Structure Of Wave Field Research Articles

Global eigenmodes of low frequency waves in field-reversed configuration plasmas

Global eigenmodes of low frequency waves in field reversed configuration (FRC) plasmas have been obtained using the magnetohydrodynamic (MHD) model and one-dimensional equilibrium model. Dispersion relation and radial structure of the global wave fields are shown for the azimuthal mode number m=0. The results are compared with the results of a low frequency wave heating experiment. Possibilities of ion heating by the ion cyclotron damping, the transit-time magnetic damping, and Landau damping are discussed.

Measurement of 2-D sea surface elevation fields using complex synthetic aperture radar data

A method is presented to derive two-dimensional sea surface elevation fields from complex synthetic aperture radar (SAR) data. Applied to spaceborne SAR data as acquired by European Remote Sensing 2 (ERS-2) or the Environmental Satellite (ENVISAT), the method allows to analyze the structure of ocean wave fields, e.g., wave grouping or individual wave heights on a global scale. The technique, thus, provides wave parameters not obtained with common SAR wave retrieval schemes, which are designed to estimate the 2-D wave spectrum, i.e., second-order statistical moments of the wave field. Estimates of sea surface elevation fields are obtained based on the existing theory of SAR ocean wave imaging, i.e., the modulation of the SAR image intensity due real aperture radar and motion-related effects. A power series expansion is derived for SAR intensity images that enables the analysis of nonlinear effects as well as to derive a quasi-linear approximation of the SAR imaging model in the spatial domain. A statistical analysis is performed based on a global dataset of 2D wave spectra provided by the European Centre for Medium-Range Weather Forecast. Distributions are given for the relative error of the quasi-linear approximation in the spatial domain. It is shown that the error can be reduced by smoothing the SAR image in the azimuthal direction at the cost of lower resolution. Smoothed elevation fields are retrieved by the minimization of a cost function defined in the Fourier domain based on the quasi-linear approximation of the imaging process. A multilook technique is applied to infer the information on wave propagation directions, which is required because the SAR transfer function is non-Hermitian, i.e., the SAR image is not determined by the frozen sea surface, but wave motion has a significant impact. The method is applied to simulated SAR images as well as to data acquired by ERS-2. The errors of the retrieved wave field due to image noise, uncertainties in the SAR imaging model, and bandwidth limitations are analyzed. In particular, the fact that the estimated elevation field is smoothed due to the finite system resolution and smearing effects associated with wave motion is discussed. A statistical test is proposed to check the homogeneity of the SAR image. The method makes sure that atmospheric effects are not misinterpreted as being caused by ocean waves.

Observations of inertial waves in a rectangular basin with one sloping boundary

Inertial waves in a homogeneous rotating fluid travel along rays that are inclined with respect to the rotation axis. The angle of inclination depends solely on the ratio of the wave frequency and twice the angular frequency. Because of this fixed angle, the waves can become focused when reflected at a sloping wall. In an infinitely long channel with a sloping wall, the repeated action of focusing may lead to the approach to a limit cycle, the so-called wave attractor, where the energy is concentrated. This effect is studied in the laboratory in a rectangular tank with one sloping wall, placed excentrically on a rotating table. The waves are excited by modulation of the background rotation. Several frequency ratios are used to study different wave attractors and one standing wave. The observations consist mainly of particle image velocimetry data in horizontal and vertical cross-sections in one half of the basin. The attractors are observed in the vertical cross-sections. They show continuous phase propagation, which distinguishes them from the standing wave where the phase changes at the same time over the whole cross-section. However, particle motion of inertial waves is three-dimensional and the actual basin is not an ideal twodimensional channel but is of finite length. This implies that the waves must adapt to the vertical endwalls, although a prediction of the nature of these adaptations and the structure of the three-dimensional wave field is at present lacking. For critical waves, whose rays are parallel to the slope, clear three-dimensional behaviour is observed. The location of most intense motion along this critical slope attractor changes in the horizontal direction and horizontal phase propagation is observed, with a wavelength between 1/5 and 1/4 of the basin length. For the other attractors there is little evidence of phase propagation in the horizontal direction. The motion along the attractor is however stronger near the vertical endwalls for attractors with wave rays of slopes close to 1 or larger. The standing wave and the other attractors are more clearly visible near 1/5 of the tank length.

