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.     

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 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.     

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.     

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.     

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.     

Beam and tissue factors affecting Cherenkov image intensity for quantitative entrance and exit dosimetry on human tissue

This study's goal was to determine how Cherenkov radiation emission observed in radiotherapy is affected by predictable factors expected in patient imaging. Factors such as tissue optical properties, radiation beam properties, thickness of tissues, entrance/exit geometry, curved surface effects, curvature and imaging angles were investigated through Monte Carlo simulations. The largest physical cause of variation of the correlation ratio between of Cherenkov emission and dose was the entrance/exit geometry (?50%). The largest human tissue effect was from different optical properties (?45%). Beyond these, clinical beam energy varies the correlation ratio significantly (?20% for X‐ray beams), followed by curved surfaces (?15% for X‐ray beams and ?8% for electron beams), and finally, the effect of field size (?5% for X‐ray beams). Other investigated factors which caused variations less than 5% were tissue thicknesses and source to surface distance. The effect of non‐Lambertian emission was negligible for imaging angles smaller than 60 degrees. The spectrum of Cherenkov emission tends to blue‐shift along the curved surface. A simple normalization approach based on the reflectance image was experimentally validated by imaging a range of tissue phantoms, as a first order correction for different tissue optical properties.

     

Influence of the normal Doppler effect on the Cherenkov beam instability in an electrodynamic system of finite length

The possibility is studied of attenuating the feedback wave in electron-beam-based Cherenkov microwave oscillators at the expense of its resonant interaction with the beam cyclotron wave under normal Doppler effect conditions. Oscillators operating in the regimes of the collective and single-particle stimulated Cherenkov effects are considered. Stability conditions for a system with a beam that is subject to the Cherenkov and cyclotron resonances at the emission frequency are found. Applications to particular problems in plasma microwave electronics are discussed.     

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.     

A procedure for the Cherenkov counting of high energy β and γ emitting radionuclides in coloured plant extracts

Summary Elimination of count rate variations caused by the absorption of Cherenkov radiation by pigments in coloured solutions was achieved by placing these solutions in opaque walled cylinders immersed in colourless liquids contained in standard counting vials. Good counting efficiencies for a range of and emitting radionuclides were obtained by selecting colourless liquids with high refractive index.     

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.     

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.     

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.     

Classical and quantum description of electron trapping during the Cherenkov beam instability in plasma

A nonlinear quantum theory of the Cherenkov instability of a nonrelativistic monoenergetic electron beam in a cold plasma is constructed. It is shown that the instability of a low-density beam is almost purely quantum in nature and results from the emission of one quantum of a plasma wave—a plasmon—by the beam electrons. The number of emitted (and absorbed) plasmons increases with beam density, so, in the limit of high-density beams, the instability becomes a classical Cherenkov beam instability in plasma. Some analytic solutions and estimates are found, detailed numerical results are obtained, and the evolution of the quantum distribution function of the beam electrons in different regimes of the beam instability is investigated.     

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.     

Boundary conditions for the electromagnetic field in a waveguide with a thin-walled annular plasma in the context of application to plasma microwave electronics

Effective boundary conditions for the electromagnetic field of the slow surface waves of a thinwalled annular plasma in a metal waveguide are derived and justified. With the boundary conditions obtained, there is no need to solve field equations in the plasma region of the waveguide, so that the dispersion properties of plasma waveguides can be investigated analytically for an arbitrary strength of the external magnetic field. Examples are given that show how to use the effective boundary conditions in order to describe surface waves with a normal and an anomalous dispersion. The boundary conditions are then employed to construct a theory of the radiative Cherenkov instabilities of a thin-walled annular electron beam in a waveguide with a thinwalled annular plasma. The single-particle and collective Cherenkov effects associated with low-and high-frequency surface waves in an arbitrary external magnetic field are studied analytically. The method of the effective boundary conditions is justified in the context of application to the problems of plasma relativistic microwave electronics.     

Electromagnetic beam-plasma interactions in a magnetic field

The excitation of plasma oscillations in a thin-walled annular plasma by an annular electron beam in a cylindrical waveguide is considered in the linear approximation. The instability growth rates and spatial amplification coefficients in the beam-plasma system under the conditions of the Cherenkov and anomalous Doppler resonances are obtained and compared with those in a transversely homogeneous system. The contributions from different instability mechanisms are analyzed.     

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.     

Propagation of wave pulses in the regimes of single-particle and collective cherenkov effects during convective and absolute instabilities

Asymptotic solutions to the problem of the time evolution of delta-shaped wave pulses excited during resonant instabilities of electron beams in slowing-down electromagnetic media are found and investigated analytically. Convective and absolute instabilities developing under the conditions of collective and single-particle Cherenkov effects are considered. The results obtained apply to an arbitrary linear nonequilibrium dispersive medium that can be described by a set of first-or second-order differential transport equations.     

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.