Noise characteristics of a plasma relativistic microwave amplifier

Reasons for the occurrence of microwave noise at the output of a plasma relativistic amplifier have been analyzed. It is found that, in the absence of an input signal, the emission spectrum of the plasma relativistic microwave amplifier is similar to that of an electron beam in vacuum. It is concluded that microwave noise at the output of the amplifier appears as a result of amplification of the intrinsic noise of the electron beam. The emission characteristics of a relativistic electron beam formed in a magnetically insulated diode with an explosive emission cathode in vacuum have been studied experimentally for the first time. An important point is that, in this case, there is no virtual cathode in the drift space.     

The use of a high-current electron beam in plasma relativistic microwave oscillators

Relativistic microwave electronics faces the problem of using high currents of relativistic electron beams; i.e., it is possible to use beams the current of which is lower than that of actually existing high-current accelerators. We show the possibility of increasing the power of radiation generated in a plasma relativistic microwave oscillator (PRMO) due to an increase in the absolute value of current. For the beam currents close to the value of limiting vacuum current, the efficiency of microwave generation decreases; therefore, we study PRMO schemes with a high value of limiting vacuum current, i.e., schemes with a small gap between a hollow relativistic electron beam and the waveguide wall. The results of the experiment and numerical simulation are discussed.     

Repetitively rated plasma relativistic microwave oscillator with a controllable frequency in every pulse

A repetitively rated microwave oscillator whose frequency can be varied electronically from pulse to pulse in a predetermined manner is created for the first time. The microwave oscillator has a power on the order of 10⁸ W and is based on the Cherenkov interaction of a high-current relativistic electron beam with a plasma preformed before each pulse. Electronic control over the plasma properties allows one to arbitrarily vary the microwave frequency from pulse to pulse at a pulse repetition rate of up to 50 Hz.     

Coherent interaction of a relativistic electron beam with a plasma

Results are presented from experimental studies of the interaction of a modulated relativistic electron beam with a plasma. The electron energy spectra at the exit from the interaction chamber are measured for electron beams with energies of about 50 and 20 MeV. The coherent interaction of an electron beam with a microwave-driven plasma is studied. It is shown that, in strong electric fields that can be generated in the coherent interaction, the beam current is very sensitive to the phase of the microwave field.     

Fine structure of the emission spectra of a relativistic Cherenkov plasma maser

The evolution of the emission spectrum of a relativistic Cherenkov plasma maser is studied both experimentally and numerically. The frequency range of emission is 1.5–6 GHz at a power level of 50 MW and pulse duration of up to 500 ns. It is shown that the relativistic Cherenkov plasma maser is capable of producing both broadband (with a spectrum width of ～1 GHz) and narrowband (≈ 40 MHz) microwave pulses with a tunable mean frequency. Calculations by linear theory and numerical simulations provide a satisfactory explanation of the specific features and the time evolution of the spectra observed. It is suggested that the plasma nonlinearity is responsible for the experimentally observed shortening of the microwave pulses and the broadening of the emission spectrum.     

Plasma relativistic microwave electronics

The principles of plasma relativistic microwave electronics based on the stimulated Cherenkov emission of electromagnetic waves during the interaction of a relativistic electron beam with a plasma are formulated. A theory of relativistic Cherenkov plasma microwave oscillators and amplifiers is developed, and model experimental devices are elaborated and investigated. The emission mechanisms are studied theoretically. The efficiencies and frequency spectra of relativistic Cherenkov plasma microwave oscillators and ampli-fiers are calculated. The theoretical predictions are confirmed by the experimental data: the power of the devices attains 500 MW, the microwave frequency can be continuously tuned over a wide band with an upper-to-lower boundary frequency ratio of 7 (from 4 to 28 GHz), and the emission frequency bandwidth can be varied from several percent to 100 percent. These microwave sources have no analogs in vacuum microwave electronics.     

Tunable plasma relativistic microwave amplifier

A stable regime of the amplification of a slow plasma wave in a plasma waveguide during the injection of a high-current relativistic electron beam is obtained. For an input-signal frequency of 9.1 GHz, there exists a range of plasma densities in which the spectrum of the output microwave radiation lies in a 0.5-GHz-wide band. For a 40-kW input power at a frequency of 9.1 GHz, the maximum output power is 8 MW. It is shown experimentally for the first time that the beam-plasma amplifier can operate at frequencies of 9.1 GHz and 12.9 GHz. The range of plasma densities in which the regime of amplification is observed agrees with the results of calculations based on linear theory.     

