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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.

A miniature planar meander-type slow-wave structure (SWS) for a W-band traveling-wave tube is studied. Computer simulation of the SWS electrodynamic parameters is performed. A new technology for fabrication of planar microstrip SWSs with the aid of laser ablation is proposed. The S-parameters of the SWS are experimentally studied. The experimental data are in good agreement with the results of the 3D computer simulation. Output characteristics of the traveling-wave tube with a sheet electron beam and planar SWS are calculated.

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.

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 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.

Sources of millimeter and submillimeter (terahertz) band radiation are very important in modern society due to their broad application from telecommunication to non-destructive evaluation and chemical analysis. In this work, we present a review of technological approaches for fabrication of RF structures of µVEDs. Technological approaches to the microfabrication of planar slow-wave structures (SWS) on dielectric substrates operating with a sheet electron beam are considered. Such SWSs are attractive due to the simplicity of the structure, compact dimensions, low voltage operating, and wide bandwidth. We consider lithography-based technology, deep reactive ion etching, computer-numerical-control (CNC) micro- and nano-milling, electrical discharge micromachining, and technologies based on the additive manufacturing such as three-dimensional (3-D) printing, selective laser sintering, and selective laser melting. We also describe an original approach to microfabrication of planar structures based on magnetron sputtering and CNC laser ablation. Fabrication tolerance and surface roughness provided by the considered technologies are compared.

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.

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.

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.

The phenomenon of superradiance of electron bunches provides a promising method for generating high-power ultrashort electromagnetic pulses. In the present paper, it is shown that the equations describing the interaction between an electron beam and an electromagnetic wave in a BWO-type oscillator admit a self-similar solution that describes an amplifying and compressing pulse. It is demonstrated by numerical simulation that the generation of short superradiance pulses is of self-similar character at the initial stage of the transient process. The specific features of the main characteristics of such pulses (the amplitude and width of a pulse and the coordinates of its maximum) are investigated as a function of time and control parameters. It is shown that, after a transient process, the solution reaches the self-similar stage, where the pulse amplitude and the inverse of its squared width grow linearly with time.

Results of numerical simulation of a miniaturized sub-THz traveling-wave tube amplifier with sheet electron beam and planar grating slow wave structure (SWS) are presented. Cold characteristics of the SWS are calculated. Small-signal and large-signal gain regimes are studied by the 1-D parametric frequency-domain code. The results are verified by simulations using 3-D particle-in-cell codes.

Slow-wave structure (SWS) is a core part of a traveling-wave-tube (TWT) amplifier. In this letter, the planar microstrip meander SWS on a dielectric substrate at $V$ -band (50–70 GHz) is studied. The basic electromagnetic parameters of the SWS are calculated. The SWS circuits are designed and fabricated, and good transmission characteristics are measured. The SWS developed is characterized by a wide bandwidth and a relatively-large slow-wave factor, and is suitable for a low-voltage TWT with the sheet electron beam.

Peculiarities of the formation of multistability in a microwave generator with delayed reflection from the load have been studied. Characteristic scenarios of the appearance and evolution of multistable states are determined. The influence of nonisochronism on the scenario of transition to chaos is revealed.

Complex-cavity resonator with mode conversion is a promising way of improving mode selection properties of a terahertz gyrotron. In this paper, enhancement of the frequency tunability of the second-harmonic 0.4-THz gyrotron by using the complex-cavity resonator is considered. Results of detailed numerical study of the cold-cavity electromagnetic parameters are presented. Using the results of cold-cavity simulations, start-oscillation currents for different modes are calculated.

Effect of delayed reflection on operation of a second-harmonic terahertz (THz)-band gyrotron is studied. Theoretical analyses, numerical calculations, and experimental observations for the 0.394-THz Fukui University (FU) and continuous wave (CW) IIB gyrotron are presented. The reflections decrease starting current and expand frequency tunability range owing to excitation of high-order axial modes. They also increase frequency stability, i.e., reduce frequency change due to variation of the magnetic field. In addition, the reflections strongly affect mode competition causing suppress of the second-harmonic mode by the fundamental one and vice versa or, in the case of cooperative mode interaction, mutual power increase.

We consider further development of our original technology for microfabrication of millimeter-band planar microstrip slow-wave structures (SWS). The technology is based on magnetron sputtering and laser ablation methods. V-band (50-75 GHz) and W-band (75-110 GHz) SWSs are fabricated and characterized by scanning electron and optical microscopy. Electromagnetic parameters of the developed SWSs are studied by numerical simulation and cold-test measurement. We have also carried out preparations and preliminary technological steps for the microfabrication of D-band (110-170 GHz) planar microstrip slow-wave structures.

