Experimental study of a C-band long-pulse high-efficiency klystron-like relativistic cavity oscillator Open Access

The relativistic backward wave oscillator (RBWO) is one of the most promising high power microwave (HPM) sources, which has attracted great interest and has been investigated extensively.^1–5 During the past several decades, significant progress has been made in enhancing output power,⁶ improving conversion efficiency,^7–9 decreasing the guiding magnetic field,^10,11 and expanding operation frequency.¹² So far, the output power of RBWO has reached 5 GW or even higher, the conversion efficiency has exceeded 40%, some RBWOs have realized permanent magnet package and the operation frequency has extended to Ka-band or even higher. However, as the research goes further, the researchers have gradually recognized that there exists an upper limit to the output power of the HPM source, which is governed by its power capacity. As a result, extending the pulse duration to increase the pulse energy of the RBWO has been currently of significant interest. In addition, there exist several works concerning about this important issue.^13–16 However, compared with the devices working at short pulse regime, the long-pulse RBWOs, especially for the ones with a pulse duration greater than 100 ns, have a relatively lower output power in general. Also, the conversion efficiency of the long-pulse RBWOs is mostly less than 40%.

In this paper, a comparative study of a well-designed C-band long-pulse high-efficiency klystron-like relativistic cavity oscillator (RCO) is carried out. Based on the elimination of the influence of the returning electrons, a peak output power of 4.4 GW with a pulse duration of 96 ns and efficiency of 45% is obtained in the experiment. The remainder of this paper is organized as follows: In Sec. II, we present a brief introduction to the physics model. In Sec. III, the experimental setup is described. In Sec. IV, the phenomenon of returning electrons, its influence on the output microwave, and the suppression method are described in detail. Also, some typical experimental waveforms are given in this section. Finally, some conclusions are given in Sec. V.

The proposed C-band high-efficiency klystron-like RCO is shown in Fig. 1. The device has consisted of five parts, including a foilless diode, an explosive emission cathode, a resonant reflector, a nonuniform slow wave structure (SWS), and a tapered beam collector. In the device, an intense relativistic electron beam is generated from the explosive cathode at the diode region and then injected into the high-frequency structure. Under the confinement of magnetic field, the electron beam passes through the high-frequency structure, becomes highly bunched clusters, and gives out its kinetic energy to the microwave. Then, the residual energy of the beam is dumped by the tapered beam collector. To avoid unwanted collector plasma disturbing the operation of the device, the electrons are deposited several centimeters distant away from the interaction region. Moreover, to avoid local field enhancement inducing microwave breakdown, the edges of the extraction cavity have been filleted to round corners.

Compared with the conventional oversized RBWO with a resonant reflector, the significant difference is that a two-sectional nonuniform SWS is adopted to increase the beam bunching depth and enhance the conversion efficiency. The fore part of the SWS is a uniform three-period modulation cavity with relatively shallow corrugation whose function is to further bunch the electron beam to achieve high bunching depth. To reduce the beam energy spread induced by the modulating electric field, the corrugation depth of the modulation cavity is relatively shallow so that the electric field in it is moderate. Meanwhile, in the modulation cavity, the net power exchange between the beam and microwave is slight, so the average velocity of the beam changes a little. To maintain the synchronization with the electron beam, the period of the modulation cavity is relatively long to increase the phase velocity of the modulation cavity. The latter part of the SWS is a nonuniform two-period extraction cavity with relatively deep corrugation whose function is to extract the kinetic energy of the highly bunched electron beam and convert it to an intense microwave pulse. To improve the conversion efficiency, the corrugation depth of the extraction cavity is relatively deep so that the electric field in it is strong. Meanwhile, to maintain the synchronization with the decelerated beam since the electrons gradually lose their energy in the extraction cavity, the period of the extraction cavity is shortened to reduce the phase velocity of the extraction cavity.

The performance of the proposed device is verified by the particle-in-cell code CHIPIC.¹⁷ Also, some brief simulation results are given as follows. Figure 2 shows the temporal plots of the output power and its envelope waveform. Figure 3 is the spectrum of the output electric field. In the simulation, the input parameters are a beam voltage of 690 kV, a current of 14.5 kA, and a magnetic field of 1.3 T. The simulation obtains an output with a power of 4.8 GW, efficiency of 48%, and frequency of 4.28 GHz. Mode competition is not observed in the simulation as the output power envelope is flat and the output frequency spectrum is pure.

