INTRODUCTION

Interest in sources of intense microwave radiation is due significantly to studies of the electromagnetic compatibility of electronic devices and to developments for electronic warfare. Pulse-periodic relativistic microwave oscillators and amplifiers operating either in the quasistationary generation regime (the duration of a microwave pulse is close to the duration of the feeding electron beam and is about 100 oscillation cycles) or in the regime of ultrashort (few-cycle) pulses (USPs) [1–3] are primarily used as such sources. In the latter regime, the peak power of USPs can exceed the power of the electron beam. In both regimes, the maximum repetition frequency of microwave pulses is determined by the capabilities of a source of high-voltage nanosecond pulses applied to the vacuum diode of the microwave oscillator, where a high-current electron beam is generated, and is usually limited to a value of about 1 kHz. Approaches and schemes were proposed in theoretical works [4–6] to significantly increase the repetition frequency of USPs. In particular, combinations of relativistic backward-wave and traveling-wave oscillators, one of which was used as an active element (amplifier) and the other served as a nonlinear saturated absorber in the feedback circuit, were analyzed in [4, 5]. This scheme was experimentally confirmed in [7]. Another approach [6] is based on the partial reflection of USPs from the output of the relativistic backward-wave oscillator in the superradiance regime. The numerical simulation showed that the repetition frequency of USPs in such devices is determined by the characteristic time in the “wave pulse–electron beam” feedback circuit and reaches hundreds of megahertz, and the peak power of USPs exceeds the power of the feeding electron beam. To estimate the efficiency of such regimes, the conversion coefficient K that is the ratio of the peak power of USPs to the power of the electron beam is used [2].

In this work, we report the results of the experiment on the generation of the periodic sequence of USPs conducted with a relativistic superradiant backward-wave oscillator with wave reflectors at the edges of the interaction region described in [6]. The preliminary numerical experiment showed that a periodic sequence of USPs with a repetition frequency of about 200 MHz and \(K \approx 2\) is formed during the current beam pulse.

EXPERIMENTAL SETUP AND THE SYSTEM OF DETECTION OF MICROWAVE SIGNALS

The layout of the experimental setup with the microwave detection system is shown in Fig. 1. High-voltage pulses were obtained from a SINUS high-current pulsed generator [8] with a triple forming line (1), which provides voltage pulses with an amplitude up to 330 kV and a FWHM duration of 36 ns. The tubular relativistic electron beam was generated in a coaxial diode with magnetic insulation and an edge explosive emission cathode 35 mm in diameter. A pulsed solenoid (2) with the length of the uniform magnetic field segment of about 600 mm was used to transport the beam through the electrodynamic system of the microwave oscillator. The operation of the relativistic backward-wave oscillator in the superradiance regime is based on the cumulative transfer of the energy from electrons to an ultrashort electromagnetic pulse propagating against the electron beam [2, 3]. To fabricate the electrodynamic system under study (Fig. 2), we performed the numerical simulation using the axisymmetric 2.5-D version of the completely electromagnetic particle-in-cell code KARAT [9]. The system had two reflectors, one of which was placed at the input of the slow-wave structure from the side of the cathode unit and ensured the total reflection of the incident microwave wave. The second reflector, placed at the output of the generator from the side of the electron collector, returned about 5% of power to the slow-wave structure. Because of the presence of this feedback circuit, each formed USP initiates the next pulse. The slow-wave structure of the generator consisted of 45 corrugations with a period of 12 mm and an average diameter of approximately 1.3λ, where λ is the radiation wavelength. The depth of the corrugation increased smoothly from the cathode edge of the system to the collector edge. The last seven corrugations had the same amplitude and composed a uniform segment, in which each USP was formed. A directional coupler (3) based on a circular waveguide placed at the output of the microwave oscillator was used, together with lamp detector no. 1, to detect the amplitude and shape of USPs in the output waveguide. The transient attenuation of the coupler measured using an Agilent 8719 ET (50 MHz–12.5 GHz) network analyzer in the frequency range of 9–12 GHz was 69–71 dB. A conical horn (4) with an output window about 200 mm in diameter was used to extract radiation. Receiving antennas in the form of the open end of the 23 × 10-mm rectangular waveguide were placed at a distance of 4.0 m from the aperture of the emitting horn and were used to detect the amplitude and shape of USPs in open space (antenna 5 together with lamp detector no. 2) and for spectral measurements (antenna 6). The radiation spectrum was determined by the heterodyne method (generator 7 and mixer 8 in Fig. 1) by the fast Fourier transform of the intermediate-frequency signal from a Tektronix MSO 64 (6 GHz, 25 GSa/s) oscilloscope. The antenna measurement region was separated from the environment by microwave absorbers. To visually control the spatial distribution of the microwave power flux density, we used a neon lamp panel. High-frequency cable runs (RK50-4-47 cable) were calibrated using a G5-84 generator, which formed video pulses with the FWHM duration of about 1 ns.

