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.     

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.     

Formation and emission of intense electromagnetic pulses by means of an insulated rod antenna excited by a short-duration high-current relativistic electron beam

The possibility of forming and emitting high-power electromagnetic pulses by means of an insulated rod antenna excited by a short-duration high-current electron beam is studied. It is found experimentally that the amplitude of the emitted pulses and their characteristic period depend on the antenna length. The potentialities of the method proposed as applied to the generation of intense videopulses are discussed.     

Nonlinear dispersion in a plasma with a relativistic electron beam

The nonlinear interaction of a relativistic electron beam with a plasma is investigated numerically on the basis of the extended notions of the physical quantities that enter the linear dispersion relation. Extending the notions of the wave frequency, wavenumber, and wave phase velocity to the nonlinear stage of an instability makes it possible to analyze the evolution of the Cherenkov and plasma resonances and to study how they affect the saturation of the wave amplitude. A model of the beam-plasma instability in which the growth rate is calculated from the corresponding linear hydrodynamic formula on the basis of the results obtained using a numerical kinetic model makes it possible to establish the applicability range of the hydrodynamic approximation for beams with different energies.     

Fundamental parameters of a relativistic runaway electron avalanche in air

A relativistic runaway electron avalanche in air is simulated numerically by the Monte Carlo method with allowance for a large number of elementary processes involving electrons, positrons, and photons. The characteristic time scale of the avalanche amplification is calculated as a function of the overvoltage δ relative to the minimum value of the drag force between the electrons and the atomic particles of the medium. The dynamics of the formation of the electron energy distribution is investigated. The steady-state mean electron energy depends weakly on δ. Over a wide range of δ values, there exists a universal electron energy distribution, which is essentially independent of δ. The angular distributions of electrons integrated over energies, as well as the angular distributions for different energy groups, are calculated. Analytic approximations for the energy and angular distributions are obtained.     

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.     

Unsteady processes during stimulated emission from a relativistic electron beam in a quasi-longitudinal electrostatic pump field

The problem of stimulated emission from a relativistic electron beam in an external electrostatic pump field is studied. A set of nonlinear time-dependent equations for the spatiotemporal dynamics of the undulator radiation amplitude and the amplitude of the beam space charge field is derived. The beam electrons are described by a modified version of the macroparticle method. The regimes of the single-particle and collective Cherenkov effects during convective and absolute instabilities are considered. The nonlinear dynamics of radiation pulses emitted during the instabilities of the beam in its interaction with the forward and backward electromagnetic waves is investigated.     

Surface waves on the boundary of a conducting medium and their excitation by a relativistic electron beam

Excitation of surface waves by a relativistic electron beam propagating over a conducting cylindrical medium (metal or highly ionized plasma) is investigated theoretically. Dispersion relations describing the linear interaction of surface electromagnetic waves with a monoenergetic electron beam are derived, and the growth rates and spatial amplification factors of excited waves are determined. Condition for the nonlinear trapping of the beam electrons by a surface wave is used to determine the maximum amplitude of the excited wave and the optimal radiator length. The electric field of a surface wave excited by an electron beam is estimated for a particular case.     

Computational modeling of stabilizing the instability of a relativistic electron beam in a dense plasma

The nonlinear dynamics of the instability developed upon the interaction between a relativistic electron beam and a dense plasma as a function of the beam density is numerically modeled. The appropriate solutions are obtained and analyzed.     

Output power variations in a plasma relativistic microwave amplifier during a 500-ns relativistic electron beam current pulse

A relativistic plasma microwave amplifier with a gain of about 30 dB and an output power of about 60–100 MW in the frequency range from 2.4 to 3.2 GHz is studied experimentally. The total duration of the output microwave pulse is equal to the duration of the current pulse of the driving relativistic electron beam (500 ns); however, the maximum output power is observed only within 200 ns. It is shown that variations in the output microwave power during the current pulse of the annular relativistic electron beam are caused by variations in the beam radius and thickness. Analysis of the experimental data and results of numerical simulations show that the thickness of the electron beam is determined by the density of the cathode emission current.     