The experiment is performed on a self-developed compact repetitive PFN-Marx generator.¹⁸ The Marx generator is a voltage-multiplying system, which is charged in parallel and discharged in series. The PFN-Marx adopts a two-cell pulse forming module instead of the conventional capacitor to generate a quasi-square pulse with a width of 150 ns. Under the matching condition with the load impedance of 50 Ω, the developed Marx generator has a maximum output with a voltage of 1 MV and a current of 20 kA. The total Marx generator is immersed in an oil tank, and its output high-voltage pulse is fed into the coaxial diode through an inner conductor. The schematic diagram of the coaxial diode is shown in Fig. 4. A planar insulator with a sinusoidal ripple on the surface is used to support the inner conductor and separate oil from the vacuum. A pair of shielding bowls is used to uniform the electric field on the insulator surface and shield the triple-point.

The proposed C-band device is connected to the coaxial diode through the flange. The machined prototype of the device is shown in Fig. 5. In addition to the electrodynamical structure described above, a water-cooling structure is integrated into the tapered beam collector to transfer heat from electron bombardment to the water.

In the experiment, the whole system, from the planar insulator to the radiation window, is in a vacuum environment with a pressure of 1 × 10⁻³ Pa. Also, the required guiding magnetic field is generated by a solenoid magnet.¹⁹ The beam voltage is measured with a resistive voltage divider in the oil tank of the Marx generator. The beam current is measured with the Faraday cup, and its schematic diagram is shown in Fig. 6. In Sec. IV, the Faraday cup current is an important parameter to evaluate the introduction efficiency of the intense electron beam.

The microwave generated from the device is radiated into the air through a conical horn. Moreover, a series of pyramidal horns arranged at different angles around the circle 7 m away from the radiation horn are used to receive the radiation microwave pulse and draw the radiation pattern. By integrating the radiation pattern, the radiation power is obtained.

Based on the simulation results of the proposed C-band device and the experimental setup, the initial experiment is carried out. Figure 7 is typical waveforms of the beam voltage and RF-detected signals at different receiving angles in the radiation field. Meanwhile, the figure shows a reference voltage waveform pre-stored in the oscilloscope, which is colored dark green. When the input power is 10 GW (the input pulsed power is determined by the charging voltage of the pulse forming module), the measured diode voltage is about 620 kV, which is lower than the expected voltage of 700 kV under this A-K gap. Moreover, compared with the voltage pulse, the detected microwave pulse is delayed by about 20 ns. For this reason, the microwave pulse duration is only about 78 ns. By integrating the received power at different angles, it can be calculated that the total power generated by the device is about 3.2 GW.

Since the input pulsed power is constant, which is determined by the charging voltage, it can be expected that the beam current would increase as the diode voltage decreases. However, the results from the Faraday cup test are contrary to expectations. In the experiment, the Faraday cup is arranged at the entrance of the foilless diode to measure the beam current introduced into the device. As shown in Fig. 8, the measured Faraday cup current colored in blue is about 12.1 kA, which is also lower than the reference Faraday cup current of 14 kA colored in dark blue in the figure. Accordingly, the total injected beam power is about 7.5 GW, since the input pulsed power is about 10 GW, there is a power loss of 2.5 GW when the electron beam is introduced into the foilless diode.

To determine whether there are other power loss paths, a piece of heat-sensitive paper is pasted at the entrance of the coaxial diode, as shown in Fig. 4. In the figure, the location of the pasted paper is indicated by a red line. As expected, after the Marx generator operates for several shots, the obvious changes observed on the paper are that the color of the paper has changed and some parts of the paper have been burnt out, which indicates that there is heat deposition on the paper. Furthermore, the ablation trace is 1 cm away from the entrance of the coaxial diode. To verify these phenomena observed in the experiment, the particle in cell (PIC) simulation model of the C-band high-efficiency RCO with the coaxial diode is established to study. To simplify the PIC model, the shielding bowl in front of the insulator is replaced by a metal plate, as shown in Fig. 9.

