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Aim. This article presents a review of the non-stationary nonlinear phenomena in backward-wave oscillators (BWO). Methods. Numerical modeling using the nonstationary (time-domain) 1-D, 2-D, and 2-D nonlinear theory of electron beam interaction with a backward electromagnetic wave in the slowly varying amplitude approximation. Results. Main results of nonstationary nonlinear theory of O-type and M-type BWO are presented. The typical bifurcation scenario is described, which is observed with an increase of electron beam current in numerical simulations as well as in experiments. Different kinds of chaotic behavior are demonstrated. Nonstationary phenomena in BWOs with oversized electromagnetic systems are discussed, namely, the diffractive mode selection as well as the generation of Cherenkov superradiance pulses by short electron bunches. Conclusion. The nonstationary nonlinear theory is a powerful tool for modeling of beam-wave in BWO as well as in other microwave tubes. Using this theory, algorithms and computer codes for time-domain simulation have been developed, which are widely used in fundamental and applied research. These codes not only provide analysis of different modes of interaction in existing electron devices, but also allow to propose and analyze new schemes for which the standard stationary approach is ineffective.

This article presents the results of a design study of an electron-optic system (EOS) for a sheet-beam ${G}$ -band traveling-wave tube. An electron gun providing a 0.1-A, 20-kV sheet beam emitted by a 0.8 mm $\times0.8$ mm curved cylindrical cathode is designed. The beam dimensions at waist position are 0.05 mm $\times0.8$ mm with a compression ratio of 16 in the vertical direction. A magnetic system providing 1.1 T magnetic field, which is nearly seven times higher than the Brillouin field, is designed, and beam transmission in the 0.1 mm $\times0.85$ mm beam tunnel is studied by 3-D particle-in-cell (PIC) simulation. It is demonstrated that the beam has a complex structure of particle distribution, i.e., a high-density central part (core) and a peripheral low-density part (halo). The effect of assembly tolerance on beam transmission is studied. The prototype gun is fabricated, which compresses the beam to 0.1 mm by electrostatic field only. The 135-mA current with 95% transmission through the 0.2-mm anode aperture is measured.

We study mutual synchronization in a system of two delay-coupled gyrotrons. The results of the bifurcation analysis are presented in the approximation where the delay time is short compared with the oscillation onset duration. The conditions of the stability of in-phase and antiphase synchronization regimes are analyzed for various values of parameters. Synchronization regions are plotted on the detuning–coupling coefficient parameter plane. Special attention is given to the mechanisms of appearance and disappearance of the bistability of synchronous regimes during parameter variations. A simple and physically justified way to switch between the in-phase and antiphase modes is proposed, which can be useful in many applications.

The effect of delayed reflection on frequency stabilization and pulling in a gyrotron oscillator is studied. Simple theoretical formulas for start-oscillation current, oscillation frequency, and frequency stabilization rate are derived in the framework of the linear (or small-signal) theory and verified by numerical simulation for the gyrotron with fixed axial profile of the RF field. Capabilities of increasing frequency stability are analyzed. A possibility of expanding frequency tunability range owing to excitation of high-order axial modes is demonstrated.

In this article, the design approach for a ${V}$ -band miniaturized oscillator with a pseudospark-based high-current-density sheet electron beam source is presented. The hollow cathode electron gun has been designed and developed. In the experiment, the ~10-A current in the hollow-cathode phase has been measured. The high-frequency structure comprised of a truncated sine waveguide slow wave structure (TSW SWS) with wideband-matched output couplers has been designed, optimized, and simulated. The simulations show good transmission characteristics of the structure. The operation of a backward-wave oscillator with the designed TSW SWS driven by a 10-A, 40-kV sheet electron beam has been investigated by using 3-D particle-in-cell simulations. The maximal output power of 70 kW has been attained in the simulation. Frequency tuning within the 10-GHz frequency band has been demonstrated.

In this article, an investigation has been performed to analyze the role of hollow cathode aperture wall profile on pseudospark (PS) discharge-based single gap sheet electron beam source. A simulation study using COMSOL Multiphysics has been carried out for different hollow cathode aperture wall profile parameters, such as thickness and radius of curvature of aperture wall. The role of hollow cathode aperture wall thickness “ $t$ ” and the radius of curvature of aperture wall “ $R$ ” for different gas pressures, 16–20 Pa, and the corresponding applied gap voltage 16–20 kV have been studied. The hollow cathode aperture wall thickness has been analyzed for the range of ~1–3 mm, keeping the constant aspect ratio 12:1, while the radius of curvature of aperture wall has been analyzed for the range of 0–3 mm for different wall thicknesses. Experimental studies have also been performed to analyze the role of the thickness of the aperture wall on PS discharge. A good correlation has been obtained between the simulation and experimental studies.