We study a 0.2-THz traveling-wave tube (TWT) with a grating slow-wave structure (SWS) and sheet electron beam focused by reversal magnetic field. Change in the direction of the guiding magnetic field causes change in the direction of beam curling and can suppress the diocotron instability, which is a main problem for sheet beam focusing. Electron gun with a converging sheet beam is designed and fabricated. Over 100 mA current was measured. The results of small-signal and large-signal TWT gain analysis are presented.

In recent years, the problem of control of gyrotron radiation by partial reflection of the output power from a remote load has attracted a considerable interest. In this paper, we study a reflection influence on mode-competition scenario in a multimode gyrotron. A possibility of controlling the mode competition processes by proper adjustment of reflection factors for different modes is discussed.

The possibility of high-efficiency single-mode regimes in a sub-megawatt power 250-GHz gyrotron, which is developed for the DEMO project, is studied. Nonlinear mode interaction at the front of accelerating voltage pulse/current is discussed. It is shown that for these scenarios a single-mode high-efficiency regime is possible within a fairly broad band of cyclotron frequency mismatch. Stability of such a regime with respect to the excitation of spurious modes is studied.

THz range gyrotrons operating in continuous mode are of great interest for many applications, such as spectroscopy, plasma diagnostics, biomedical research, etc. These applications require high frequency stability. In addition to the existing methods of spectrum generation control, the use of various types of synchronization has recently attracted interest. In particular, mutual synchronization of two coupled gyrotrons, which is presented in this article. The mechanism of transition to synchronization at the desired frequency is considered.

Design and simulation of a sub-THz traveling-wave tube amplifier with a grating slow-wave structure (SWS) is discussed. A Pierce-type electron gun with a converging sheet electron beam emitted from a cylindrical curved cathode is designed. Beam focusing by the uniform and reversal magnetic field is compared. The results of gain and output power calculations are presented.

The equations describing the interaction of an electron beam with an electromagnetic wave in Cherenkov-type vacuum tube devices allow a self-similar solution describing amplification and compression of short electromagnetic pulses. In this paper, we discuss the main features of the self-similar solutions and present the results of detailed numerical simulations, which confirm the theoretical analysis.

A traveling wave tube amplifier (TWTa) operating in V-band (62–65 GHz) was designed considering a planar slow wave structure (SWS). Particle in cell simulations were performed to calculate the gain and the output power of the TWT. The simulated TWT showed a maximum gain of 36 dB at 64 GHz and an output power of 16 W. The planar SWS was then fabricated with a laser machining technique. S parameters measurements of the SWS showed excellent matching and low losses in the operating frequency band.

We report the results of the design, simulation, fabrication, and cold-test measurements of millimeter-band 2D planar microstrip slow-wave structures (SWSs) on dielectric substrates. Such structures have a high slow-wave factor, which allows for low-voltage operation and reduction in the size and weight of the device. A low-cost and flexible fabrication technology based on magnetron sputtering and subsequent laser ablation has been developed and is reported in the paper. Microstrip meander-line SWS circuits at V-, W-, and D-bands have been fabricated and characterized. The fabrication of ring-bar planar SWSs by the photolithographic method is also discussed. Experimental measurement of S-parameters of the fabricated structures reveals good transmission properties. Return loss (S11) does not exceed −10 dB and attenuation is about 2 dB/cm in the V-band, 10 dB/cm in the W-band, and 8.5 dB/cm in the D-band.

For a relativistic backward-wave oscillator (RBWO), various nonstationary phenomena, such as irregular transients, mode competition, self-modulation, and chaos, are typical. Phase locking by injection of the external signal helps to minimize transient times and to stabilize a single-frequency regime of operation. In this paper, phase locking of an RBWO with end reflections is considered. The results of time-domain numerical modeling are presented, which reveal an intricate pattern of the phase-locked operation. In particular, a possibility of rapid frequency switching by RF priming is demonstrated.

We report on the results of a numerical investigation of the synchronization of two coupled klystron oscillators with an external feedback circuit. Simulation has been carried out using the particle-in-cell method. We have also considered the results of a numerical analysis of an amplifier klystron and an isolated klystron oscillator, which make it possible to choose the optimal values of parameters of coupled klystrons. The structure of the synchronization domain for various parameters has been analyzed. The possibility of increasing the total output power with an appropriate choice of parameter of coupling between the oscillators has been revealed.

Self-injection locking of a gyrotron by a delayed signal is considered. The results of theoretical analysis and numerical simulations explaining gyrotron frequency stabilization by time-delayed part of the output power are presented. A simple quasi-linear model is studied, and formulas for the frequency-stabilization rate and the locking bandwidth are derived. The theory is verified by a numerical simulation for the 0.67-THz gyrotron.

