Fig. 7(a). The output power, output frequency, and saturation time are 548 MW, 29.0 GHz, and 20 ns, respectively, aligning with the results in Fig. 5. Furthermore, the axial field distribution of the SWS II (t = 80 ns) is examined, as shown in Fig. 7(b), and it is a typical cross-sectional electric field distribution of quasi-TEM mode. The 3D PIC simulation results demonstrate that there is no self-excitation of asymmetric modes in the Ka-band PKC-RCG.
(a) Envelope curve of the output power and spectrum of the output microwave. (b) Axial field distribution of SWS II in 3D simulation.
(a) Envelope curve of the output power and spectrum of the output microwave. (b) Axial field distribution of SWS II in 3D simulation.
D. Investigation of phase-locking bandwidth
Phase-locking bandwidth is one of the most remarkable features of phase-locked HPM devices. For the Ka-band PKC-RCG proposed in this paper, the alignment of IREB’s pre-modulated frequency and self-excited frequency of the energy exchange region is the most significant representation of its phase-locking capacity. Thus, the frequency response characteristic of the proposed PKC-RCG is investigated, and the pertinent findings are shown in Fig. 8(a), when the injection power is stabilized at 4 kW and the injection frequency ranges from 28.97 to 29.03 GHz. The output frequency is obtained by FFT of the output HPM, and the predominant frequency and the subordinate frequency are displayed as the scatter plot in Fig. 8(a). Notably, no discernible subordinate frequency is observed and the predominant frequency is similar to the injection frequency when the injection frequency ranges from 28.99 to 29.02 GHz, meaning that the phase of the output HPM can be locked in this frequency range.
(a) Frequency and input power ratio (IPR) of the output HPM under different injection frequencies. (b) Peak pre-modulation current of the pre-modulation region.
(a) Frequency and input power ratio (IPR) of the output HPM under different injection frequencies. (b) Peak pre-modulation current of the pre-modulation region.
The input power ratio of the output HPM is displayed in the line chart in Fig. 8(a). The input power ratio curve is marked with a solid line when the output power of the device is stable, while a dashed line is applied when the power is fluctuating. When the injection frequency increases from 28.99 to 29.02 GHz, the spectrum of the output microwave is pure, but the input power ratio gradually increases. The increment of the input power ratio is equal to the decrement of the output power and efficiency. The insufficient modulation of IREB is regarded as the cause of this phenomenon, as the intrinsic frequencies of the input cavity and buncher I are below 29.0 GHz. Moreover, when the injection frequency is outside the range of 28.99–29.02 GHz, an HPM with an input power ratio below −50.7 dB can also be obtained.
Moreover, it merits the emphasis that the phase-locking bandwidth of 30 MHz is achieved under the condition that the injection power is steadfastly maintained at 4 kW. Under this specified condition, the peak pre-modulation current of the pre-modulation region is shown in Fig. 8(b), and the peak current diminishes sharply with any deviation of the injection frequency from the designed frequency of 29.0 GHz. Simulation results reveal that by augmenting the injection power to match the peak pre-modulation current across different injection frequencies with that at 29.0 GHz, the phase-locking bandwidth of the device experiences a modest expansion. Nonetheless, realizing this enhancement necessitates an increase in the injection power to the order of hundreds of kW, significantly exceeding the maximum power that the signal source can provide. Consequently, this scenario is not explored further in the present study. In addition, while the peak pre-modulation currents at 28.98 and 29.02 GHz are comparable, the phase-locking state is attainable at the frequency of 29.02 GHz, whereas it is not feasible at 28.98 GHz. This phenomenon is attributed to the system’s free-running frequency being 29.007 GHz. To sum up, the peak pre-modulation current and the injection frequency’s alignment with the natural frequency of the system are crucial for successful phase-locking.
Operating characteristics under different injection frequencies. (a) Phase differences. (b) Output powers.
Operating characteristics under different injection frequencies. (a) Phase differences. (b) Output powers.
This phenomenon can be explained as follows: the pre-modulation depth of IREB decreases as the injection frequency diverges from the presupposed frequency (29.0 GHz), and a smaller pre-modulation depth will lead to a slower phase-locked time. To sum up, the phase-locking bandwidth of the proposed Ka-band PKC-RCG is about 30 MHz (28.99–29.02 GHz).
