It has been shown that the frequency of an ultrashort microwave pulse of a lowest axisymmetric electric mode at the interaction with a counterpropagating relativistic tubular electron beam under the cyclotron resonance conditions can be doubled due to re-emission into a mode having resonance at the second harmonic of the gyrofrequency. The conversion of the 3-cm 1-ns gigawatt microwave pulse in a circular waveguide from the TM01 mode to the TM02 mode with the doubling of the frequency, reduction of the duration to 0.22 ns, and the achievement of the peak power above the initial value has been demonstrated in a numerical experiment. The possibility of forming an intense ultrashort frontal splash of oscillations with the doubled frequency has been shown for longer initial pulses with a subnanosecond front.

A periodic sequence of ultrashort superradiance pulses during the current pulse of an electron beam with a duration of about 40 ns has been generated in an experiment with a relativistic backward-wave oscillator with wave reflectors at the edges of the electron–wave interaction region. The pulse repetition period has been specified by the electron–wave feedback time and is 5.9 ns, which corresponds to the repetition frequency of 170 MHz at a FWHM duration of about 0.8 ns. The frequency of microwave oscillations is 10 GHz. The peak power of pulses is 0.8–1.3 GW. The corresponding conversion coefficients defined as the ratio of the peak power of the ultrashort microwave pulse to the power of the electron beam are 0.7–1.2.

In order to expand the range of mechanical tuning of generation frequency in a subgigawatt Cherenkov microwave oscillator, it is proposed to use а configuration of relativistic backward-wave oscillator (BWO) having no reflectors with the radiation output in the direction opposite to the electron beam. In a numerical experiment using KARAT electromagnetic PiC code, it is demonstrated that in this case, due to only variation of the slow-wave structure (SWS) period, it is possible to change the oscillation frequency by tens of percent preserving the TM01 operation mode. The frequency tuning range is thereby limited from below by the lower boundary of the SWS passband, near which the BWO oscillation regime is displaced by the orotron regime, and from above by high-frequency excitation of the competing TM02 mode. A moderately relativistic microwave oscillator is simulated with a tuning band between 2.73 and 4.15 GHz (frequency ratio 1.52) at the (−3 dB) level of the maximum microwave power (520 MW at 3.85 GHz). The feeding electron beam having 460 keV particle energy and 4.7 kA current is transported by the magnetic field with an induction of 1.0 T. Additional simulations demonstrate that the frequency tuning range is extendable to approximately an octave at the cost of lower generation efficiency.

Coaxial transmission lines filled with saturated ferromagnetic material have been used for pulse sharpening purposes and high-frequency oscillation generation for a long time. These phenomena have been well studied experimentally, but have no exact analytical description; simplified models provide only qualitative agreement with the experiment. For quantitative description, it is necessary to solve Maxwell equations together with Landau-Lifshitz equation for the magnetization vector. The paper presents numerical simulation of high-voltage pulse sharpening process and excitation of high-frequency oscillations in coaxial lines filled with saturated ferrite. The modeling was performed using the KARAT code in three versions: axisymmetric (RZ) and three-dimensional Cartesian (XYZ) and cylindrical ( RΘZ). The results are compared with previous experiments.

A quasistationary generation mode was experimentally implemented in a moderately relativistic microwave generator of twistron type with an efficiency of energy conversion from the driving electron beam to electromagnetic radiation of 29 ± 7%. With a guiding magnetic field of 1.9 T, an accelerating voltage of 210 kV, and an electron beam current of 1.5 kA (50 ns pulse duration), the microwave power was 156 ± 34 MW corresponding to the power conversion efficiency of 50 ± 12%. The width of 10.62 GHz microwave pulses was 26 ns, with no visual microwave pulse shortening. In a numerical simulation using the KARAT code, the potential influence of a collector plasma on the oscillator operation has been studied.

Using numerical simulation, the operating mode of a relativistic Cherenkov microwave generator of the twistronic type has been demonstrated. The generator includes an electrodynamic system based on a backward-wave oscillator and modulating reflector with nonmonotonous, highly nonuniform energy exchange along the length of the system. The efficiency of power conversion from the electron beam to electromagnetic radiation is 56%, and the electronic efficiency is 66%. For an accelerating voltage of 340 kV and an electron beam current of 3.3 kA, the simulated generation power is 630 MW at a frequency of 9.7 GHz and a guiding magnetic field of 2.2 T.