We study the oscillation regimes for the model of a gyrotron with a fixed Gaussian longitudinal field structure and three modes of an equidistant spectrum (an operation mode and two satellites symmetrically spaced by frequency) during autonomous operation and under the action of an external monochromatic signal. The two-parameter (dimensionless current and the cyclotronresonance mismatch for an operating mode) plane is partitioned into the regions corresponding to various regimes. It is shown that the presence of a maximum at the leading edge of the voltage pulse can lead to excitation of the parasitic modes in the process of the power-source switch-on and to quenching of oscillation of the operating mode. These undesirable effects can be suppressed by locking the operation-mode frequency by an external monochromatic signal, which provides oscillation at the operation mode.

Equi-distantly distributed multi-peak frequency spectrum was observed in a high-power 300-GHz band gyrotron for the case of strong reflection off the vacuum window. An oscillation mode different from the design mode can oscillate by adjusting the magnetic field in the cavity. However, a large fraction of the output wave is reflected by the vacuum window. The reflected wave returns to the cavity through an internal mode converter. The azimuthal rotating direction of the reflected wave is opposite to that of the oscillating mode. A theoretical calculation of mode competition between the oscillating co-rotating mode and the counter-rotating mode originating from the reflected wave very well reproduces the observed frequency spectrum. The multi-peak frequency spectrum stems from periodic amplitude oscillation caused by the mode competition between the co-rotating mode and the counter-rotating mode. The frequency interval between the peaks is not simply decided by the round-trip time between the cavity and the vacuum window but determined by the period of the amplitude oscillation.

For advanced telecommunications and radar systems, high-power miniaturized millimeter-band traveling-wave tubes (TWTs) are required. In this letter, we propose a meander-line slow-wave structure (SWS) that is suitable for multiple sheet beam interaction that helps achieve high power. The simulation of cold electromagnetic parameters of the V-band SWS demonstrates good transmission characteristics, wide bandwidth, and high interaction impedance. Hot performance of the V-band TWT amplifier with the proposed SWS is also studied. The 3-D particle-in-cell (PIC) simulation predicts that the designed circuit yields a stable gain in the 50 – 70 GHz frequency range with a 25 – 30-dB small-signal gain. 250-W average output power is attained from a 1.5 – 2.0-W input driving signal at 68.1 GHz.

Systems of mutually coupled oscillators with delay coupling are of great interest for various applications in electronics, laser physics, biophysics, etc. Time delay usually originates from the finite speed of propagation of the coupling signal. In this paper, we present the results of detailed bifurcation analysis of two delay-coupled limit-cycle (Landau–Stuart) oscillators. First, we study the simplified case when the delay time is much smaller than the oscillation build-up time. When the coupling signal propagates between the two counterparts, it acquires a phase shift, which strongly affects the synchronization pattern. Depending on this phase shift, the system may demonstrate the behavior typical for either dissipative or conservative (reactive) coupling. We examine stability of the in-phase and anti-phase synchronous states and reveal the complicated pattern of the synchronization domains on the frequency mismatch—coupling strength parameter plane paying a special attention to the mechanisms of appearance and disappearance of the phase multistability. We demonstrate that taking into account reactive phase nonlinearity the coupling signal acquires an additional phase shift, which depends on the signal intensity. We also examine the more complicated case of finite delay time. The increase of the reactive nonlinearity parameter and the delay time leads to transformations of synchronization domains similar to those that occur when the phase shift increases. For the bifurcation analysis, we employ XPPAUT and DDEBifTool package and verify the results by direct numerical integration.

In this paper, the modified quasilinear model of a gyrotron injection locking by an external signal is presented and theoretical study of the scenarios for the transition to the synchronization mode is carried out. We considered the situation when the gyrotron is in the hard excitation mode, since in that case maximum interaction efficiency is provided. Using the developed model, we derive the stability conditions of the synchronization modes and discuss the possibility of reaching maximal interaction efficiency in the mode of synchronization.

Planar microstrip slow-wave structure (SWS) consisting of two electrically connected meander lines is under study in this paper. Such SWS is suitable for millimeter-band traveling-wave tube (TWT) operating with two low-voltage sheet electron beams. The use of two beams leads to an increase in the total current while maintaining the current density and therefore leads to an improvement in the output characteristics of the device.

