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 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.     

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.     

On the nonlinear theory of collective Cherenkov interaction of a high-density relativistic beam with a plasma

The nonlinear dynamics of the instability of a straight high-density relativistic electron beam under the conditions of the stimulated Cherenkov effect in a plasma waveguide is studied both analytically and numerically. It is shown that, for a beam of sufficiently high density such that the stabilizing factors are nonlinear frequency shifts and for a plasma described in a linear approximation, the basic equations have soliton-like solutions and the electron beam after saturation of the instability relaxes to its initial, weakly perturbed state, provided that only one harmonic of the plasma and the beam density is taken into account. The analytical solutions obtained here for this case correlate well with the numerical ones. A more general model that accounts for the generation of higher harmonics of the plasma and the beam density does not yield soliton-like solutions for the time evolution of the amplitudes of the plasma and beam waves. In such a model, the instability will be collective again: it can be described analytically (at least, up to the time at which it saturates) by using equations with cubic nonlinearities and the method of expansion of the electron trajectories and momenta.     

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.     

Relativistic diamagnetic equilibrium of a thin-walled annular electron beam in an external magnetic field

A self-consistent equilibrium state of a thin-walled annular electron beam in an external magnetic field is investigated with allowance for diamagnetic effect and relativistic effects in the beam rotational motion. An equation for the relativistic angular velocities of the beam rotation is derived in the hydrodynamic approximation. The main parameters of the beam equilibrium state are obtained analytically and are calculated numerically. The parameters of a longitudinally homogeneous, relativistic diamagnetic high-density electron beam are determined.     

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.     

Low-frequency instability of an ion beam in the field of a high-current REB

A study is made of the linear and nonlinear stages of the low-frequency instability of an ensemble of ions that execute radial oscillations in the electric field of the space charge of an unneutralized high-current relativistic electron beam. Nonlinear mechanisms for stabilizing the low-frequency ion instability are considered. It is shown, in particular, that, under certain conditions, the development of the low-frequency instability can lead to the ejection of ions onto the walls of the drift chamber.     

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.     

Slow electromagnetic solitons in electron-ion plasmas

A set of nonlinear differential equations that describe moving relativistic solitons is investigated analytically and solved numerically. The influence of the ion motion on the soliton structure is investigated. It is demonstrated that, depending on the propagation velocity, relativistic solitary waves can occur in the form of bright solitons, dark solitons, or collisionless electromagnetic shock waves. In the limit of a low propagation velocity, a dark soliton can trap the ions and accelerate them. In the case of a bright soliton, the effects of ion dynamics limit the soliton amplitude. The constraint on the maximum amplitude is related to either the breaking of ion motion or the intersection of electron trajectories. The soliton breaking provides a new mechanism for ion and electron acceleration in the interaction of high-intensity laser pulses with plasmas.     

Quantum theory of Cherenkov beam instabilities in plasma

A quantum theory of stimulated Cherenkov emission of longitudinal waves by an electron beam in an isotropic plasma is presented. The emitted radiation is interpreted as instability due to the decay of the de Broglie wave of a beam electron. Nonrelativistic and relativistic nonlinear quantum equations for Cherenkov beam instabilities are obtained. A linear approximation is used to derive quantum dispersion relations and to determine the instability growth rates. The mechanisms for nonlinear saturation of quantum Cherenkov beam instabilities are investigated, and the corresponding analytic solutions are found.     

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.     

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.     

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.     

Deep modulation of a high-current relativistic electron beam in a system of coupled cavities

The excitation of inphase (0-type) and antiphase (π-type) electromagnetic oscillations by a relativistic electron beam in a system of identical coupled cavities is considered. It is shown that, in the case of excitation of antiphase oscillations, instability develops in a shorter system of cavities than it does when inphase oscillations are excited. In the nonlinear stage of the excitation of antiphase oscillations in a system of coupled cavities, a virtual cathode forms that breaks the initially uniform relativistic electron beam into a periodic sequence of spatially separated short bunches.     

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.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Nonlinear theory of coupled waves exemplified by beam-plasma instability

The nonlinear stage of instability of an annular electron beam spatially separated from an annular plasma is investigated. The equations describing coupled waves for an arbitrary ratio between the beam and plasma densities are derived. It is shown that instability saturates at distances on the order of several inverse spatial growth rates. The saturation is caused by relativistic nonlinearity, generation of the second harmonic, and low-frequency modulation of the electromagnetic field. At larger distances, resonant generation of low-frequency beam oscillations becomes a dominant factor. In the case of a low-density beam, an expression for the maximum power of the generated plasma wave is obtained in an explicit form.     

Electrostatic Solitary Pulses in a Dusty Electronegative Magnetoplasma

The nonlinear characteristics of dust-electron-acoustic (DEA) waves in a dusty electronegative magnetoplasma system consisting of nonextensive hot electrons, inertial cold electrons, positively charged static ions, and negatively charged immobile dust grains has been investigated. In this observation, the well-known reductive perturbation technique is employed to determine different types of nonlinear dynamical equations, namely, magnetized Korteweg–de Vries (KdV), magnetized modified KdV (mKdV), and magnetized Gardner equations. The stationary solitary wave and double layer solution of these three equations, which describe the characteristics of solitary waves and double layers of DEA waves, are obtained and numerically analyzed. It is noticed that various plasma parameters (viz., hot electron nonextensivity, positive ion-to-cold electron number density ratio, dust-to-cold electron number density ratio, etc.) significantly affect the basic properties of DEA solitary waves (DEASWs) and Gardner solitons (GSs). The prodigious results found from this theoretical investigation may be useful for researchers to investigate the nonlinear structures in various space and laboratory plasmas.     

Dynamics of a coaxial back-wave ubitron

A theory of a coaxial back-wave ubitron pumped by a high-current relativistic electron beam is constructed. The start currents of an ubitron are determined. The nonlinear dynamics of microwave generation at different electron beam currents is investigated.