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.     

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.     

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.     

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.     

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 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 dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

Simulation of the development and interaction of instabilities in a relativistic electron beam under variation of the beam wall thickness

The development and interaction of Bursian and diocotron instabilities in an annular relativistic electron beam propagating in a cylindrical drift chamber are investigated analytically and numerically as functions of the beam wall thickness and the magnitude of the external uniform magnetic field. It is found that the interaction of instabilities results in the formation of a virtual cathode with a complicated rotating helical structure and several reflection regions (electron bunches) in the azimuthal direction. It is shown that the number of electron bunches in the azimuthal direction increases with decreasing beam wall thickness and depends in a complicated manner on the magnitude of the external magnetic field.     

The Infrared (Far Terahertz) Generation by Nonlinear Interactions of Two Visible Laser Beams in a Metallic Background: Infrared Surface Plasmon Effect

This paper presents an investigation of infrared (IR) radiation generation by nonlinear interaction of two visible laser beams in a metallic background. Two laser beams of Gaussian and Laguerre Gaussian (LG) profiles and background metals such as silver, copper, gold, and aluminum are utilized for IR generation. Effects of laser beam characteristics and structural properties of metals on the evolution of IR electric field amplitude are examined. Considering laser frequencies in the non-transparent region give rises to generation of IR surface plasmon (IRSP). An optimized relation is proposed for achieving efficient surface plasmon waves on a metal surface.

     

Intrinsic breaking of internal solitary waves in a deep lake

Based on simulations with the Dubreil-Jacotin-Long (DJL) equation, the limiting amplitude and the breaking mechanisms of internal solitary waves of depression (ISWs) are predicted for different background stratifications. These theoretical predictions are compared to the amplitude and the stability of the leading internal solitary waves of more than 200 trains of ISWs observed in the centre of a sub-basin of Lake Constance. The comparison of the model results with the field observations indicates that the simulated limiting amplitude of the ISWs provides an excellent prediction of the critical wave height above which ISWs break in the field. Shear instabilities and convective instabilities are each responsible for about half of the predicted wave breaking events. The data suggest the presence of core-like structures within the convectively unstable waves, but fully developed and stable cores were not observed. The lack of stable trapped cores in the field can be explained by the results from dynamic simulations of ISWs with trapped cores which demonstrate that even slight disturbances of the background stratification cause trapped cores to become unstable.     

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.     

Microwave amplification in a coaxial slow-wave plasma transmission line

Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely with plasma. The eigenmodes of the plasma-filled coaxial line are studied, as well as how they are affected by the plasma density. It is shown that, in the presence of a plasma, the microwaves are amplified to a significantly greater extent and the spectrum of the generated microwaves is broader. The nonlinear amplification regime is analyzed. The maximum possible amplitude of the longitudinal electric field and the interaction efficiency are determined as functions of the plasma density. A comparison between the results obtained and the analogous parameters of a vacuum structure shows that plasma-filled hybrid structures are more promising than vacuum sources.     

Feasibility of stabilizing a vacuum-diode X-ray source with a laser-plasma cathode

Results are presented from experimental studies of discharge instabilities and the energy and temporal characteristics of a vacuum-diode X-ray source with a laser plasma cathode over a wide range of energies, intensities, and durations of the plasma-forming laser pulse. It is experimentally shown that the vacuum-discharge dynamics and radiation processes in different discharge stages substantially depend on the parameters of the laser radiation. The shortest recorded pulse duration (10 ns) of Ti K-line radiation (4.5 keV) with a total photon number of 10¹¹ is achieved when the laser plasma cathode is produced by a laser pulse with a duration of 27 ps and an intensity of 10¹³ W/cm². It is found that the contrast of characteristic emission against the bremsstrahlung background is maximum when discharge instabilities are suppressed and the accelerating voltage is three to four times higher than the threshold voltage for line excitation.     

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.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Dynamics of a relativistic electron beam in the vicinity of a spherical injecting body in space plasma

The dynamics of a relativistic electron beam in the vicinity of an injector in the form of a spherical conducting body in a space plasma is considered. An equation describing the radial evolution of a steady electron beam with a self-similar density profile in the electric field of the injector is formulated. A method for calculating the radial evolution of a relativistic electron beam in the vicinity of an injector is developed. The method is based on the numerical integration of a set of ordinary differential equations for the beam radius and field potential in the space charge region under the relevant boundary conditions at the injector surface. Results are presented from numerical simulations of the radial dynamics of an electron beam in the vicinity of a spherical screen system for neutralizing the electric charge carried away by the beam. The numerical results show that the electric field of the injector hastens the beam expansion.     

Formation and nonlinear dynamics of the squeezed state of a helical electron beam with additional deceleration

Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.     

Excitation of magnetic fields by a circularly polarized laser pulse in a plasma channel

The excitation of quasistatic magnetic fields by a circularly polarized laser pulse in a plasma channel is considered. It is shown that, to second order in the amplitude of the electric field of the laser pulse, circular rotation of the plane of polarization of the laser radiation in a radially nonuniform plasma gives rise to a nonlinear azimuthal current and leads to the excitation of the radial and axial components of the magnetic field. The dependence of the magnetic field distribution over the plasma channel on the spatial dimensions of the pulse and on the channel width is investigated for a moderate-power laser pulse. The structure of the magnetic fields excited by a relativistic laser pulse in a wide plasma channel is analyzed.     

Experimental study and numerical simulations of a plasma relativistic microwave amplifier

The dependences of the radiation parameters of a plasma relativistic microwave amplifier on the external factors have been studied both experimentally and numerically. The calculated dependences are found to agree qualitatively with the measured ones. In contrast to experimental studies, numerical simulations make it possible to examine physical processes occurring inside the plasma waveguide. Good agreement between the measured and calculated dependences of the radiation parameters on the external factors shows that information provided by numerical simulations of the processes occurring inside the plasma waveguide can be considered quite reliable. The electromagnetic field structure and electron beam dynamics inside the plasma waveguide have been investigated.