THz-range gyrotrons operating in a continuous-wave mode are of great interest for many applications, such as spectroscopy, plasma diagnostics, biomedical research, etc. Some of these applications require fast frequency tuning. In this paper, we demonstrate the possibility of fast stepwise frequency tuning by switching between the modes of in-phase and anti-phase synchronization in the system of two coupled gyrotrons.

Reflections may have a strong effect on mode-competition scenario in a multimode gyrotron. In this work, we study self-injection locking by delayed reflection of the multimode gyrotron with fixed Gaussian profile of the RF field. We demonstrate a possibility of expanding the domain of stable single-mode generation of the fundamental mode by suppressing the spurious modes.

In this paper, we present the results of design and development of the multiple-tunnel meander-line slow-wave structure (SWS) for a high-power traveling-wave tube (TWT) with multiple sheet electron beam operating at millimeter band. Electromagnetic parameters of the SWS with different number of beam tunnels are simulated. The results of 3-D PIC modeling of small-signal and large-signal hot-test operation are presented. Technologies for fabrication of the multiple-tunnel SWS are discussed.

The results of fabrication and cold-test study of the slow-wave interaction structure for the V-band backward-wave oscillator with a pseudospark-sourced sheet electron beam are presented. The proposed interaction structure is comprised of a truncated sine waveguide with wideband-matched output couplers. The slow-wave structure is designed, simulated, and fabricated by CNC-micro milling. The results of characterization of the microfabricated SWS sample by the scanning electron microscopy and stylus profilometry technique are presented. Preliminary results of experimental studies of electromagnetic parameters and their comparison with the numerical simulation are presented. The electron gun providing a high-current-density pseudospark sheet electron beam is also developed.

The goal of this work is an investigation of peculiarities of the molybdenum-copper alloys formation by magnetron sputtering to meet the requirements of low thermal expansion coefficient together with high electrical/thermal conductivity of the material for potential use in microfabrication of slow-wave structures for miniaturized millimeter-band vacuum electron devices. The study is focused on controlling the roughness and adhesion of the fabricated thin Cu-Mo alloy films. The roughness mainly determines the transmission losses at millimeter and THz frequencies, whereas the adhesion of the film is quite important for further processing, such as laser ablation.

Travelling-wave-tube (TWT) power amplifiers with planar microstrip slow wave structures (SWS) on dielectric substrates are very promising for operation at high frequencies due to their low-voltage operation, small size and relatively high output power. Recently, the interest to the planar SWSs has increased since their using can significantly decrease the complexity of microfabrication process. In our previous work, we reported successful fabrication of millimeter-band microstrip planar SWSs using the scalable and cost-effective laser ablation process with nanosecond pulse duration. However, the SWS samples fabricated by nanosecond laser ablation suffer from surface distortions and debris on the borders of the ablated zone. In order to improve the quality of resulting structures, here we propose deposition of a supplementary metallic (Al or Ti) layer on top of copper film prior to laser treatment. Such coating is aimed to prevent defects formation in the course of laser irradiation. In the proposed system, debris and distortions from Cu layer irradiation, naturally sediment on the sacrificial layer instead of sticking to the copper layer itself. Sacrificial aluminium coating can later be easily chemically removed together with sedimented debris leaving a clean underlying patterned Cu surface. In contrast, titanium layer prevents sticking of copper debris due to the higher melting temperature of Ti, thus preventing attachment of those to the surface in the first place.

Many applications, such as high-data-rate wireless communications, spectroscopy, high-resolution radar, biomedical imaging, security, etc. require compact high-power sources of sub-THz radiation. Traveling wave tube (TWT) amplifiers are the most promising candidates for such sources combining 10–100 W power and wide bandwidth. Here we present the results of design and simulation of a 0.2-THz TWT with a grating slow-wave structure (SWS) and electron-optical system (EOS) with a converging sheet electron beam. The designed EOS provides substantial improvement of the amplifier performance as compared with the EOS with straight beam immersed in a uniform magnetic field. In particular, it facilitates beam focusing and allows reduce of the focusing magnetic field and cathode current density. The latter allows increase of lifetime and makes possible operation in a continuous-wave mode. In addition, decrease of the beam thickness allows reduce of the beam tunnel height accordingly, which leads to nearly 2.5-times increase of the Pierce coupling impedance resulting in increase of gain and decrease of the required driving power. The simulation predicts small-signal gain over 30 dB in 180–200 GHz frequency band and over 80 W saturated power. Keywords: Traveling-wave tube, Sheet electron beam, Electron gun, Slow-wave structure, Terahertz band

In this paper, we present the results of the study of a multiplier based on a traveling wave tube with a sheet electron beam and slow-wave double-grating structures. Device configurations with the possibility of obtaining an output power above 60 W at the second harmonic frequency of 190 GHz with an input power of about 10 W at the first harmonic frequency were determined.