Laser radiation guiding in a plasma channel created by a relativistic electron beam

The diffraction broadening of laser radiation restricts its efficient utilization in many applications. In this work, a method for laser radiation guiding in a density channel formed in a plasma by a relativistic electron beam is considered. The conditions and parameters of the relativistic beam ensuring the guiding are examined.     

An annular high-current electron beam with an energy spread in a coaxial magnetically insulated diode

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.     

Experimental observation of electron beam generation in the paraxial region of a high-current discharge due to a pinch effect

The phenomenon of “runaway” of electrons in the paraxial region of a Z-pinch discharge in the heavy element environment has been experimentally observed using the methods of pulsed optical shadowgraphy, X-ray pinhole imaging, and time-of-flight measurements.     

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.     

Dynamics of a relativistic electron beam in the vicinity of a spherical injecting body in space plasma

The dynamics of a relativistic electron beam in the vicinity of an injector in the form of a spherical conducting body in a space plasma is considered. An equation describing the radial evolution of a steady electron beam with a self-similar density profile in the electric field of the injector is formulated. A method for calculating the radial evolution of a relativistic electron beam in the vicinity of an injector is developed. The method is based on the numerical integration of a set of ordinary differential equations for the beam radius and field potential in the space charge region under the relevant boundary conditions at the injector surface. Results are presented from numerical simulations of the radial dynamics of an electron beam in the vicinity of a spherical screen system for neutralizing the electric charge carried away by the beam. The numerical results show that the electric field of the injector hastens the beam expansion.     

Nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in a dielectric medium

A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.     

Differential rotation of plasma in the GOL-3 multiple-mirror trap during injection of a relativistic electron beam

Results of spectral and magnetic diagnostics of plasma differential rotation in the GOL-3 multiplemirror trap are presented. It is shown that the maximum frequency of plasma rotation about the longitudinal axis reaches 0.5 MHz during the injection of a relativistic electron beam into the plasma. The data of two diagnostics agree if there is a region with a higher rotation frequency near the boundary of the electron beam. Plasma differential rotation can be an additional factor stabilizing interchange modes in the GOL-3 facility.     

Nonlinear theory of the low-frequency interaction of ion beams with the virtual cathode of a relativistic electron beam

A study was made of the nonlinear low-frequency interaction of a longitudinal ion beam with a virtual cathode of a relativistic high-current electron beam injected into a cylindrical drift chamber. Cases are considered in which the electron and ion beams have the same radii and in which the radius an ion beam is greaterthan that of an electron beam.     

Nonlinear theory of the collective Cherenkov interaction of a dense relativistic electron beam with a dense plasma in a waveguide

A nonlinear theory of the instability of a straight relativistic dense electron beam in a plasma waveguide is derived for conditions of the stimulated collective Cherenkov effect. A study is made of a waveguide with a dense plasma such that the plasma wave excited by the beam during the instability can be escribed, with a good degree of accuracy, as a potential wave. General relativistic nonlinear equations are btained that describe the temporal dynamics of beam-plasma instabilities with allowance for plasma nonlinearity and the generation of harmonics of the initial perturbation. Under the assumption that the resonant interaction between the beam waves and the plasma waves is weak, the general equations are reduced to relativistic equations with cubic nonlinearities by using the method of expansion in small perturbations of the trajectories and momenta of the beam and plasma electrons. The reduced equations are solved analytically, the time scales on which the instability saturates are determined, and the nonlinear saturation amplitudes are obtained. A comparison between analytical solutions to the reduced equations and numerical solutions to the general nonlinear equations shows them to be in good agreement. Nonlinear processes caused by the relativistic nature of the beam are found to prevent stochastization of the system in the nonlinear stage of the well-developed instability. In contrast, a nonrelativistic electron beam is found to be subject to significant anomalous nonlinear stochastization.