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.     

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.     

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.     

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 relativistic quantum theory of Cherenkov emission of longitudinal Langmuir waves in a plasma

A nonlinear relativistic quantum theory of stimulated Cherenkov emission of longitudinal waves by a relativistic monoenergetic electron beam in a cold isotropic plasma is presented. The theory makes use of a quantum model based on the Klein-Gordon equation. The instability growth rates are obtained in the linear approximation and are shown to go over to the familiar growth rates in the classical limit. The mechanisms for the nonlinear saturation of relativistic Cherenkov beam instabilities are described with allowance for quantum effects, and the corresponding analytic solutions are derived.     

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.     

Anomalous Doppler effect and stimulated Cherenkov effect in a plasma waveguide with a thin-walled annular electron beam

A dispersion relation for the complex frequencies of the E modes excited by a thin-walled annular low-density beam in a cylindrical plasma waveguide is derived using the methods of perturbation theory. The cases of an annular and a uniform plasma filling are considered, and the corresponding wave growth rates are determined. A condition is obtained under which the primary mechanism for the excitation of the waveguide is the anomalous Doppler effect. The possibility is discussed of suppressing Cherenkov generation in a plasma resonator at the expense of the normal Doppler effect.     

Interaction of a high-current electron beam with hybrid waveguide and plasma modes in a dielectric Cherenkov maser with a plasma layer

The characteristics of a high-current electron beam-driven microwave amplifier—a dielectric Cherenkov maser—are investigated in the framework of linear theory for the case of a plasma layer present at the surface of the maser slow-wave structure. The dispersion relation for axisymmetric perturbations is obtained for the conventional configuration (a circular dielectric-lined waveguide and a thin annular beam propagating within the vacuum region inside the annular plasma) in the model of a fully magnetized plasma and beam. The results of numerically solving the dispersion relation for different beam and plasma parameters are presented, and an analysis based on these results is given with regard to the features of the beam interaction with the hybrid waves of the system (both hybrid waveguide and hybrid plasma modes). For the hybrid waveguide mode, the dependences of the spatial growth rate on the frequency demonstrate an improvement in the gain at moderate plasma densities, along with narrowing the amplification band and shifting it toward higher frequencies. For the hybrid plasma mode, the interaction with a mildly relativistic (200–250 keV) beam, when the wave phase velocity is close to the speed of light in the dielectric medium, is most interesting and, therefore, has been studied in detail. It is shown that, depending on the beam and plasma parameters, different regimes of the hybrid plasma mode coupling to the hybrid waveguide mode or a usual, higher order plasma mode take place; in particular, a flat gain vs. frequency dependence is possible over a very broad band. The parameters at which the ?3-dB bandwidth calculated for the 30-dB peak gain exceeds an octave are found.     

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.     

Nonlinear dynamics of the interaction of a modulated electron beam with a plasma

The excitation of plasma waves during the injection of an unmodulated and a density-modulated electron beam into a semi-infinite cold plasma is investigated. It is shown that the Langmuir oscillation energy accumulated in the plasma increases substantially near the plasma boundary and that the dimension of the region where the Langmuir oscillation energy is localized decreases with time.     

On the theory of a Cherenkov relativistic plasma emitter with a coaxial electrodynamic system

A plasma microwave amplifier based on a relativistic electron beam in an electrodynamic system in the form of a coaxial waveguide with a thin tubular plasma in a strong external magnetic field has been considered. Dispersion relations for determining the spectra of plasma and beam waves in the coaxial waveguide, as well as the general dispersion relation describing beam-plasma interaction, have been obtained in the linear approximation. The frequency dependences of the spatial growth rates for different plasma radii and different plasma frequencies, as well as the characteristic frequencies of the plasma amplifier, have been obtained by numerically and analytically solving the dispersion relations. The parameters of the plasma amplifier and generator with the coaxial electrodynamic system have been estimated for their experimental implementation.     

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.     

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.     

Quantum theory of stimulated Cherenkov emission and stimulated compton scattering of electromagnetic waves by a low-density relativistic electron beam

A quantum theory of instabilities of a relativistic electron beam due to the stimulated Cherenkov effect in a dielectric and the stimulated Compton effect in vacuum is presented. The instability growth rates are found in a linear approximation and are shown to go over to the familiar growth rates in the classical approximation. A nonlinear theory of instabilities in the quantum case is developed. Analytic solutions are obtained that describe the nonlinear saturation of the amplitudes of the electromagnetic waves emitted by the beam.     

Amplification of surface waves in a plasma waveguide by a straight relativistic electron beam in a finite magnetic field

The problem of the excitation of electron waves in a thin-walled annular cold plasma in a cylindrical waveguide by a straight relativistic electron beam in a finite magnetic field is considered. The dispersion properties of a waveguide system with parameters close to the experimental ones are investigated. It is shown that the growth rate of the excited high-frequency plasma wave is comparable to that of the low-frequency wave, which is weakly sensitive to the strength of the longitudinal magnetic field.     

Effect of the plasma electron motion on the development of Cherenkov instability in a waveguide

A linear theory of the Cherenkov amplification in a transversely nonuniform waveguide in an infinitely strong magnetic field is constructed with allowance for both ordered and thermal motions of plasma electrons. The effect of these electron motions on the threshold for the onset of Cherenkov instability is investigated. The amplification coefficients and the conditions for the onset of the instability are determined.     

Nonlinear oscillations of a semiconductor plasma with a nonrelativistic electron beam

Nonlinear oscillations of a semiconductor plasma with a low-density electron beam in the absence of an external magnetic field are studied in the hydrodynamic approximation. The beam is assumed to be nonrelativistic and monoenergetic. Cases are studied in which the Langmuir frequency of the electron oscillations in a semiconductor is much higher or much lower than the electron momentum relaxation rate. The self-similar solution obtained for the first case describes the damping of the nonlinear oscillations of the wave potential. Numerical analysis of the second case shows that the electric field distribution in the beam may correspond to that in a shock wave.     

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.     

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.