Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma IV. Excitation of Nonresonant Waves

A system of nonlinear equations derived in a previous paper which describes the evolution of nonresonant waves in beam-plasma systems is solved numerically. It is given a physical interpretation of essential features of the nonresonant beam-plasma instability. The significant influence of higher harmonics on the evolution of an electron beam in the plasma which is modulated on a nonresonant unstable frequency, is investigated. The interaction of unstable nonresonant and resonant waves in beam-plasma systems is examined. It is shown that the evolution of resonant waves can be essentially influenced by an initial modulation of the beam on an unstable non-resonant frequency. The role of an initial velocity modulation of the beam for the influence of the wave spectrum is demonstrated.     

Electromagnetic Forces on Plasma Particles in the Presence of Resonant and Nonresonant Plasma Turbulence

Nonlinear forces on plasma particles in the presence of a test nonresonant wave and resonant plasma wave turbulence are calculated. The important feature of the considered nonlinear effect is that the forces due to the nonresonant test wave act on the plasma particles in the absence of linear and nonlinear resonances between the wave and the particles. Although in a closed plasma-wave system the process is balanced by the quasilinear interaction between the plasma resonant turbulence and plasma particles (leading to nonstationarity and inhomogeneity of the system), in open systems the effect can be significant.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. V. Excitation of Waves in Strong Dissipative Plasmas by a Monoenergetic Beam

A system of nonlinear equations derived in a previous paper which describes the evolution of the beam-plasma instability in strong dissipative plasmas is solved numerically. It is shown that there are three characteristic solutions of the system of equations: the resonant dissipative instability, the nonresonant instability with strong dissipation and the nonresonant dissipative instability. A physical interpretation of essential features of these instabilities is given. The interaction of resonant and nonresonant waves in the system electron beam-strong dissipative plasma is examined. Some conclusions for the transport problem of electron beams in strong dissipative plasmas are obtained in this paper.     

Generation of pulses upon nonresonant acousto-electromagnetic interaction

New mechanisms of generation of acoustic and electromagnetic soliton-like pulses in an optoelastic medium upon nonlinear nonresonant interaction of the polarization components of an electromagnetic field with acoustic oscillations in the medium are considered. It is shown that the acousto-electromagnetic interaction in such a system may lead to the formation of coherent soliton excitations in a thin crystal plate. It is found that a modulation instability occurs in an extended medium, which is caused by the spatial effects and leads to the generation of transverse sound waves. The evolution of a light field in a one-dimensional extended periodic optoelastic medium is also considered. It is shown that acoustic and electromagnetic solitons can be generated due to the mixing of direct and backward optical waves and their nonresonant interaction with a sound wave.     

Nonlinear Resonant Interaction of Three Extra-ordinary Waves in a Hot Electron Plasma

The coupled mode equations and coupling coefficients for the resonant nonlinear interaction of three extra-ordinary waves in a hot magnetized plasma are derived by Whitham's method of averaged Lagrangian. The wave vectors of the three waves are taken as noncollinear and perpendicular to the external uniform magnetic field. Of the three waves one is of high frequency mode and the other two are of low frequency mode.     

Observation of non-phase-matched parametric amplification in resonant nonlinear optics

The coupling between a resonant excitation and a nonresonant parametric process in a nonlinear system is studied experimentally under non-phase-matched conditions. Our study performed in the context of anti-Stokes stimulated Raman scattering provides a clear observation of the self-induced phase matching of a parametric process. A close agreement with theoretical predictions is observed.     

Heating of ions by Alfvén waves via nonresonant interactions

Finite-amplitude intrinsic Alfvén waves exist pervasively in astrophysical and solar-terrestrial environment. It is generally believed that linear wave-particle resonant interaction between thermal protons and Alfvén waves is ineffective when the proton beta is low. However, this Letter demonstrates that the ions can be heated by Alfvén waves via nonresonant nonlinear interaction. Contrary to the customary expectation, it is found that the lower the plasma beta value, the more effective is the heating process. It is also shown that the ion temperature increase is more prominent along perpendicular direction.     

Stability of ion acoustic turbulent states

Several proposed renormalized theories for strong ion acoustic turbulence are compared to the direct interaction approximation. These are applied to the calculation of the stability of ion acoustic turbulent states to the excitation of Langmuir waves. A kinetic instability proposed by Tsytovich, Stenflo, and Wilhelmsson is shown to be stabilized by resonant and nonresonant decay processes. The global kinetic stability of the Langmuir spectrum is enhanced through the coupling of opposite phase velocity Langmuir waves by the decay processes and by nonresonant scattering to regions of strong Landau damping.     