Axial structure of plasma column sustained by non‐symmetric electromagnetic surface wave

AbstractThis article presents the results of theoretical study of the axial structure of gas discharge that is sustained by a non‐symmetric electromagnetic surface wave (SW) with azimuth wavenumber m = –2. The phase and attenuation characteristics of the wave, and the spatial wave field structure were studied as well. The wave considered propagates along the magnetized slightly nonuniform in axial direction plasma column and sustains it. The influence of external magnetic field value and finite plasma column radius on the discharge stability, on the plasma density axial profile and on the SW properties has been studied in the case of the diffusion regime of gas discharge sustaining.

Self-Focusing and Channeling of Wave Beams in a Nonuniform Magnetic Field under Conditions of Ionization Nonlinearity

We study experimentally the effect of ionization self-channeling of waves at the whistler frequencies in a nonuniform magnetic field. It is shown that the formed plasma nonuniformity localizes the radiation from a short high-frequency source inside a discharge channel stretched along an external magnetic field. We found a possibility to control the parameters of the formed plasma-wave channel as well as the dispersion characteristics and structure of wave fields in wide limits by varying the magnetic field in a specified spatial region. We propose a method for the formation of a plasma resonator and test this method in the laboratory experiment. The spatial plasma and field distributions in this resonator are similar to those along a geomagnetic field tube of the magnetospheric resonator. We reveal the plasma instability in such a resonator in the vicinity of the frequency of electron bounce oscillations between magnetic mirrors.

Canonical transform method for processing radio occultation data in the lower troposphere

The methods of processing radio occultation data in multipath zones which were used up to now have very strong restrictions of the applicability. In this paper, we introduce a new approach to the problem of deciphering the ray structure of wave fields in multipath zones using the short‐wave asymptotic solution of the wave problem. In geometric optics a canonical transform resolves multipath by introducing new coordinate and momentum in such a way that different rays are distinguished by their coordinates. The wave field is processed by a Fourier integral operator associated with the canonical transform. The transformed wave function can then be written in the single‐ray approximation, which allows for the determination of refraction angles from the derivative of the eikonal. The new method retains all the advantages of the back propagation such as the removal of effects of diffraction in free space and the enhancement of the vertical resolution in retrieved profiles, but it has much wider applicability limits. The method is convenient for operational applications. We discuss a fast numerical implementation of the method and present the results of numerical simulations confirming the applicability of the method.

Ion sense of polarization of the electromagnetic wave field in the electron whistler frequency band

Abstract. It is shown that the left-hand (or ion-type) sense of polarization can appear in the field interference pattern of two plane electron whistler waves. Moreover, it is demonstrated that the ion-type polarized wave electric fields can be accompanied by the presence at the same observation point of electron-type polarized wave magnetic fields. The registration of ion-type polarized fields with frequencies between the highest ion gyrofrequency and the electron gyrofrequency in a cold, overdense plasma is a sufficient indication for the existence of an interference wave pattern, which can typically occur near artificial or natural reflecting magnetospheric plasma regions, inside waveguides (as in helicon discharges, for example), in fields resonantly emitted by beams of charged particles or, in principle, in some self-sustained, nonlinear wave field structures. A comparison with the conventional spectral matrix data processing approach is also presented in order to facilitate the calculations of the analyzed polarization parameters.Key words. Ionosphere (wave propagation) Radio science (waves in plasma) Space plasma physics (general or miscellaneous)

Collapse and revival of the matter wave field of a Bose-Einstein condensate.

A Bose-Einstein condensate represents the most 'classical' form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Nevertheless, the matter wave field has a quantized structure owing to the granularity of the discrete underlying atoms. Although such a field is usually assumed to be intrinsically stable (apart from incoherent loss processes), this is no longer true when the condensate is in a coherent superposition of different atom number states. For example, in a Bose-Einstein condensate confined by a three-dimensional optical lattice, each potential well can be prepared in a coherent superposition of different atom number states, with constant relative phases between neighbouring lattice sites. It is then natural to ask how the individual matter wave fields and their relative phases evolve. Here we use such a set-up to investigate these questions experimentally, observing that the matter wave field of the Bose-Einstein condensate undergoes a periodic series of collapses and revivals; this behaviour is directly demonstrated in the dynamical evolution of the multiple matter wave interference pattern. We attribute the oscillations to the quantized structure of the matter wave field and the collisions between individual atoms.