Fig. 1.
figure 1

(Color online) (1) SINUS high-current pulse generator with the triple forming line, (2) pulsed solenoid with the electrodynamic system of the generator of ultrashort pulses inside it, (3) directional waveguide coupler in the complex with lamp detector no. 1, (4) emitting horn, (5) receiving antenna in the complex with lamp detec-tor no. 2, (6) receiving antenna for measuring the generation spectrum, (7) master frequency generator G4-83, (8) mixer, (9) Tektronix TDS 7404 oscilloscope (4 GHz, 20 GSa/s).

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Fig. 2.
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(Color online) (a) Block diagram of the generator of the sequence of ultrashort pulses based on the relativistic backward-wave oscillator (RBWO) operating in the superradiance regime with the extraction of radiation toward the collector of electrons (\({\text{|}}R{\text{|}}\) is the reflection coefficient). (b) Numerical simulation of the generation of the sequence of ultrashort pulses with a carrier frequency of 10 GHz at an electron beam current of 4.0 kA, an accelerating voltage of 270 kV, 40-ns-long current pulse with the 3-ns front, and guiding magnetic field of 2.0 T. The calculated repetition frequency of ultrashort pulses is 160 MHz. The peak powers of five successive ultrashort pulses are 2.5, 2.0, 1.8, 1.5, and 1.6 GW and the respective conversion coefficients are 2.3, 1.9, 1.7, 1.4, and 1.5.

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RESULTS OF THE EXPERIMENT

At a voltage amplitude of 270 kV across the vacuum diode of the electron accelerator, a beam current of 4.0 kA, and a guiding magnetic field of 2.2 T, a periodic sequence of USPs (Fig. 3) with a FWHM duration of approximately 0.8 ns and a repetition frequency of 170 MHz (a repetition period of 5.9 ns) was generated. This pulse repetition period corresponds to the feedback period in the generator estimated as \(T = L(1{\text{/}}{{v}_{{{\text{gr}}}}} + 1{\text{/}}{{v}_{e}})\), where \({{v}_{e}}\) is the velocity of electrons in the beam, \({{v}_{{{\text{gr}}}}}\) is the group velocity of the opposite electromagnetic wave, and L is the length of the system (Fig. 2). In a series of 20 pulses, the maximum spread of the amplitudes of USPs was no more than 15% (Fig. 4). The frequency of oscillations in each USP was about 10 GHz (Fig. 5).

Fig. 3.
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(Color online) Oscillograms demonstrating the generation of the periodic sequence of ultrashort pulses: (Ch1) voltage across the vacuum diode, (Ch2) current of the vacuum diode, (Ch3) detected microwave signal from the waveguide coupler, (Ch4) detected microwave signal from the receiving antenna located at the maximum of the power flux density. The accelerating voltage and current of the electron beam at the time marked by the triangle are 270 kV and 4.0 kA, respectively.

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Fig. 4.
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(Color online) Oscillograms obtained in the storage regime during 20 successive activations of the electron accelerator.

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Fig. 5.
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(Color online) Spectrum of high-frequency oscillations measured for the first ultrashort pulse (similar spectra were recorded for other ultrashort pulses). The frequency of oscillations is \(F = {{F}_{{{\text{het}}}}} + \Delta F\), where \({{F}_{{{\text{het}}}}} \approx 7.5\) GHz is the frequency of the heterodyne and \(\Delta F \approx 2.5\) GHz is the intermediate frequency.