The possibility of reducing the radiation frequency fluctuations by a factor of 3–5 using a nonresonant or highly resonant weakly reflecting load for the gyrotrons employed in controlled-fusion facilities is shown. The ranges of system parameters where the frequency stabilization is most effective were identified both analytically and numerically.

A traveling-wave tube of the millimeter range belonging to the short-wavelength region with a sheet electron beam and a slow-wave structure of the double grating type is studied. Its dispersion characteristics and coupling impedances for various spatial harmonics are calculated. The issues of design of the electron-optical system are discussed. The focusing of a sheet electron beam with a high current density by a uniform magnetic field is modeled.

This paper reports the results of studies of super-radiance pulse amplification in the case of Cherenkov interaction of a relativistic electron beam with a traveling electromagnetic wave. 1D Nonstationary (time-domain) nonlinear models of a Cherenkov traveling-wave-tube amplifier are considered in two approximations, namely, in the cases of small variation of electron velocity and small variation of electron energy. For both cases, self-similar solutions, which describe the pulse amplification and compression, are derived and limiting transition between them is discussed. The results of numerical simulation of amplification of a seed pulse are presented showing that the main characteristics of the pulse (peak amplitude, pulse width, etc.) behave in time and space in good agreement with the self-similar solutions.

A novel technology for microfabrication of millimeter-band planar microstrip slow-wave structures is considered. The technology is based on magnetron sputtering and laser ablation methods. The magnetron sputtering method is used to deposit a thin layer of metal (copper) on a dielectric substrate. Then laser ablation is utilized to cut a slow wave structure from the copper layer. V-band (50–70 GHz) and W-band (75–110 GHz) meander-line slow wave structures are fabricated and characterized by scanning electron and optical microscopy. Electromagnetic parameters of the developed slow wave structures are studied by numerical simulation. Cold-test measurement are also carried out for microfabricated meander-line slow wave structures. The experimental results are in good agreement with the numerical ones. The proposed technology has significant advantages in cost, speed and flexibility over lithography processes commonly utilized for such applications. The future work will be aimed to expansion of the proposed technology to manufacturing of higher-frequency E-band (110–170 GHz) planar slow wave structures.

0.2-THz traveling-wave tubes (TWT) with a grating slow-wave structure (SWS) are studied. The results of design and simulation of sheet-beam and multiple-beam electron-optical systems are reported. Electromagnetic parameters of SWSs are calculated. The results of small-signal and large-signal gain analysis are presented. According the simulations, for 0.l-A 20-kV sheet beam, peak small-signal gain and saturated power are about 39 dB and 80 W, respectively.

This report presents a design of an electron-optical system (EOS) with triple electron elliptical beams. A current of each beam is 31 mA and a dimension is 300×600 ¼m2. A magnetic field of 0,55 T is used for focusing of electron beams. A technology of fabrication and assembly of a model of EOS that contains a dispenser cathode, anode, collector and magnetic system is presented. In the course of experimental investigation of a model in impulse mode total current of 93 mA was obtained at cathode temperature of 1100°C and grid potential 900-1000 V. The realized design of a model with elliptical beams demonstrates the feasibility of creating of THz TWT on the basis of a similar EOS.

Medium-power (10-100 W) THz-band gyrotrons operating in a continuous-wave (CW) mode are of great importance for many applications such as spectroscopy, plasma diagnostics, non-destructive inspection, stand-off detection of radioactive materials, biomedical applications, etc. For all these applications, high frequency stability and tunability within 1-2 GHz frequency range is typically required. Apart from different existing techniques for frequency stabilization, phase locking has recently attracted strong interest. In this paper, we present the results of numerical simulation phase locking by injection of the external driving signal, self-injection locking by delayed reflection, and mutual phase locking of two coupled gyrotrons. Mode competition effect on phase locking is investigated.

Microfabricated vacuum-tube millimeter- and THz-band sources are of great interest for numerous applications such as communications, radar, sensors, imaging, etc. Recently, miniaturized sheet-beam traveling-wave tubes for operation at sub-THz and THz bands have attracted a considerable interest. In this paper, we present the results of modeling and development of slow-wave structures (SWS) for medium power (10-100 W) traveling-wave tubes (TWT) amplifiers in near-THz frequency band. Different types of SWSs are considered, such as double-vane SWS for TWT with a sheet electron beam, folded-waveguide SWS, and novel planar SWSs on dielectric substrates.