Simultaneously, the injected RF signal is generated by a klystron in experiments, which possesses a bandwidth of tens of MHz.33,34 Therefore, it is impossible to adjust the frequency of RF sources without limitation to realize the phase-locking of the device. It is still important to fix the injection frequency to investigate the operation response of the device. When the injection power is fixed at 4 kW, and the diode voltage ranges from 380 to 450 kV, the phases of the output microwaves are locked well and the results are shown in Fig. 10(a), demonstrating that the voltage range of the proposed Ka-band PKC-RCG is about 70 kV (380–450 kV). The majority of the voltage range is less than the operation voltage of 440 kV, which is due to the higher frequency bandwidth (28.99–29.02 GHz), and the intersection frequency of the beam line and the dispersion curve increases as the voltage decreases. This result signifies that the voltage range can be seen as another form of frequency bandwidth. Furthermore, the corresponding output powers are shown in Fig. 10(b). When the diode voltage ranges from 380 to 420 kV, the output powers have an obvious fluctuation at about 20 ns. The difference between self-excited frequency and injection frequency is thought to be the main reason. In addition, this also means that the mode of the injection frequency needs a certain amount of time to obtain sufficient advantage over modes competitions, when the operation characteristics diverge from the optimum values.
Operating characteristics under different diode voltages. (a) Phase differences. (b) Output powers.
Operating characteristics under different diode voltages. (a) Phase differences. (b) Output powers.
Phase differences and output powers under different input powers are investigated and the results are shown in Fig. 11. The output powers are similar to each other, but the output phases display significant differences. The output phase can be locked well as the input power ranges from 4 to 6 kW, while the output phase seems to be slowly declining when the input power is lower than 4 kW. Thus, an input power of 4 kW is chosen and higher power can be injected to guarantee the phase-locking effect in experiments.
Operating characteristics under different injection powers. (a) Phase differences. (b) Output powers.
Operating characteristics under different injection powers. (a) Phase differences. (b) Output powers.
E. Sensitivity analysis
The developments of high-frequency-band HPM generators are partially restricted by their high dimensional sensitivity, compared with the low-frequency band.5 To ensure the successful progress of experiments, sensitivity analysis of the proposed Ka-band PKC-RCG is carried out.
The fundamental harmonic current distribution of the cascaded bunching cavities is observed, and the result is shown as the blue curve in Fig. 12. The peak value of the fundamental harmonic current is 2.32 kA, which is much higher than that at the front end of the energy exchange region (1.61 kA) in Fig. 6(a). This means that the peak fundamental harmonic current provided by the cascaded bunching cavities is much higher than that needed for phase-locking of the Ka-band PKC-RCG. Thus, a larger distance between buncher II and SWS I can be chosen in experiments to guarantee a sufficient pre-modulation depth of IREB. In addition, the fundamental harmonic current distribution under perfect electric conductor (PEC, idealized physical model with infinite electrical conductivity) is also observed, and the result is shown as the red curve in Fig. 12. The peak value of the fundamental harmonic current under real materials (2.32 kA) is only 41% that under PEC (5.65 kA), demonstrating that the ohmic loss of Ka-band electromagnetic wave is quite obvious in real metal conductor and it is necessary to consider material characteristics in the simulation of the Ka-band PKC-RCG.
Fundamental harmonic current distributions of the cascaded bunching cavities under PEC and real materials.
Fundamental harmonic current distributions of the cascaded bunching cavities under PEC and real materials.
Longitudinal dislocation of the beam–wave cavities is the main assembly error of coaxial HPM generators, and disk-loaded SWS with smooth inner conductor is employed in the proposed Ka-band PKC-RCG to decrease this error. The operation characteristics under different longitudinal dislocation of the energy exchange region are investigated and the results are shown in Fig. 13. The output frequencies are locked to be ∼29.0 GHz as the inner conductor moves forward along the +Z direction, while the output frequencies gradually deviate from the injected frequency as the inner conductor moves backward along the −Z direction.
Operation characteristics under different longitudinal dislocation of the energy exchange region.
Operation characteristics under different longitudinal dislocation of the energy exchange region.
Phase differences under different longitudinal dislocation are shown in Fig. 14, and the output phase can be locked well as the inner conductor moves forward along the +Z direction, while the output phase will decrease slightly at the initial stage and then get stable as the inner conductor moves backward along the −Z direction. The phase variation in Fig. 14 can be explained by the frequency variation in Fig. 13. In general, when the longitudinal dislocation of the energy exchange region ranges from −0.2 to 0.3 mm, the output phase can be locked. As the experimental assembly error is about hundreds of μm, on the same order of magnitude as the dislocation displayed in Figs. 13 and 14, we believe that the dimensional sensitivity of the proposed Ka-band PKC-RCG is controlled to be an experimentally acceptable level.