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The peak power in the first USP, which was obtained by integrating the spatial distribution of the power flux density (corresponding to the TM01 wave), was P1 = (1.3 ± 0.2) GW. Knowing the peak amplitudes of other USPs and power–voltage characteristic of the lamp detector, we estimated their peak powers as P2 = (1.0 ± 0.2) GW, P3 = (1.1 ± 0.2) GW, P4 = (1.0 ± 0.2) GW, P5 = (0.8 ± 0.1) GW, and P6 = (0.2 ± 0.03) GW. The conversion coefficients determined as the ratio of the peak power of each USP to the power of the electron beam at the time marked by the triangle in Fig. 3 are K1 = 1.2 ± 0.2, K2 = 0.9 ± 0.2, K3 = 1.0 ± 0.2, K4 = 0.9 ± 0.2, K5 = 0.7 ± 0.1, and K6 = 0.2 ± 0.03. The luminescence of the neon lamp panel under microwave irradiation had a ring shape.

Simultaneously, the radiation power was independently measured using the directional waveguide coupler placed in the output waveguide of the generator; a signal from the coupler was guided to lamp detector no. 1 and was processed taking into account the power–voltage characteristic of this detector. This measurement gave the estimates P1 = (1.4 ± 0.2) GW, P2 = (1.0 ± 0.2) GW, P3 = (1.1 ± 0.2) GW, P4 = (1.1 ± 0.2) GW, P5 = (0.8 ± 0.1) GW, and P6 = (0.3 ± 0.04) GW for the peak powers of the six USPs.

In a separate series of experiments involving the detection of signals using the coupler, the energy of microwave radiation was measured with the vacuum calorimeter [10], which was placed immediately behind the coupler. Several measurements performed at the parameters of the generator indicated above showed that the microwave energy per measurement is in the range of 8.5–9.6 J. The analysis of the corresponding oscillograms under the assumption that “noisy” generation at frequencies near 10 GHz primarily occurs in intervals between single USPs gives an estimate of 1.4–1.5 GW for the peak power of the first USP. Suggesting that the total duration of microwave generation is about 30 ns (Fig. 3), the average microwave power during the electron beam pulse can be estimated as \(\bar {P}\) = 8.5–9.6 J/30 ns = 0.28–0.32 GW. The energy efficiency of the generator defined as the ratio of the microwave energy to the energy of the electron beam is about 23%.

The maximum peak power of the first USP and its reduction for the next pulses should be attributed primarily to the gradual deviation of the parameters of the generator from the optimal parameters during the electron beam pulse because of the expansion of the cathode plasma. This expansion is indicated by the monotonic decrease in the voltage in the vacuum diode during the pulse (Figs. 3, 4). The accumulation of decelerated electrons in the device, which are produced in a significant quantity in each event of generation of USPs, probably also makes a contribution. During the interval between two USPs, such electrons do not leave the slow-wave structure, slowly drifting toward the collector and penetrating into the vacuum diode (see Fig. 3 in [6]). Numerous strongly decelerated electrons also affect the formation of the electron beam and the electron–wave interaction and change the conditions of generation of all USPs except for the first. At the same time, this negative effect in the considered system with end reflectors is weaker than that in the single-pass generator without reflectors, where the power of the second USP was several times lower than the power of the first USP.

CONCLUSIONS

The experimental results have demonstrated the efficiency of the proposed generation scheme of the periodic sequence of USPs and have confirmed that the theoretical model of the device is applicable. At the same time, the peak powers of USPs and the corresponding conversion coefficients obtained in the experiment proved to be approximately half the values obtained in the axisymmetric particle-in-cell simulation. The most probable reason for this relation is the diocotron instability in an initially azimuthally homogeneous electron beam, which is developed over the entire length of its transport and results in the azimuthal filamentation and radial spread of the beam. Comparison of the signatures of the beam on polycaprolactam targets placed at the input and output of the slow-wave structure of the device in the regime without microwave generation has shown that the thickness of the wall of the tubular beam increases from 0.8 mm near the edge of the cathode to 3 mm in the region with the maximum depth of corrugation. As a result, in this region, where USPs are formed, the estimated coupling impedance of the TM01 operating wave with the electron beam is approximately half the value in the absence of instability. The azimuthal inhomogeneity of the beam can promote the development of asymmetric oscillations, but the generated microwave spectrum and power flux density distribution obtained in the described experiments indicate the selective excitation of the TM01 mode.