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.     

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.     

Theoretical and experimental investigations of the excitation of high-frequency oscillations in an ion collective accelerator model based on the Doppler effect

Results are presented from studies of a two-beam scheme of ion acceleration by a high-frequency field excited by an electron beam due to the instabilities associated with anomalous and normal Doppler effects. The dynamics of the excitation of eigenmodes in a periodic slow wave structure (SWS) by a relativistic electron beam via the anomalous Doppler effect is investigated theoretically. Mechanisms for the saturation of the instability are considered, analytical expressions for the maximum field amplitude and the efficiency with which the energy of beam electrons is converted into the energy of the excited wave are derived, and the results of numerical simulations of such excitation are presented. An experimental stand designed to test the principles and possibility of proton acceleration up to an energy of 8 MeV at a current up to 3 A is described. A double resonance (associated with anomalous and normal Doppler effects) occurring in the interaction of an electron beam with a helical SWS is studied experimentally. In this case, an increase in the efficiency with which the accelerating high-frequency field is excited is observed.     

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.     

Wakefield excitation by a relativistic electron bunch in a magnetized plasma

The excitation of a wake wave by a relativistic electron beam in an unbounded magnetized plasma and a plasma waveguide is studied theoretically. It is shown that, in a waveguide partially filled with a plasma, the energy that the electrons of the accelerated beam can gain is 37 times higher than the energy of the electrons of the beam generating wakefield.     

The Use of a Coaxial Electrodynamic System for Amplification of Microwave Range Waves During the Development of Beam–Plasma Instability

Plasma Physics Reports - A coaxial electrodynamic system for the amplification of microwaves with plasma filling, through which a relativistic electron beam moves, is studied theoretically. The...     

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.     

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.     

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.     

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.     

An annular high-current electron beam with an energy spread in a coaxial magnetically insulated diode

An elementary theory of an annular high-current electron beam in a uniform transport channel and a coaxial magnetically insulated diode is generalized to the case of counterpropagating electron beams with a spread over kinetic energies. Expressions for the sum of the absolute values of the forward and backward currents in a uniform transport channel and for the flux of the longitudinal component of the generalized momentum in a coaxial magnetically insulated diode as functions of the maximum electron kinetic energy are derived for different values of the relative width of the energy distribution function. It is shown that, in a diode with an expanding transport channel and a virtual cathode limiting the extracted current, counterpropagating particle flows are established between the cathode and the virtual cathode within a certain time interval after the beginning of electron emission. The accumulation of electrons in these flows is accompanied by an increase in their spread over kinetic energies and the simultaneous decrease in the maximum kinetic energy. The developed model agrees with the results of particle-in-cell simulations performed using the KARAT and OOPIC-Pro codes.     

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.     

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.     

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.     

Surface waves on the boundary of a conducting medium and their excitation by a relativistic electron beam

Excitation of surface waves by a relativistic electron beam propagating over a conducting cylindrical medium (metal or highly ionized plasma) is investigated theoretically. Dispersion relations describing the linear interaction of surface electromagnetic waves with a monoenergetic electron beam are derived, and the growth rates and spatial amplification factors of excited waves are determined. Condition for the nonlinear trapping of the beam electrons by a surface wave is used to determine the maximum amplitude of the excited wave and the optimal radiator length. The electric field of a surface wave excited by an electron beam is estimated for a particular case.     

Effect of plasma nonlinearity on the beam-plasma interaction in a hybrid plasma waveguide

A study is made of the characteristic features of the effect of plasma nonlinearity in a slow-wave structure on microwave generation by an electron beam and on electron beam energy losses. Theoretical results on the plasma density variation, the amplitude of the excited microwaves, and the velocity distribution function of the beam electrons are compared with the experimental data. It is shown that the self-consistency between the decreasing plasma density gradient and the spatial variation of the amplitude of an amplified wave in a slowwave structure leads to a significant (severalfold) increase in the efficiency with which the electron beam energy is converted into microwave energy in short pulses. The predictions of the theoretical model developed to describe the non-steady-state beam-plasma interaction agree well with the experimental data.     

Influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam

In plasma microwave oscillators, electrons fall onto the surface of a graphite collector, which leads to the generation of secondary electrons. The influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam propagating in a strong longitudinal magnetic field was studied experimentally and by numerical simulations. It is shown that the penetration of the reflected electrons into the drift space can lead to a substantial increase in the depth of the potential well in the drift space, a decrease in the velocity of the beam electrons, and a broadening of the electron energy distribution function.     

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.     

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.