Internal gravity wave emission from a pancake vortex: An example of wave–vortex interaction in strongly stratified flows

At small Froude numbers the motion of a stably stratified fluid consists of a quasisteady vortical component and a propagating wave component. The vortical component is organized into layers of horizontal motions with well-pronounced vertical vorticity and often takes the form of so-called “pancake” vortices. An analytical model of such a vortex that is a solution of the Euler–Boussinesq equations at a vanishing Froude number is constructed as a superposition of horizontal two-dimensional Kirchhoff elliptic vortices. This vortex is nonstationary and internal gravity waves are, therefore, excited by its motion. The radiation properties are studied by matching the vortex field with the far internal gravity wave field according to the procedure applied in acoustics to determine vortex sound. The structure of the gravity wave field is completely quantified. By calculating energy and angular momentum fluxes carried by outgoing waves and attributing them to the adiabatic change of the vortex parameters, we calculate the backreaction of the internal gravity waves radiation and show that, as in the case of acoustic radiation by the Kirchhoff vortex, this adiabatic evolution leads to an elongation of the vortex, and its eventual destabilization.

Wave-field structure in active bubble systems in shock tubes with discontinuities in cross section

The wave structure in active bubble media in shock tubes with sudden changes of profiles in the form of “discontinuities” in cross section and a one‐phase liquid waveguide is analyzed numerically. In axisymmetric formulation, the paper studies wave amplification due to reflection from a wall and focusing at the butt‐end of a rigid rod aligned coaxially with the channel. In this configuration, the amplification effect results from two‐dimensional cumulation of the shock wave after it leaves the annular channel and reaches the butt‐end of the rod. A Mach configuration forms in the focus spot. The geometrical characteristics of the shock tube allow one to control (to some extent) the amplification coefficient and the coordinates of the focus spot. In particular, it is shown that the wave can be focused near the second discontinuity of cross section — a rigid wall (in the region of passage through the interface to the waveguide) — and intensified upon reflection. If the waveguide radius is equal to the height of the Mach stem, the reflected wave has a maximum amplitude.

Poincaré vortices

Traditional interferometric methods for measuring the vortex structure of complex wave fields suffer from many intrinsic problems and seldom yield results of any accuracy. Using the unique properties of what I call Poincaré vortices, I develop a radically different method based on Stokes parameters that offers many practical advantages. The theory of this new method is discussed, and its unique capabilities are illustrated by reconstruction with high accuracy of the vortex structure of a simulated random field containing numerous vortices, including several closely spaced vortex pairs that would be difficult, if not impossible, to resolve by traditional means.

Diagnosing the effective parameters of the ionospheric fine structure from statistical characteristics of radio waves in the vicinity of a regular caustic

This paper is concerned with the oblique propagation of decametric radio waves in the ionosphere with random electron density irregularities. Effective parameters are introduced for calculating the influence of irregularities on the wave field structure. A technique is proposed for determining these parameters from measurements of statistical characteristics of the signal in the vicinity of a regular caustic. The technique uses asymptotic expressions obtained using the interference integral method and perturbation theory, as well as matching them to the numerical solution on the basis of the method of characteristics. A global semi-empirical model that is updated for current ionospheric conditions is used to specify the background medium. The proposed technique has been tested using data from a number of mid-latitude paths. Results obtained in this study testify that the technique deserves a practical implementation.

The spatial structure of the acoustic wave field generated in the atmosphere by a point explosion

The Mill Race experiment is used as an example to demonstrate the possibility of calculating the propagation characteristics of acoustic impulses generated by surface point explosions up to ionospheric heights with the use of the models that are based on the known exact solutions for homogeneous media with corrections for inhomogeneity. It is shown that, in the terrestrial atmosphere, the height where the amplitude of the particle velocity of an acoustic impulse reaches its maximum is independent of both the explosion power and the angle of departure of an acoustic ray. This height is about 120 km and depends mainly on the vertical atmospheric density profile.

Quadrupole and Octopole Electromagnetic Waves in Slightly Non-Uniform Magnetized Plasma Column

The paper presents the results of a theoretical study of the dispersion properties, wave field structure and energy characteristics of travelling electromagnetic nonsymmetric surface waves that propagate along a magnetized plasma column surrounded by an infinite vacuum region. The waves with azimuth wave numbers m = ±2, ±3 were considered. An external constant magnetic field parallel with respect to the axis of the waveguide system is applied. The theoretical study is carried out using a hydrodynamic model of a cold, radially uniform plasma. The influence of external magnetic field strength and the finite plasma column radius on the dispersion, attenuation and radial wave field structure is studied in the approximation of weak longitudinal plasma density non-uniformity. It is shown, that the external magnetic field essentially affects the dispersion, radial wave field structure and wave damping. Research carried out allows one to estimate the possibility of quadrupole and octopole modes use for gas discharge sustaining. The analysis of the obtained results makes it possible to estimate the plasma density, that can be sustained in gas discharges on quadrupole and octopole waves.

