The non-linear interaction of a powerful light beam with crystal lattice vibrations

The interaction of a powerful light beam with a one dimensional crystal lattice consisting of anisotropic and axially symmetric molecules is discussed. Translational and rotational vibrations are taken into account.     

Diffraction of X-ray spatially inhomogeneous beam in a crystal with cubic nonlinearity

Diffraction of a spatially inhomogeneous X-ray wave was theoretically studied in a crystal with cubic nonlinear response to the strength of an external electric field. Using numerical calculations in case of two-beam diffraction of a narrow incident beam, the intensity distributions on the output surface of the crystal was investigated depending on the thickness and intensity of the incident beam. The results of numerical calculations of integral (spatial) coefficients of transmission and reflection are given as functions of incident wave intensity for fixed thickness of the crystal.     

The effect of the vertical divergence of an X-ray beam on rocking curves of a mosaic crystal

The effect of the vertical divergence of a beam on the maximum and integrated intensity and width of rocking curves of a mosaic crystal is studied in this paper. Equations are derived expressing to what extent the geometrical arrangement reduces the intensity of the rays that do not lie in the goniometer plane. By means of these relations it is possible to estimate what slit height is to be chosen at the given arrangement so that the reflections of all blocks of the crystal may be registered and the area of the rocking curve may give the integrated intensity of the reflection. The change of the width of the rocking curve in dependence on the change of slit heights is influenced by the distribution of orientations of the blocks. Calculated relations were verified by the measurement of rocking curves of an iron-silicon alloy crystal.     

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.     

Instability of a cholesteric liquid crystal in an ultrasonic field

A new approach to the analysis of orientation instability of a cholesteric liquid crystal in an ultrasonic field is substantiated experimentally. The approach employs the ideas of nonequilibrium hydrodynamics and takes account of the relaxational properties of the mesophase. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 866–870 (10 June 1996)     

High-efficiency volume reflection of an ultrarelativistic proton beam with a bent silicon crystal

The volume reflection phenomenon was detected while investigating 400 GeV proton interactions with bent silicon crystals in the external beam H8 of the CERN Super Proton Synchrotron. Such a process was observed for a wide interval of crystal orientations relative to the beam axis, and its efficiency exceeds 95%, thereby surpassing any previously observed value. These observations suggest new perspectives for the manipulation of high-energy beams, e.g., for collimation and extraction in new-generation hadron colliders, such as the CERN Large Hadron Collider.     

Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness

Vortex-wave beams are beams that carry angular momentum. Their specific feature is a ring-like transverse distribution of wave intensity with zero intensity at the axis. A method for generating an ultrasonic vortex beam by combining a single-element transducer and a phase plate with a nonuniform thickness is proposed. The method is examined theoretically and tested experimentally. In the theoretical analysis, the acoustic field was calculated using the Rayleigh integral. Experiments were performed in water with a focusing piezoceramic source with a frequency of the order of 1 MHz; the radiation from it was transmitted through a 12-sector organic-glass phase plate. The beam vorticity was established by setting the correct thickness of sectors. The results of scanning the field with a miniature hydrophone confirmed that the amplitude and phase distributions of the generated wave field were in fact consistent with a vortex beam. The capacity of the obtained beam to induce the rotation of scatterers positioned in the focal region was demonstrated.     

Magnetostriction of a single crystal of nickel observed with an X-ray four-circle goniometer

We proposed a technique to observe magnetostrictive coefficients of a single crystal specimen with X-ray diffraction. An angle between a direction of crystallographic orientation and a direction of magnetic field could be estimated with two kinds of diffraction peaks which were found with an X-ray four-circle goniometer. The magnetostriction was measured by a shift of Bragg angle. This technique was suitable for a case to observe the magnetostrictive coefficient which varied as a function of the magnetic field direction. We applied the technique to a single crystal specimen of nickel and showed dependences of the magnetostriction on the magnetic field strength and its direction around an axis of easy magnetization at room temperature.     

