The structural features of wave collapse in medium with normal group velocity dispersion

The dynamic characteristics of self-action in three-dimensional wave packets described by the nonlinear Schrödinger equation with a hyperbolic space operator were studied analytically and numerically. The class of the initial wave field distributions for which self-focusing effects predominated over dispersion spreading and caused the arising of wave collapses was considered. The collapse of tubular wave packets was shown to be accompanied by packet shape changes during its contraction to the axis of the system. The nonlinear stabilization of collapses resulted in wave field fragmentation in the longitudinal direction followed by the expansion of the bunches thus formed along the axis. The dynamics of collapses was numerically studied taking into account medium nonlinearity saturation and nonlinear dissipation.     

部分Bessel形电磁波

给出了满足Maxwell方程的自弯曲电磁波解(部分Bessel函数), 其可以通过发射调制初始相位和发射方向的一组平面波干涉合成来实现. 自弯曲电磁波在一定传播距离内保持波束形状不变, 其传播轨道接近圆形. 这类曲线加速的电磁波不同于Ariy波束, 其中部分Bessel波束的弯曲角度可以远大于Ariy波. 半Bessel 波束的Poynting矢量表明主瓣能够保持能量不扩散且偏转接近180°. 此外, 同时发射一对半Bessel电磁波能够在一定区域内实现对消, 即在该域内实现电磁波自屏蔽.     

Nonlinear gravitational waves on the surface of viscous fluid: Lagrangian approach

The problems of the asymptotic theory of weakly nonlinear surface waves in viscous fluid are discussed. For standing waves on deep water, the solutions obtained in the first- and second-order approximations in a small parameter—wave steepness—are analyzed. The evolution equation for the amplitude of wave packet envelope is obtained where the inverse Reynolds number is equal to the squared steepness. It is shown that this is a nonlinear Schrödinger equation with linear dissipation.     

Modulational Instability of Ion-Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting ofwarm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schrodinger equationincluding one additional term that comes from the effect of relativistic electron beam is derived. It is found that theinclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could notadmit any stationary soliton waves.     

A stationary phase argument for the modal wave beam deviation in the time-space domain for anisotropic multilayered media

The aim of the paper is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic multilayered media by a monochromatic incident beam and then by a time depending signal. A modal beam is generated in the structure and, due to the anisotropy of the media constituting the structure, is deviated with respect to the sagittal plane of the incident bounded beam. Using a stationary phase approach, it is possible to determine the deviation direction of the modal beam in the far field at a given frequency. This direction is normal to the modal curve, at the point corresponding to the main modal wave vector. Using Lagrange multipliers, it is possible to obtain the equation of an oblique plane in which the modal beam reradiates in the external fluid. As the modal waves are dispersive, the group velocity and the direction of propagation of the principal modal wave vary with the frequency. So, in the far field, for a time depending signal, the different monochromatic components of the main modal wave are found in different directions. In general, the main crest line of this modal wave packet is not a straight line.     

Excitation of wake-field waves in plasma by a microtron beam

The experimental study of excitation of wake-field waves in plasma by a sequence of electron bunches of a microtron beam has been carried out. Results of measurement of the spectrum of electrons after their passage through plasma confirm the effect of adding of waves from a sequence of about 100 bunches which leads to the increase in the amplitude from 1 V/cm up to 100 V/cm.     

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.     

Atom-optics holograms

The temporal evolution of atomic wave packets interacting with object and reference electromagnetic waves is investigated, and an analytical solution for the off-resonant density matrix is presented. It is shown that, under certain physical conditions, the diffraction of an ultracold atomic beam by an inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram. We show that high diffraction efficiencies can be realized if one restricts the extent of the atomic hologram in the time domain rather than in space. The hologram, thus, can work in a pulsed regime pumping atoms from the beam or from the initial wave packet into the reconstructed matter wave. The suggested regime is well compatible with the Raman cooling methods and the recent realization of an atom laser, which are capable of repeatedly reproducing coherent, or almost coherent, atomic wave packets necessary for the actual implementation of the reading beam. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis, a new method for the reconstruction of the object image with matter waves is offered. The latter may have useful practical applications, ranging from atom lithography, to the manufacturing of microstructures, and quantum microfabrication.     

