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.     

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.     

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.     

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.     

On the theory of Cherenkov emission in a plasma

The Cherenkov emission of transverse-longitudinal waves in an anisotropic plasma is considered by applying a Hamiltonian method and by drawing an analogy between the equations for the Cherenkov emission of purely transverse and purely longitudinal waves in isotropic media and the equations for the emission of transverse-longitudinal electromagnetic waves in a highly anisotropic medium (a magnetized plasma). A formula for the emitted power is derived, as well as an expression for the directional pattern of the emitted waves in an anisotropic plasma.     

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.     

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.     

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.     

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 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.     

On the theory of Cherenkov emission from a short laser pulse in a magnetized plasma

Cherenkov emission from a short laser pulse propagating in an underdense plasma along a constant magnetic field is considered. The spectral, angular, energy, and spatiotemporal parameters of the emitted radiation are investigated. It is shown that the spectral content of the radiation and its directionality depend sensitively on the plasma and laser-pulse parameters. For instance, the most intense backward radiation at the upper hybrid frequency is generated by a tightly focused laser pulse.     

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.     

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.     

Classification of the regimes of Cherenkov beam instabilities in plasma waveguides

The regimes of the instabilities of an annular relativistic electron beam in a waveguide with an annular plasma are systematically analyzed and classified. The growth rates of the instabilities are calculated different limiting cases, and the resonance conditions for the development of the instabilities are determined. The fastest growing instability of a high-current relativistic electron beam in a waveguide with a dense plasma is considered. The possible onset of a low-frequency instability of a beam in a waveguide with a low-density plasma is investigated. Typical examples of how the growth rates depend on the perturbation wavenumbers are presented for systems with parameters close to the experimental ones.     

Visualization of the microwave beam generated by a plasma relativistic microwave amplifier

A method based on the detection of emission of a dielectric screen with metal microinclusions in open air is applied to visualize the transverse structure of a high-power microwave beam. In contrast to other visualization techniques, the results obtained in this work provide qualitative information not only on the electric field strength, but also on the structure of electric field lines in the microwave beam cross section. The interpretation of the results obtained with this method is confirmed by numerical simulations of the structure of electric field lines in the microwave beam cross section by means of the CARAT code.     

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.     

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.