Thickening of a smectic membrane in an evanescent X-ray beam

We report an unusual thickening of smectic membranes under the influence of X-ray irradiation below the critical angle. In the case of a four-layer film the thickness was found to grow at the footprint of the beam, reaching within minutes tens of layers. The effect is attributed to the localized energy dissipation of the evanescent wave. The island thus created is not connected to the meniscus and after the beam is switched off the film returns to its original state. A possible explanation is given in terms of a local disrupture of the tension of the smectic membrane.Received: 22 July 2004, Published online: 1 October 2004PACS: 61.30.-v Liquid crystals - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 52.25.Os Emission, absorption, and scattering of electromagnetic radiation     

On the weakly damped vibrations of a vertical beam with a tip-mass

In this paper the wind-induced, horizontal vibrations of a weakly damped vertical Euler-Bernoulli beam with and without a tip-mass will be studied. The damping is assumed to be boundary damping and global Kelvin-Voigt damping. The boundary damping is assumed to be proportional to the velocity of the beam at the top. The horizontal vibrations of the beam can be described by an initial-boundary value problem. In this paper, the multiple-timescales perturbation method will be applied to construct approximations of the solutions of the problem. Also it will be shown that a combination of boundary damping and Kelvin-Voigt damping can be used to damp the wind-induced vibrations of a vertical beam with tip-mass uniformly.     

Non-linear vibrations of a simple-simple beam with a non-ideal support in between

A simply supported Euler-Bernoulli beam with an intermediate support is considered. Non-linear terms due to immovable end conditions leading to stretching of the beam are included in the equations of motion. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the intermediate support is assumed to allow small deflections. An approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. Ideal and non-ideal frequencies as well as frequency-response curves are contrasted.     

X射线在折射率连续变化等离子体介质中的传播

 从Maxwell方程出发，得到了X射线光束在非均匀等离子体介质中传播的类衍射积分解，并从理论和数值模拟上着重讨论了折射率梯度效应对光束参数的影响。结果表明，在等离子体电子密度分布较高的区域，梯度效应明显，它直接影响光束的光强分布、衍射效应和光束的偏转程度。     

X射线在折射率连续变化等离子体介质中的传播

从Maxwell方程出发,得到了X射线光束在非均匀等离子体介质中传播的类衍射积分解,并从理论和数值模拟上着重讨论了折射率梯度效应对光束参数的影响。结果表明,在等离子体电子密度分布较高的区域,梯度效应明显,它直接影响光束的光强分布、衍射效应和光束的偏转程度。     

Dynamic behaviour of a beam subjected to a force of time-dependent frequency

It is a well-known fact that, for an ideal system in which damping is ignored, the deflection of a beam becomes infinite for the case where the constant frequency of a steady-state external force is equal to the critical frequency of the beam. In this paper, the external force is assumed to be proportional to $\text{sin}\text{(}\text{at}{}^2\text{2}\text{+}\text{bt}{}^3\text{3}\text{)}$ with respect to time, where a and b are constants, and the effect of time-dependent frequency on the dynamic behaviour of the beam is investigated. Integrations involved in the theoretical results are carried out by Simpson's rule. From the results of the theoretical analysis, it is evident that the maximum values of the dynamic deflection are much affected by the time-dependence of the frequency of the external force when it passes through the critical frequency, increasing or decreasing.     

Transient vibrations of a beam/mass system fixed to a rotating body

Transient flexural vibrations of a beam/mass system fixed to a rotating body are investigated. The rotating body is driven so as to have a velocity profile of trapezoidal shape. The governing ordinary differential equations of the beam mass system are derived by use of the extended Galerkin method, and the transient response is obtained by the Laplace transformation. Then the effects of the flexibility of the beam and the rotational period of the rotating body upon the flexural vibrations are investigated.     

Forced non-linear vibrations of a damped sandwich beam

Forced, damped, non-linear, low-frequency flexural motions of a clamped-clamped sandwich beam with thin face sheets and a soft viscoelastic core are examined experimentally and theoretically. The theory employed neglects the extensional rigidity of the core and treats the face sheets as membranes. The non-linearity stems from axial stretching of the face sheets. Damping is taken into account by modeling the core as a Kelvin solid, with the material parameters used being obtained experimentally as functions of frequency and temperature. Theoretical frequency-amplitude relations are obtained using Galerkin's procedure and the method of harmonic balance. Results on fundamental natural frequencies, mode shapes, and stability are also presented. In the experiment, mechanical contact with the specimen was avoided by employing electromagnetic forcing and using a proximeter to measure displacements. Also, special attention was given to the interface bonds and to the reproduction, as close as possible, of clamped-clamped conditions. Agreement between the theoretical and experimental results is, in general, quite good.