Поступило в Редакцию 7 июля 2016 г

This article presents time-dependent numerical modeling of V-band relativistic orotron: a high-power microwave generator with a TM03 oscillation mode in an oversized (D/λ ∼ 2.7) electrodynamic structure and diffractive output in the TM02 mode. Single-mode operation of the oscillator is ensured by the cyclotron selection of the working axisymmetric mode, with simultaneous depression of competing non-axisymmetric modes by means of cutting longitudinal slits in the wall of the slow-wave structure. The simulated output microwave power is 350 MW with a power conversion efficiency of 31% when using a 3.6 kA, 310 keV electron beam transported in the 3.9 T magnetic field. The simulation employed 2.5D axisymmetric and 3D Cartesian versions of the KARAT code.

The paper proposes a new scheme of high-power microwave oscillator of twistron type using a moderately relativistic high-current electron beam. In numerical experiment using axisymmetric version of the completely electromagnetic PiC code KARAT, a 56% conversion efficiency of electron beam power to electromagnetic radiation was demonstrated. With 340 kV accelerating voltage, 3.3 kA electron beam current, and 2.2 T guiding magnetic field strength, the simulated microwave power was 630 MW at 9.7 GHz. The "electronic efficiency" of the source reaches 66%.

The results of experimental studies of different types of cathodes—carbon-epoxy rods, carbon-epoxy capillary, edged graphite, and metal-dielectric—under the application of high-voltage pulses with an amplitude of several hundreds of kV and pulse duration of several nanoseconds are presented. The best diode performance was achieved with the edged graphite and carbon-epoxy-based cathodes characterized by uniform and fast (<1 ns) formation of explosive emission plasma spots and quasi-constant diode impedance. This result was achieved for both annular cathodes in a strong magnetic field and planar cathodes of a similar diameter (∼2 cm) with no external magnetic field. The cathodes based on carbon-epoxy rods and carbon-epoxy capillaries operating with an average current density up to 1 kA/cm2 showed insignificant erosion along 106 pulses of the generator and the generated electron beam current showed excellent reproducibility in terms of the amplitude and waveform.

Accumulation of electrons in course of transportation of tubular high-current electron beam in a coaxial diode with magnetic insulation was studied in the situation of counterstream electron motion occurring due to the formation of a virtual cathode. Accumulation of electrons in these flows is accompanied by gradual increase in their relative energy spread and simultaneous decrease in the maximum kinetic energy. The process is described analytically and confirmed in numerical modeling. The theory is an extension of the known theory of coaxial magnetically insulated diode (based on the conservation of axial component of the generalized momentum) taking into account the spread of electron energies. The numerical modeling employed the KARAT electromagnetic PiC-code. Experiments were performed using high-current electron accelerator SINUS-7 (pulsewidth 50 ns) in the range of diode voltages 350-800 kV, magnetic fields 8-24 kOe, electron beam currents 2-12 kA. A gradual increase of potential of the electron beam between the explosive-emission cathode and the virtual cathode was observed, which accompanies accumulation of circulating electrons as predicted in theory.

The competition of oscillations in a relativistic backward wave oscillator (RBWO) based on a coaxial waveguide has been studied by theoretical and experimental methods. It is established that the starting current for asymmetric magnetic TE (m1) type waves is lower than that for the TEM wave. Predominant excitation of the former waves is confirmed by numerical simulations using the PIC-code KARAT. In an experimental RBWO prototype, the excitation of asymmetric oscillations was suppressed by longitudinal cuts in the central conductor of the coaxial waveguide. As a result, stable generation of the TEM wave has been achieved at a frequency of 1.23 GHz, a peak power of 260 MW, and a 28% efficiency of electron-beam-power conversion into radiation power for a microwave-pulse duration of 33 ns.

Current characteristics and operating lifetime of the explosive emission cathode based on a carbon microfiber are investigated in the pulsed-periodic mode of operation with pulse duration of about 5 ns. Long-term (for up to 3.6 million pulses) tests of the cathode operating lifetime are carried out. Specific ablation of the fiber material equal to 2.4·10 –4 g/C is obtained. Change in the morphology of the fiber surface during long-time operation caused by deposition of carbon from the cathode plasma is revealed. The microscopic electric field strength on the fiber surface is estimated taking into account the surface microrelief. The efficiency of microwave generation comparable with that of a velvet cathode in low (200 kV/cm) average electric field in the gap is obtained for the Cherenkov microwave generator with vacuum diode without external magnetic field of decimeter wavelength range based on the SINUS-7 pulsed-periodic high-current electron accelerator with current pulse duration of 50 ns. The operating lifetime no less than 10 5 pulses is demonstrated for the carbon fiber-based cathode of the microwave generator operating in the mode of pulse batch with duration of several seconds and pulse repetition frequency of 20–50 Hz.