As shown by the electron trajectory colored in red, as the input voltage increased, the electric field strength on the surface of the cathode supporting rod would exceed the emission threshold and begin to emit electrons. Different from the emission of the cathode blade, some electrons originating from the cathode rod would move toward the coaxial diode under the action of the electric field and the guiding magnetic field.²⁰ Once the magnetic field in the coaxial diode region is not strong enough, the returning electrons would hit the outer wall of the coaxial diode. Since the outer wall is electrical grounding, this part of the beam power is lost.

Figure 10 is the temporal plot of the input diode voltage. At the rising edge of the input voltage, there have two dips in the waveform. The first dip occurs around 9 ns, which indicates the cathode blade begins to emit and the foilless diode is turned on at this moment. Owing to the structure of the foilless diode and the local field enhancement in the cathode blade, when the input voltage increases to about 300 kV, the electric field at the cathode blade first reaches the emission threshold and the explosive emission starts. The turn-on of the foilless diode leads to a drop in the input voltage. The second dip occurs around 24 ns, which indicates the returning electrons hit the coaxial diode entrance at this moment. Since the electric field on the surface of the cathode supporting rod is lower than that on the cathode blade, until the input voltage increases to about 500 kV, the electric field at the cathode rod reaches the emission threshold.

To eliminate the influence of the returning electrons, the magnetic field at the diode region should be enhanced so that the returning electrons could be guided to the shielding bowl in front of the insulator, not to the outer wall of the coaxial diode. As the shielding bowl is under the same potential as the cathode, the returning electrons would not shunt the input power. By increasing the turn number of the windings at both ends of the solenoid, the magnetic field at the end plane of the solenoid is increased from 0.74 to 0.83 T, as shown in Fig. 12.

As shown by the electron trajectory colored in blue, as shown in Fig. 9, after solenoid compensation, the returning electrons originating from the cathode rod would hit the metal plate, which is under the same potential as the cathode. Figure 13 is the temporal plots of the beam current and the diode current after solenoid compensation. It is shown that the influence of the returning electron beam is eliminated, and the saturated diode current is about 14.5 kA, which equals the saturated beam current.

Figure 14 shows the comparison of the output microwave power of the device before and after solenoid compensation. Before compensation, for the voltage rising edge of 40 ns, the startup time of the device is about 50 ns, and the saturated output power is about 3.5 GW. In contrast, after compensation, the startup is advanced by 15 ns, and the pulse duration is increased by 20 ns. The output power of the device is increased to 4.8 GW, which is consistent with the simulation results obtained in Sec. II where the returning electron beam is not considered.

Figure 15 is typical waveforms of the beam voltage and RF detected signals after the solenoid compensation. Compared with Fig. 7, the microwave startup process is advanced and the pulse duration is increased to 96 ns. The output power is about 4.4 GW with a conversion efficiency of 45%. The typical waveform of the RF signal is shown in Fig. 16. Through the FFT analysis, it can be obtained that the output frequency generated by the device is 4.25 GHz. Moreover, the frequency spectrum is pure, and no other frequencies are observed. Both the simulation and experimental results prove that the influence of the returning electrons is eliminated successfully, and the output power and the pulse duration have been greatly improved.

In this paper, an experimental study of a C-band long-pulse high-efficiency klystron-like RCO is carried out. By observing the changes in the heat-sensitive paper pasted at the entrance of the diode, it is found that some returning electrons that originate from the cathode supporting rod would hit the entrance of the diode in the initial experiment. And the changes in the diode voltage and the Faraday cup current also confirm this discovery. Owing to the shunt of the returning electrons, the diode impedance is reduced, as well as the beam power injected into the device, which would delay the startup and reduce the output power of the device. As a result, the initial experiment only obtains a microwave pulse with an output power of 3.2 GW and a duration of 78 ns. To suppress the influence of returning electrons, the configuration of the solenoid is compensated. And the turn number of winding layers at both ends of the solenoid is increased so that the magnetic field at the diode region is enhanced. Then, the returning electrons would be guided to the shielding bowl in front of the insulator. As the shielding bowl is under the same potential as the cathode, the returning electrons would not shunt the input power. In contrast, after solenoid compensation, the device could generate an output power of 4.4 GW with a duration of 96 ns and an efficiency of 45%.

The author has no conflicts to disclose.

Yang Wu: Investigation (lead); Writing – original draft (lead).

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