Phase differences under different longitudinal dislocation of the energy exchange region.
Phase differences under different longitudinal dislocation of the energy exchange region.
F. Diode and solenoid design
Furthermore, the corresponding diode and solenoid of the Ka-band PKC-RCG have been investigated, and their schematic configurations can be seen in Fig. 15(a). The diode is composed of a cathode, an anode, and an emitter. The cathode is composed of an emitter and a supporting barrel, with the former made of graphite and the latter made of stainless steel. When a high-voltage pulse is loaded onto the diode, the graphite cathode generates an annular intense relativistic electron beam (IREB) by explosive emission of the cold cathode, which will be guided by the solenoid magnetic field. Line1 and line2 in Fig. 15(a) mark the end of the emitter and the SWS II.
(a) Schematic configuration of the Ka-band PKC-RCG with diode and solenoid. (b) Distribution map of the magnetic field line of the solenoid. (c) Magnetic field distribution curve of the solenoid on the observe line.
(a) Schematic configuration of the Ka-band PKC-RCG with diode and solenoid. (b) Distribution map of the magnetic field line of the solenoid. (c) Magnetic field distribution curve of the solenoid on the observe line.
The distribution map of the magnetic field line of the solenoid is shown in Fig. 15(b), and the magnetic field distribution curve of the solenoid on the observe line is shown in Fig. 15(c). As can be seen in Figs. 15(b) and 15(c), the emitter is completely immersed in the uniform magnetic field region, which helps to reduce the envelope size of the IREB and ensure its longitudinal propagation. In addition, the magnetic field distribution curve gradually deflects at the end of the SWS II, directing the IREB to bombard the outer conductor.
Figure 16 displays the diagram of phase space and real space of the IREB. The red scatter plot in Fig. 16(a) displays the clustering status and location of IREB in real space. The IREB emits uniformly at the cathode, gradually modulates and clusters along the Z direction, and reaches the optimal clustering state at the SWS II. The drift tube width is 4.4 mm, and the beam envelope width is about 1.4 mm, which means that the designed solenoid can achieve the guidance of the IREB. The orange scatter plot in Fig. 16(b) displays the momentum distribution of IREB in phase space. The IREB modulates slowly in the pre-modulation region, then modulates quickly and completes beam–wave energy conversion in the energy exchange region.
Diagram of (a) real space and (b) phase space of the IREB (Pz is the momentum of the IREB).
Diagram of (a) real space and (b) phase space of the IREB (Pz is the momentum of the IREB).
IV. CONCLUSIONS AND PERSPECTIVES
To achieve a coherent power combination of Ka-band HPMs, a phase-locked klystron-type coaxial relativistic Cherenkov generator (PKC-RCG) with an input power ratio of −51.4 dB and phase-locking bandwidth of 30 MHz is proposed. The PKC-RCG is composed of two parts: a pre-modulation region adapted from TKA and an energy exchange region adapted from RCG. The pre-modulation region is used for the initial speed modulation of IREB, ensuring that the frequency of the output HPM is consistent with that of the injection signal. The energy exchange region is used for deep clustering of the IREB and achieving efficient beam–wave energy conversion. In addition, the feasibility of experiments is considered. Outer rippled and inner smooth SWSs are employed to reduce assembly errors. Finally, an HPM with power of 550 MW and frequency of 29.0 GHz is obtained when the diode voltage, current, magnetic field, and injected RF microwave power are 440 kV, 5.35 kA, 1 T, and 4 kW, respectively. Furthermore, verified by 3D PIC simulation, no self-excitation of asymmetric modes is observed in the proposed PKC-RCG.
In summary, a Ka-band PKC-RCG with weak dimensional sensitivity and low input power ratio is proposed in this paper. The topological structure of the proposed PKC-RCG can be extended to the design of HPM sources or klystron with high peak power operation at higher frequency bands. It has the potential to achieve coherent power combination in the Ka-band and relevant experimental research is underway.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China under Grant No. 61771481, the National Natural Science Foundation of China under Grant No. 61771482, the HuXiang Young Elite Program under Grant No. 2018RS3082, and National University of Defense Technology research program under Grant No. ZK18-03-04.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Yunxiao Zhou: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Jinchuan Ju: Methodology (equal); Writing – review & editing (equal). Wei Zhang: Methodology (equal); Project administration (equal). Dian Zhang: Supervision (equal). Ying Li: Validation (equal). Tengfang Wang: Validation (equal). Fugui Zhou: Visualization (equal). Zhuang Yu: Visualization (equal). Hongtao Yao: Visualization (equal). Jun Zhang: Methodology (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.