Элементарная теория трубчатого сильноточного электронного пучка в однородном канале транспортировки и в коаксиальном диоде с магнитной изоляцией обобщена на случай встречных потоков электронов с разбросом по кинетической энергии. Для различных величин относительной ширины энергетического распределения получены выражения для суммы абсолютных величин прямого и обратного токов в однородном канале транспортировки и для потока продольной компоненты обобщенного импульса в коаксиальном диоде с магнитной изоляцией как функций максимальной кинетической энергии электронов. Показано, что в диоде с расширением канала транспортировки и виртуальным катодом, ограничивающим величину отбираемого тока, через определенное время после начала эмиссии электронов на отрезке между катодом и виртуальным катодом устанавливаются встречные потоки частиц. Накопление электронов в этих потоках сопровождается увеличением их относительного энергетического разброса и одновременным уменьшением максимальной кинетической энергии. Развитые модельные представления не противоречат результатам детальных нестационарных расчетов, выполненных PiC-методом с использованием кодов KARAT и OOPIC-Pro.

An elementary theory of an annular high-current electron beam in a uniform transport channel and a coaxial magnetically insulated diode is generalized to the case of counterpropagating electron beams with a spread over kinetic energies. Expressions for the sum of the absolute values of the forward and backward currents in a uniform transport channel and for the flux of the longitudinal component of the generalized momentum in a coaxial magnetically insulated diode as functions of the maximum electron kinetic energy are derived for different values of the relative width of the energy distribution function. It is shown that, in a diode with an expanding transport channel and a virtual cathode limiting the extracted current, counterpropagating particle flows are established between the cathode and the virtual cathode within a certain time interval after the beginning of electron emission. The accumulation of electrons in these flows is accompanied by an increase in their spread over kinetic energies and the simultaneous decrease in the maximum kinetic energy. The developed model agrees with the results of particle-in-cell simulations performed using the KARAT and OOPIC-Pro codes.

The currents of 5-ns pulsed high-current electron beams produced in a planar vacuum diode with explosive-emission cathodes made of various materials with no external magnetic field at an average electric field strength in the gap of about 300 kV/cm have been measured and time-integrated observation of the optical luminescence of the cathode surface have been performed. Cathodes with a ceramic bushing and spring metal contacts, with ceramic plates set in a magnetic iron matrix, with blades made of stamped exfoliated graphite (Graflex), with blades made of foil fiberglass plastic, and a composite cathode made of crystalline boron and copper powders were tested. The current carried by one emission center has been estimated to range between 5 and 20 A for various cathodes. For the metal-dielectric cathode, the velocity of expansion of the cathode plasma over the ceramic surface has been estimated as 2·10 7 cm/s. The lifetimes of the cathodes at a pulse repetition rate of 50 Hz have been investigated.

The possibility of developing a two-channel nanosecond relativistic microwave oscillator with a phase stability in each channel sufficient for coherent summation of their electromagnetic fields is demonstrated experimentally. In experiments, vacuum diodes of two independent superradiant backward wave oscillators operating in 10-GHz frequency range were connected to a common voltage source with a subnanosecond pulse rise time, which ensured the fixation of the initial phase of electromagnetic oscillations. The measured values of the phase difference jitter of the channel electromagnetic oscillations amount to several percent of the oscillation period.

We present the results of investigations of a resonance S-band relativistic backward wave oscillator (RBWO) that employs a submicrosecond pulsed high-voltage source based on a Marx generator scheme with a water-filled pulse-forming line. It is shown that the spontaneous limitation of the microwave pulse duration in the RBWO is caused by the emission of charged particles from plasma generated at the surface of a slow-wave system under the action of intense high-frequency fields. An increase in the electric strength of the electrodynamic system of the resonance RBWO, which was achieved by processing the surface with a high-current low-energy electron beam, allowed the pulse energy to be increased to 250 J at a peak output radiation power of about 3 GW.