Interaction of Solitons as Compound Structures in the Gardner Model

Analysis of the modernized approximate description of the interaction of solitary waves as particles allows one to find a new representation of the known exact N-soliton solutions which have the form of a superposition of solitons whose parameters vary relatively slowly. The approximate solutions have the same form as the exact ones, differing from the latter by only the accuracy of representation of the spatio-temporal dependence of the solitary-wave parameters. The approximate description exhibits efficiently the details of the collision, which significantly complements the general picture of soliton interaction within the framework of particular models. These statements are discussed using the example of soliton interaction within the framework of the Gardner model. The specific features of the interaction in this case are caused by the compound structure of solitons, which allows one to analyze them as a superposition of kinks (field steps) of different polarity. We develop a clear and rigorous picture of soliton interaction, which enables us to find previously unknown solutions. In particular, such solutions can have the form of envelope kinks changing the structure of the initial wave field during propagation along infinite sequences (chains) of solitons.

The Transmission and Transformation of Baroclinic Rossby Waves by Topography*

Abstract The transmission of westward propagating baroclinic Rossby waves incident on a gappy meridional barrier is studied in the context of the two-layer, quasigeostrophic model. The meridional barrier models the presence of very steep topography such as the midocean ridge system or extensive island arcs. The nature of the transmission depends strongly on the nature of the gaps in the meridional barrier. If the gaps extend throughout the depth of the fluid, the Rossby waves propagate through the barrier, as a consequence of Kelvin’s theorem, with no change in vertical structure. On the other hand, if the gaps in the barrier are partial and extend only over a single layer, there is a significant transformation of the vertical structure of the wave field as it traverses the barrier. In particular, waves of baroclinic vertical structure in the model are transformed on the western side of the barrier into barotropic waves that radiate from the segment of the barrier between two such gaps. Such segments act ...

On the investigation of the stressed state of the elastic and piezoelectric bodies

The solutions of the set of dynamic problems on the oscillations of the electroelastic prestressed medium is the basis of the detailed analysis of the influence of the initial stressed state’s type and initial stress’s value to the structure of the surface wave field and to the resonance phenomena arising from the interaction between the medium and the external concentrated elements. The initial stressed state is considered to be homogeneous or changing with the depth. It has been defined by the parameters of the external concentrated elements under which the initial stress’s influence to the dynamics is maximal. The high efficiency of using the resonance phenomena for the nondestructive control of stressed state’s character and the initial (residual) stress’s value has been established. [Work supported by RFFI.]

Nonclassical Dense Gas Flows for Simple Geometries

Two-dimensional shock wave reflection and refraction phenomena for dense gases in the high pressure and density region near the thermodynamic critical point are compared and contrasted to shock phenomena over well-known configurations for dilute, perfect gases. Both transient and steady wave fields are simulated using a time-accurate, predictor-corrector total variation diminishingscheme that solves the Euler equations incorporating the van der Waals thermodynamic model. Detailed displays of wave field structure for both perfect gas and dense gas flowfields are shown. Nonclassical wave phenomena, such as disintegrating shocks, expansion shocks, and shock-fan composite waves for wedges, ramps, circular arcs, and other geometries, demonstrate significant differences in dense gas flowfields from those of perfect gases

Toroidal mode conversion in the ICRF

Mode conversion is studied in the ion cyclotron range of frequencies (ICRF), taking into account the toroidal geometry relevant for tokamaks. The global wavefields obtained using the gyrokinetic toroidal PENN code illustrate how the fast wave propagates to the neighbourhood of the ion-ion hybrid resonance, where it is converted to a slow wave that deposits the wave energy through resonant Landau and cyclotron interactions with the particles. The power deposition profiles obtained are dramatically different from the toroidal resonance absorption, showing that Budden's fluid model is not a good approximation in the torus. Radially and poloidally localized wavefield structures characteristic of slow wave eigenmodes are predicted, which could be used in experiments to form transport barriers and to interact with fast particles.

Whistler waves emission by a modulated electron beam: Nonlinear theory

The nonlinear theory for the interaction of a thin modulated electron beam with a monochromatic whistler wave is considered. On the basis of wave field structures calculated previously in the linear approach, equations describing the wave amplitude evolution inside and outside the beam are obtained. These equations, together with the equations for particle motion in the drift approximation, form the self-consistent nonlinear model. Double and single pole resonance cases are considered. The full system of equations (taking into account the finite size of the beam) is resolved by a computer code which yields clear physical results. This code avoids the heavy structure and the long computer time inherent in the usual Particle-In-Cell simulation codes.