Normal Doppler effect in experiments on the interaction of relativistic electron beams with plasma: Plasma relativistic microwave amplifier

The Cherenkov interaction of a high-current relativistic electron beam with a spatially bounded plasma was studied experimentally. In the generation of electromagnetic radiation, an important role is played by the counterpropagating plasma wave produced due to the reflection from the end of the plasma column. It is shown that, at the resonant value of the magnetic field, the normal Doppler effect occurs and the amplitude of the counterpropagating wave decreases. This effect was used to design and create a plasma relativistic microwave amplifier in which 10% of the beam energy is converted into radiation. The radiation frequency is 9.1 GHz, and the radiation spectrum width (±0.17%) is determined by the microwave-pulse duration. The maximum radiation power is 100 MW, the gain factor being 32 dB.     

Influence of Plasma Unsteadiness on the Spectrum and Shape of Microwave Pulses in a Plasma Relativistic Microwave Amplifier

Dependence of the shape of a microwave pulse in a plasma relativistic microwave amplifier (PRMA) on the initial plasma electron density in the system is detected experimentally. Depending on the plasma density, fast disruption of amplification, stable operation of the amplifier during the relativistic electron beam (REB) pulse, and its delayed actuation can take place. A reduction in the output signal frequency relative to the input frequency is observed experimentally. The change in the shape of the microwave signal and the reduction in its frequency are explained by a decrease in the plasma density in the system. The dynamics of the plasma density during the REB pulse is determined qualitatively from the experimental data by using the linear theory of a PRMA with a thin-wall hollow electron beam. The processes in a PRMA are analyzed by means of the KARAT particle-in-cell code. It is shown that REB injection is accompanied by an increase in the mean energy of plasma electrons and a significant decrease in their density.     

Specific features of virtual cathode formation and dynamics with allowance for the magnetic self-field of a relativistic electron beam

The conditions and mechanisms of virtual cathode formation in relativistic and ultrarelativistic electron beams are analyzed with allowance for the magnetic self-field for different magnitudes of the external magnetic field. The typical behavior of the critical current at which an oscillating virtual cathode forms in a relativistic electron beam is investigated as a function of the electron energy and the magnitude of the uniform external magnetic field. It is shown that the conditions for virtual cathode formation in a low external magnetic field are determined by the influence of the magnetic self-field of the relativistic electron beam. In particular, azimuthal instability of the electron beam caused by the action of the beam magnetic self-field, which leads to a reduction in the critical current of the relativistic electron beam, is revealed.     

Beam-plasma interaction in a hybrid plasma waveguide in the pulsed mode of microwave generation

Results are presented from experimental studies of the energy spectra of an electron beam in a model beam-plasma oscillator based on a hybrid plasma waveguide in the pulsed mode of microwave generation with a pulse duration of 1 µs or shorter. The beam energy spent on sustaining the beam-plasma discharge in a slow-wave structure is measured. A correlation between the type of excited waves and the generation of a group of accelerated beam electrons with energies exceeding the injection energy is revealed. It is shown that the pulsed mode of microwave generation is related to the time variations in the plasma density profile in the waveguide and the trapping of beam electrons by the excited microwave field.     

Present status of the theory of relativistic plasma microwave electronics

Theoretical research on high-power microwave sources based on stimulated emission from relativistic election beams in plasma waveguides and resonators is reviewed. Both microwave amplifiers and oscillators are investigated. Two mechanisms for stimulated emission—resonant Cherenkov emission from a relativistic electron beam in a plasma and nonresonant Pierce emission arising from the onset of a high-frequency Pierce instability—are studied theoretically. The theory developed here is motivated by recent experiments carried out at the Institute of General Physics of the Russian Academy of Sciences and is aimed at creating high-power pulsed plasma microwave sources [both narrowband (Δω/ω<0.1) and broadband (or noisy, Δω/ω≈1)] based on high-current relativistic electron beams. Although the paper is devoted to theoretical problems, all analytic estimates and numerical calculations are made with real experiments in mind and theoretical results are compared with reliable experimental data. Special attention is paid to the opportunity to progress to short (millimeter) and long (decimeter) wavelength ranges. Some factors that influence the formation of the wave spectra excited by relativistic electron beams in plasma sources are discussed.     

Plasma relativistic microwave amplifier with smooth frequency tuning from 2.4 to 3.2 GHz

Earlier, it was shown that the plasma relativistic microwave amplifier can operate at two frequencies, 2 and 3.2 GHz. In the present work, it is shown that, by varying the plasma density from one microwave pulse to another, it is possible to amplify the input signals to a power of 50?C80 MW at any frequency in the range 2.4?C3.2 GHz.     

Influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam

In plasma microwave oscillators, electrons fall onto the surface of a graphite collector, which leads to the generation of secondary electrons. The influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam propagating in a strong longitudinal magnetic field was studied experimentally and by numerical simulations. It is shown that the penetration of the reflected electrons into the drift space can lead to a substantial increase in the depth of the potential well in the drift space, a decrease in the velocity of the beam electrons, and a broadening of the electron energy distribution function.     

Control over the radiation spectrum of a microwave plasma relativistic oscillator

General features of the operation of microwave oscillators based on the Cherenkov resonance interaction of a high-current relativistic electron beam with a preformed plasma are considered. Emphasis is placed on the presence of longitudinal modes of the plasma-beam resonator that make it possible to tune the radiation frequency. Methods by which the radiation frequency can be varied severalfold continuously or in discrete controlled steps and the width of the spectrum of simultaneously generated frequencies can be changed substantially are described. The results of numerical simulations are compared with available experimental data.     

Experimental study of the plasma effect on the generation of microwave radiation in systems with a virtual cathode

Results are presented from experimental studies of the plasma effect on the generation of microwave radiation in systems with a virtual cathode. Using a triode with a virtual cathode as an example, it is shown that the cathode and anode plasmas reduce the generation efficiency; in particular, the power of the generated microwave radiation decreases and the radiation frequency and the microwave pulse duration change appreciably. It is demonstrated that, at high microwave powers, the power radiated into free space can be reduced by the plasma generated at the surface of the output window. This plasma appears due to discharges developing on the window surface under the combined action of bremsstrahlung, UV radiation, electrons and ions arriving from the beam formation zone, and the microwave electric field.     

Simulation of the development and interaction of instabilities in a relativistic electron beam under variation of the beam wall thickness

The development and interaction of Bursian and diocotron instabilities in an annular relativistic electron beam propagating in a cylindrical drift chamber are investigated analytically and numerically as functions of the beam wall thickness and the magnitude of the external uniform magnetic field. It is found that the interaction of instabilities results in the formation of a virtual cathode with a complicated rotating helical structure and several reflection regions (electron bunches) in the azimuthal direction. It is shown that the number of electron bunches in the azimuthal direction increases with decreasing beam wall thickness and depends in a complicated manner on the magnitude of the external magnetic field.     

Experimental study and numerical simulations of a plasma relativistic microwave amplifier

The dependences of the radiation parameters of a plasma relativistic microwave amplifier on the external factors have been studied both experimentally and numerically. The calculated dependences are found to agree qualitatively with the measured ones. In contrast to experimental studies, numerical simulations make it possible to examine physical processes occurring inside the plasma waveguide. Good agreement between the measured and calculated dependences of the radiation parameters on the external factors shows that information provided by numerical simulations of the processes occurring inside the plasma waveguide can be considered quite reliable. The electromagnetic field structure and electron beam dynamics inside the plasma waveguide have been investigated.     

Solution of a set of Maxwell-Lorentz equations for a ring relativistic electron beam

Nonlinear solutions to a set of Maxwell’s equations and the relativistic equations of electron motion are obtained that describe the equilibrium of a high-power ring relativistic electron beam against the background of immobile ions. By transforming the basic equations, a set of equations for a three-component vortex vector field is derived that describes ring beam configurations for plasma confinement. An example of a numerical calculation of the steady state of a compact beam torus of immobile ions and relativistic electrons is presented.     

Nonlineart theory of relativistic beam-plasma instabilities in the regime of the collective Cherenkov effect

A general mathematical model is proposed that is based on the Vlasov kinetic equation with a self-consistent field and describes the nonlinear dynamics of the electromagnetic instabilities of a relativistic electron beam in a spatially bounded plasma. Two limiting cases are analyzed, namely, high-frequency (HF) and low-frequency (LF) instabilities of a relativistic electron beam, of which the LF instability is a qualitatively new phenomenon in comparison with the known Cherenkov resonance effects. For instabilities in the regime of the collective Cherenkov effect, the equations containing cubic nonlinearities and describing the nonlinear saturation of the instabilities of a relativistic beam in a plasma are derived by using the methods of expansion in small perturbations of the trajectories and momenta of the beam electrons. Analytic expressions for the amplitudes of the interacting beam and plasma waves are obtained. The analytical results are shown to agree well with the exact solutions obtained numerically from the basic general mathematical model of the instabilities in question. The general mathematical model is also used to discuss the effects associated with variation in the constant component of the electron current in a beam-plasma system.