Millimeter-band traveling-wave tubes with multiple electron beams have attracted an increasing interest thanks to higher output power. In this work, we report the results of the development of the technological approach to microfabrication of a meander-line slow-wave structure for millimeter-band traveling-wave tubes with multiple sheet electron beams. We used a precision CNC laser machine equipped with a 1064-nm pulsed YAG:Nd fiber laser maintaining regimes with the duration of laser pulses from 200 ns to 8 ns. Several SWS samples have been fabricated and studied by scanning electron and optical microscopy methods

Peer-to-peer locking is a promising way to combine the power of high-power microwave oscillators. The peer-to-peer locking of gyrotrons is especially important because arrays of coupled gyrotrons are of special interest for fusion and certain other applications. However, in case of coupled microwave oscillators, the effect of delay in coupling is very significant and should be taken into account. In this article, we present the model of two delay-coupled gyrotrons. We develop an approximate theory of phase locking based on the generalized Adler’s equation, which allows for the treatment of in-phase and anti-phase locking modes. We also present a more rigorous bifurcation analysis of phase locking by using XPPAUT software under the limitation of small delay time. The structure of the phase-locking domains on the frequency-mismatch–coupling-strength plane of parameters is examined. Finally, we verify the results by numerical simulations in the case of finite delay time. The simulations reveal various regimes, including peer-to-peer locking, the suppression of one gyrotron by another, as well as the excitation of one gyrotron by another.

Results of research aimed at the development of traveling-wave tubes (TWT) with multiple sheet electron beam at short part of the millimeter band are presented. The designs of the double-tunnel meander and double grating slow-wave structures (SWS) are studied. Electromagnetic parameters of the SWSs are simulated. The results of 3D PIC-simulation of TWT performance in linear and nonlinear operating modes are presented. Technologies for microfabrication of the SWSs are discussed.

Gyrotrons are the most powerful radiation sources in sub-THz and THz bands, which are of great importance for many applications, such as electron-cyclotron plasma heating, DNP/NMR spectroscopy, plasma diagnostics, biomedical applications, etc. All of these applications require frequency-stable, single-mode operation. Apart from the traditional methods for frequency stabilization, several other approaches have attracted a considerable interest. In this paper, we present a review of recent studies aimed at deeper understanding of injection locking of a gyrotron by an external signal, as well as of self-injection locking by partial reflection of the output power from a remote load. The increasing of frequency stability, expanding of the frequency tunability range, and the possibility of suppressing of the parasitic modes are discussed.

In this paper, we present the results of time-domain self-consistent simulation of the second-harmonic 0.394-THz gyrotron with delayed reflection. We demonstrate the possibility of improving frequency stability and enhance of the frequency tunability by using the reflection. The influence of different reflection parameters on oscillation power and frequency is studied.

A complex cavity was fabricated to improve the mode selection property of a gyrotron for the 400 GHz second-harmonic oscillation. A combination of the TE 8,3 and the TE 8,5 modes was selected to provide resonant coupling. In the experiment, many fundamental and several second-harmonic modes oscillated independently in either the first or the second cavity. However, no fundamental oscillation was observed in the operation magnetic field region of the TE 8,3 /TE 8,5 mode. The fabrication error of the cavity radii was successfully controlled to be smaller than 1 $\mu\mathrm{m}$ . The oscillation of the design mode was observed by the frequency measurements. However, a mode competition with the TE3,5 mode occurred.

The method for calculation of start-oscillation conditions based on the stationary theory of a gyrotron with non-fixed (self-consistent) axial profile of the RF field is described. The calculations of start-oscillation currents and start-oscillation frequencies are presented for the 0.4-THz second-harmonic gyrotron with delayed reflections from the remote load at different parameters of the reflected signal. Increase of the reflection magnitude leads to increase of the number of oscillation zones observed at fixed beam current and, thus, to is extension of the frequency tunability range.

