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.     

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.     

Electromagnetic instability of an anisotropic relativistic plasma in the context of the evolution of galactic and intergalactic high-energy particle sources

The electromagnetic instability of a relativistic space plasma is considered. The instability manifests itself during transverse oscillations in an anisotropic plasma either when the wavelength is sufficiently long and the velocity distribution is fixed or when the plasma is strongly anisotropic and the wavelength is fixed. The critical wavenumber is estimated for a velocity distribution in the form of an oblate ellipsoid of revolution.     

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.     

Dependence of the ion energy on the parameters of the laser pulse and target in the radiation-pressure-dominated regime of acceleration

When the dominant mechanism for ion acceleration is the laser radiation pressure, the conversion efficiency of the laser energy into the energy of relativistic ions may be very high. Stability analysis of a thin plasma layer accelerated by the radiation pressure shows that Raleigh-Taylor instability may enhance plasma inhomogeneity. In the linear stage of instability, the plasma layer decays into separate bunches, which are accelerated by the radiation pressure similarly to clusters accelerated under the action of an electromagnetic wave. The energy and luminosity of an ion beam accelerated in the radiation-pressure-dominated regime are calculated.     

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.     

Present status of the theory of relativistic plasma microwave electronics

Theoretical research on high-power microwave sources based on stimulated emission from relativistic election beams in plasma waveguides and resonators is reviewed. Both microwave amplifiers and oscillators are investigated. Two mechanisms for stimulated emission—resonant Cherenkov emission from a relativistic electron beam in a plasma and nonresonant Pierce emission arising from the onset of a high-frequency Pierce instability—are studied theoretically. The theory developed here is motivated by recent experiments carried out at the Institute of General Physics of the Russian Academy of Sciences and is aimed at creating high-power pulsed plasma microwave sources [both narrowband (Δω/ω<0.1) and broadband (or noisy, Δω/ω≈1)] based on high-current relativistic electron beams. Although the paper is devoted to theoretical problems, all analytic estimates and numerical calculations are made with real experiments in mind and theoretical results are compared with reliable experimental data. Special attention is paid to the opportunity to progress to short (millimeter) and long (decimeter) wavelength ranges. Some factors that influence the formation of the wave spectra excited by relativistic electron beams in plasma sources are discussed.     

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.     

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.     

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.     

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 dynamics of beam–plasma instability in a finite magnetic field

The nonlinear dynamics of beam–plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam?plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B ₀ = 4.5 kG (Ω ~ ωB _p ) and 20 kG (Ω _B ? ω_p). For B ₀ = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.     

A possible interpretation of the zebra pattern in solar radiation

The nature of the zebra pattern in continual type-IV solar radio bursts is discussed. It is shown that, when a weakly relativistic monoenergetic proton beam propagates in a highly nonisothermal plasma, the energy of the slow beam mode can be negative and explosive instability can develop due to the interaction of the slow and fast beam modes with ion sound. Due to weak spatial dispersion, ion sound generation is accompanied by cascade merging, which leads to stabilization of explosive instability. The zebra pattern forms due to the scattering of fast protons by ion sound harmonics. The efficiency of the new mechanism is compared with that of previously discussed mechanisms.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Numerical investigations and analysis on the effects of geometrical parameters on the group velocity of transverse magnetic pump mode and free electron laser instability

In this paper, we have numerically investigated the effects of various geometrical parameters of a backward wave oscillator, filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate R ₀ of a seeded free electron laser. On changing mean radius corrugation amplitude h and corrugation period z ₀ of backward wave oscillator; the ponderomotive potential of space charge wave changes. This in turn, changes the coupling strength of TM mode with negative beam space charge mode and hence the growth rate of parametric instability of free electron laser. A dispersion relation is derived and numerically solved for various geometrical parameters of backward wave oscillator and beam profile. A relation for Γ is also derived and computed numerically. The instability growth scales directly to the square root of beam density and inversely as seven power of relativistic gamma factor γ₀. Published in Russian in Fizika Plazmy, 2009, Vol. 35, No. 2, pp. 179–184. This text was submitted by the authors in English.     

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.     

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 Wave Interaction with Positron Beam in a Relativistic Plasma: Evaluation of Hypersonic Dust Ion Acoustic Waves

Plasma Physics Reports - We studied the propagation of small-amplitude dust ion acoustic (DIA) solitary waves in four-component relativistic plasma comprised of nonthermal electrons, mobile...     

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.     

Ultrawideband Plasma Relativistic Microwave Source

Plasma Physics Reports - An ultrawideband (UWB) plasma relativistic microwave source based on the amplification of self-noise of a relativistic electron beam in plasma is described. There is a...