Self-injection locking by delayed reflection becomes a popular method for improving frequency stability and enhance of the frequency tunability of a gyrotron oscillator. In this paper, we develop a theoretical model of a self-injection-locked gyrotron and analyze the influence of reflections on frequency tuning by magnetic field. The results of theoretical analysis are verified by numerical simulation of time-dependent fixed-field and self-consistent models of a gyrotron.

A novel technology for microfabrication of millimeter and THz band planar microstrip slow-wave structures (SWS) is proposed. The technology is based on magnetron sputtering and laser ablation methods. The magnetron sputtering method is used to deposit a thin layer of metal (copper) on a quartz substrate. Then laser ablation is utilized to fabricate a slow wave structure from the copper layer. V-band (50–70 GHz) meander-line SWSs were fabricated and characterized by scanning electron and optical microscopy. The proposed technology has significant advantages in cost, speed and flexibility over lithography processes commonly utilized for such applications. The future work will be aimed to expansion of the proposed technology to manufacturing of higher-frequency W-band (75–110 GHz) and E-band (110–170 GHz) planar SWSs.

In this work we report the results of numerical simulation and cold-test measurements of electromagnetic parameters of the V-band (50–70 GHz) meander-line slow wave structure. The microstrip meander-line slow wave structure is suitable for using in a millimeter-band traveling wave tube amplifiers. Several samples of copper microstrip meander-line slow wave structure on a quartz substrate consisting of 50 meander periods with input and output couplers were designed and fabricated. The slow wave structure was microfabricated by using our original and novel technology for microfabrication. The technology is based on magnetron sputtering and laser ablation methods. The magnetron sputtering method is used to deposit a thin layer of metal (copper) on a quartz substrate. Then laser ablation is utilized to cut a slow wave structure from the copper layer. This technique is a more facile, flexible and lower cost as compared to photolithography method. Transmission and reflection of microfabricated SWS were measured experimentally and calculated numerically. The results of the experimental cold-test measurements are verified by numerical simulations. Electromagnetic parameters of the slow wave structures were simulated using the finite-element ANSYS HFSS and COMSOL Multiphysics software packages. The results obtained with these two codes are in excellent agreement with each other and good agreement between experimental and numerical results is also observed.

Properties of microfabricated V-band (50-70 GHz) meander slow-wave structures (SWS) for low- voltage tubes with sheet electron beam are studied by numerical simulation and cold-test measurement. The SWS was microfabricated by using magnetron sputtering and laser ablation processes. Transmission and reflection of proposed SWS were measured experimentally and calculated numerically. The experimental results are in good agreement with the numerical ones.

A novel technology for microfabrication of millimeter-band planar microstrip slow-wave structures (SWS) is proposed. The technology is based on magnetron sputtering and laser ablation methods. The magnetron sputtering method is used to deposit a thin layer of metal (copper) on a quartz substrate. Then laser ablation is utilized to cut a slow wave structure from the copper layer. V-band (50-70 GHz) meander-line SWSs were fabricated and characterized by scanning electron and optical microscopy. The proposed technology has significant advantages in cost, speed and flexibility over lithography processes commonly utilized for such applications.

The results of design and simulation of a 0.2- THz traveling-wave tube amplifier with a grating slow- wave structure (SWS) are presented. An electron-optical system with a converging sheet electron beam is designed and beam transmission in a rectangular tunnel at over 45 mm distance is demonstrated in numerical simulation. Electromagnetic parameters of a double-grating staggered slow-wave structure are calculated. Small­signal and large-signal gain regimes are simulated.

Coherent operation of several gyrotrons is important for power combining applications, especially for electron-cyclotron resonance plasma heating. In this paper, a model of two coupled gyrotron oscillators is developed and basic regimes of the mutual interaction are studied. Time delay of the coupling signal traveling between two gyrotrons strongly affects the pattern of phase-locking regimes.

Effect of delayed reflection on operation of a second-harmonic THz-band gyrotron is studied. Theoretical analysis, numerical calculations and experimental observations for the 0.394 THz FU CW IIB gyrotron are presented.

Folded waveguide (FW) is a promising type of slow-wave structure (SWS) for millimeter-wave traveling-wave tubes. A modified discrete model to obtain cold characteristics parameters of the FW SWS is developed. Cold characteristics such as dispersion characteristic and interaction impedance show reasonable agreement with the results of full electromagnetic simulation.

Results of 3D modeling of the 0.2 THz double-grating half-period staggered slow-wave structure are presented. A fast and accurate finite edge elements technique for simulation of broadband input/output couplers is developed. Beam focusing in a uniform magnetic field is simulated showing very good beam transmission. Small-signal and large-signal gain regimes are simulated using CST Particle Studio 3D code.