Nonlinear distribution function for a plasma obeying Vlasov-Maxwell system of equations

The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived, which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and trapped electrons in determining the stability, is also discussed.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Radiation of a charge moving over the diffraction grating

The states of a charged particle with a finite free path are determined in the field of a resonant electromagnetic wave. The exact resonance conditions, the modulation and beam instability mechanisms, the charge and current densities (Ohm's law) are obtained for the collisionless beam of resonance particles. Quantum theory of radiation is developed for the resonant adiabatic interaction between a particle and a wave taking into account the interaction with a constant magnetic field induced at the grating surface by the charge and nonresonant waves. The radiation power, the spectrum, and the range of generated frequencies are determined. The results obtained can be used in the plasma and solid-state theories and in electronics.     

Delocalization of Quantum Kicked Rotator with a Large Denominator

We use the iterative unitary matrix multiplication method to calculate the long-time behaviour of the resonant quantum kicked rotator with a large denominator. The delocalization time is an exponential function of the denominator. The wave function delocalizes through degenerate states. We also construct a nonresonant quantum kicked rotator with delocalization.     

Ninth-order nonlinear polarization and vuv generation in Hg vapor

Interference of resonant ninth-order and nonresonant seventh-order nonlinear polarizations in Hg atoms has been studied, and direct conversion of fundamental ir radiation into the vuv has been obtained. The interference has been observed in the form of a Fano-Boitler contour. The efficiency of generation by ninth-order processes appears to be higher than that by seventh-order.     

Nonlinear interaction between acoustic and orientation waves in liquid crystals

Taking incompressibility of the medium into account is shown to lead to nonlinear coupling between acoustic and orientation waves in a nematic liquid crystal. Equations for three-wave resonant interaction are derived and the regime of nonlinear excitation of orientation waves in the course of propagation of a powerful high frequency acoustic wave in a liquid crystal is investigated.Branch of the Institute of Machine Management, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 146–152, January–February, 1995.     

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).     

Energy spectra of electrons in plasma accelerators

The acceleration of electrons in the fast (relativistic) plasma wave, generated, e.g., by intense laser pulse in an underdense plasma, is studied theoretically and numerically. The analytical method, developed to describe the energy spectrum of electrons accelerated in one-dimensional (1-D) plasma wave of an arbitrary form, predicts the “bunching” of electrons in the energy space for linear (harmonic) plasma wave in contrast to the nonlinear one. The results of one- and two-dimensional (2-D) numerical simulations of the resonant and nonresonant electron bunch acceleration are presented and discussed     

Four-wave mixing in a liquid suspension of transparent dielectric microspheres

The process of four-wave mixing in an artificial heterogeneous nonlinear medium—a liquid suspension of transparent dielectric microspheres—is considered. The dynamics of the concentration response to gradient forces that act on microspheres in the interference field of interacting waves are investigated on the basis of the Smolukhovskii equation. Kinetic equations for the amplitudes of light-induced concentration gratings that take part in the four-wave mixing are obtained with the use of the Fourier series expansion of the distribution function of microspheres. The ratios of the microsphere radius to the grating periods are obtained under which the resultant gradient force vanishes and, hence, a suspension of dielectric microspheres does not exhibit nonlinear properties irrespective of the intensities of the interacting waves. The kinetics of the process of four-wave mixing is investigated under efficient energy exchange between reference, signal, and reversed waves. It is shown that a liquid suspension of transparent dielectric spheres is a highly effective wideband nonlinear medium for reversing the wave front of low-intensity radiation of continuous-wave lasers.     

二能级系统中光场压缩与原子偶极压缩间的对称特性

揭示了共振Ｊａｙｎｅｓ-Ｃｕｍｍｉｎｇｓ模型中光场压缩与原子偶极压缩间的对称特性，并探讨了各种非线性作用包括非共振作用，虚光子过程，任意强度耦合及类Ｋｅｒ介质与腔作用对光场压缩与原子偶极压缩间的对称特性的影响，还讨论了（２ｍ＋１）量子共振下两种压缩间的内在关系     

Travelling Wave Window with Matching Gratings

At millimeter waves, travelling wave dielectric windows are advantageous over commonly used resonant ones due to the higher power capability. An attractive method to compensate the wave reflections from vacuum-dielectric and dielectric-vacuum boundaries is using anti-mirror reflection gratings (Fig. 1) [1]. In this paper, the power loss due to the finite cross-section of the wave beam and the frequency mismatch relative to the resonant value are calulated for the latter type of window.