Nonlinear transformation of wave packets in weakly dispersive media

We study the propagation of nonlinear modulated waves in weakly dispersive media within the framework of the Korteveg- de Vries equation. It is shown that strong generation of overtones and mean flow by the modulated packet results in asymmetry of the wave packet envelope with respect to both horizontal and vertical axes and makes the envelope skewed. The motion of the wave packet is accompanied by the emission of low-frequency and high-frequency waves that propagate in different directions from the packet. As a result, the mean amplitude of the wave packet decreases with distance. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 354–358, April 1999.     

Diffraction of the wave packet of a three-level Λ atom in the field of a multifrequency standing light wave

The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997)     

A plasma klystron for generating ultra-short electron bunches

A technique for producing ultra-short electron bunches (e.g., ⩽100 fs) from a continuous electron beam using a short plasma wave section and a drift space is explored. The bunches are a fraction of a plasma wavelength long and are spaced by a plasma wavelength, making them of interest for injection into plasma accelerators or for driving a klystron-like structure to produce infrared radiation     

Laser-wakefield acceleration of monoenergetic electron beams in the first plasma-wave period

Beam profile measurements of laser-wakefield accelerated electron bunches reveal that in the monoenergetic regime the electrons are injected and accelerated at the back of the first period of the plasma wave. With pulse durations ctau >or= lambda(p), we observe an elliptical beam profile with the axis of the ellipse parallel to the axis of the laser polarization. This increase in divergence in the laser polarization direction indicates that the electrons are accelerated within the laser pulse. Reducing the plasma density (decreasing ctau/lambda(p)) leads to a beam profile with less ellipticity, implying that the self-injection occurs at the rear of the first period of the plasma wave. This also demonstrates that the electron bunches are less than a plasma wavelength long, i.e., have a duration <25 fs. This interpretation is supported by 3D particle-in-cell simulations.     

Dissipative quantum chaos: transition from wave packet collapse to explosion

Using the quantum trajectories approach, we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which follows classical chaotic dynamics and whose area is proportional to the Planck constant. At weak dissipation the exponential instability of quantum dynamics on the Ehrenfest time scale dominates and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically disappears leaving place to collapse.     

Theoretical model of phase exclusion conditions for the sum-frequency wave produced by a nonlinear acoustic source

A theoretical model of the sum-frequency wave field produced by a nonlinear acoustic source with three-frequency pumping is reported. The model allows for the dissipation and diffraction of the Gaussian beam. The sum-frequency wave is represented within the second-order approximation as a superposition of two synchronous copropagating waves with equal frequencies. It is shown that the spatial and amplitude-phase characteristics of the sum-frequency wave are affected not only by the amplitude-phase relations in the pumping spectrum, but also by the diffraction-caused variations in amplitudes and phases of the primary waves. This dependence is most clearly seen under the phase exclusion conditions, when the generation of the sum-frequency wave is actually suppressed (excluded) owing to the appropriate choice of the amplitude and phase pumping spectra. The theoretical results are found to agree well with experimental data. The possible practical applications of the phase exclusion conditions are as follows: inspection of inhomogeneous media, detection of objects near interfaces, reduction of nonlinear attenuation, acoustic measurements, etc.     

Formation of ultrashort electron pulses on scattering of an electron beam by a standing laser wave of ultrashort duration

The scattering of a well collimated electron beam by a strong standing laser wave of ultrashort duration, giving rise to a great number of scattered photons, is considered. This type of scattering is found to cause an electron beam to divide effectively into two parts. Ultrashort laser pulses are shown to be capable of forming ultrashort electron bunches whose length is governed by the laser beam diameter.     

Packet waves in a reaction-diffusion system

The finite-wavelength instability gives rise to a new type of wave in reaction-diffusion systems: packet waves, which propagate only within a wave packet, are found in experiments on the Belousov-Zhabotinsky reaction dispersed in water-in-oil AOT microemulsion (BZ-AOT) as well as in model simulations. Inwardly moving packet waves with negative curvature occur in experiments and in a model of the BZ-AOT system when the dispersion d omega(k)/dk is negative at the characteristic wave number k(0). This result sheds light on the origin of anti-spirals.     

耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。