This paper investigates transportation of the sheet electron beam with high compression in the micro-sized tunnel of a sub- THz traveling-wave tube. It is known that intense spatially developed electron beams (for example, sheet and annular ones) are subject to diocotron instability, which causes the beam breakup and deposition on the tunnel walls. In view of this phenomenon, we designed an electron-optic system, which provides formation of a spatially developed electron beam and its stable transportation to the distances sufficient to obtain the required output power and gain.

Nowadays vacuum electron devices still remain the main sources of high power coherent and broadband millimeterwave radiation. Among electron beam sources the pseudospark discharge can be distinguished as a promising pulsed plasma electron beam source. The reason is that the pseudospark discharge sourced electron beam has the ability to self-focus due to the unique discharge structure and the formation of the ion channel generated by the beam front. The ion channel enables the electron beam to propagate and eliminates the need for a guiding magnetic field. Therefore the development of compact and high-power vacuum electron devices utilizing a pseudospark discharge based hollow cathode electron gun is one of the promising trends. Here the results of the design, optimization and development of a pseudospark-based high-current-density sheet electron beam source are presented. A slow-wave structure for the backward-wave oscillator driven by a pseudospark-sourced sheet electron beam was also designed and numerically studied. Preliminary results of numerical simulations of electrodynamic characteristics of the suggested slow-wave structure are shown. We are going to use a CNC-micro milling based technological approach to microfabricate the designed slow-wave structure. The first steps of microfabrication results are also presented.

Development of millimeter and submillimeter-band (THz-band) vacuum electronic devices put forward special requirements to the properties of structural materials for microfabrication of such basic electronic components as slow-wave structures. One of the promising composite materials for vacuum microelectronic devices is molybdenum-copper alloys. This composite combines high thermal and electrical conductivity of copper and low thermal expansion of molybdenum. The influence of the composition of molybdenum-copper alloy on the electrodynamics parameters (S-parameters) of the slow-wave structure was revealed with the help of numerical simulation. Two sources magnetron co-sputtering can be utilized for Mo-Cu alloys deposition with the resulting composition of the alloy controlled by varying the power of the magnetron sources, working gas pressure and the substrate temperature.

Metamaterials recently attracted a wide interest in many areas of scientific research. Particularly, application of metamaterials is very promising in vacuum electronics devices of mm and sub-THz range. Dielectric substrate with metamaterials coating was used in several devices such as travelling wave tubes and backward wave oscillators. Use of metamaterials can be quite attractive if electrical properties of those can be controlled, for example, through the variation of basic materials properties. Here Si-A1 alloy is suggested as the base material for metamaterial formation. Two source magnetron co-sputtering deposition of Si-A1 alloys was utilized to obtain series of coatings with different chemical composition and thus different resistivity. Control of composition was provided by varying the power of Al magnetron source while power of Si source was constant. Three series of samples were deposited at different substrate temperatures. A sharp decrease in surface resistivity is observed while the Al content in the film changes smoothly. This result is explained by the segregation of Si and Al atoms due to Al diffusion during film deposition process.

In this paper we consider a PLL network described by an array of interconnected noisy phase oscillators. We define optimal conditions where the entire array synchronises with the reference signal by interacting only between nearest neighbours. We develop a continuous-time model of the PLL network and analyse synchronisation of the system numerically for different architectures of coupling and variations of control parameters. We show that the bidirectional topology significantly outperforms the unidirectional topology in terms of the overall phase noise of the network.

Design and preliminary numerical simulations of D-band planar microstrip meander-line slow wave structure for lowvoltage tubes with sheet electron beam were carried out. An original approach based on magnetron sputtering and laser ablation methods was utilized for microstrip meander-line slow wave structure microfarication. An application of nanosecond and picosecond laser ablation for microfabrication of D-band (110-170 GHz) planar microstrip meander-line slow wave structure was considered. We have verified our original approach for planar slow wave structures microfabrication by using different CNC precision laser machines operating with different values of laser pulse duration (100 ns, 8 ns, 4 ns and 10 ps). Samples of slow wave structures were fabricated and characterized by scanning electron microscopy and profilometry methods. It was shown that each considered CNC precision laser machine allows fabricating D-band microstrip meander-line slow wave structure with required dimensions, but picosecond laser ablation has such advantages as the absence of ablation products (droplets, and etc.) on the slow wave structure surface. As the next step, we are going to study S-parameters of microfabricated D-band microstrip meander-line slow wave structure samples experimentally by using vector network analyzer with D-band frequency converters.