Linear Wave Transformation Research Articles

Matrix Algorithm of Approximate Solution of Wave Equations in Inhomogeneous Magnetoactive Plasma

The problem of propagation of an electromagnetic wave in plane-stratified magnetoactive plasma is analyzed. A matrix algorithm of approximate solution of a set of wave equations is proposed. The algorithm consists in successive finding of the medium-inhomogeneity-induced corrections to the local roots of the dispersion relation and local polarization vectors. The set of field equations is reduced to a set of algebraic equations. The proposed algorithm is convenient for numerical calculations. In contrast to the classical geometrical-optics approximation, the proposed algorithm allows one to take into account the weak effect of linear mode interaction. Examples of numerical calculations of the power reflection coefficient of whistler waves incident on the ionosphere from above are presented. The proposed matrix algorithm can be useful to find the coefficients of reflection and linear transformation of waves in a smoothly inhomogeneous ionosphere.

On the Effect of Small-Angle Scattering by Density Fluctuations on the Efficiency of Linear Transformation of Ordinary and Extraordinary Waves in a Toroidally Inhomogeneous Plasma

We have analyzed the efficiency of tunneling of quasi-optical wave beams through the evanescent region in the vicinity of plasma cutoff in a randomly inhomogeneous magnetoactive plasma. A new theoretical model proposed here makes it possible to study the effect of a random phase modulation induced by density fluctuations in the wave beam path on the efficiency of the linear transformation of waves in the 2D geometry corresponding to the experimental conditions for heating the overdense plasma in toroidal magnetic systems. We have derived a general analytic expression connecting the wave beam coefficient of transformation averaged over the ensemble of random wave field realizations with its phase correlation function. We have analyzed the dependence of the coefficient of transformation on the correlation length for the random phase distribution in the beam and on the traversed path length to the interaction region. The threshold value of the path length above which the fluctuations produce a dominating effect has been determined. The importance of taking into account the 2D effects has been demonstrated.

Analytical study for linear wave transformation by a trapezoidal breakwater or channel

In various field applications in coastal and ocean engineering such as design of offshore borrow pits, navigation channels, subaqueous dredged material placement sites and submerged breakwaters, numerical wave transformation models based on the mild-slope equation (MSE) are commonly used since trench/channel or shoal/breakwater slopes often do not exceed 1:1 in practice given these are controlled by the angle of repose of sediments or in the case of submerged breakwaters by design criteria which typically recommend slopes not exceed 1:1.5. MSE-based analytical solutions confirming their validity to represent important processes such as wave reflection are important. In this paper, an analytical solution to the modified MSE (MMSE) in terms of Taylor series is constructed for wave transformation by a trench or breakwater with general trapezoidal shape. This solution is superior to previous analytical solutions based on the long-wave equation and the MMSE. It is also superior to the step method and the eigenfunction expansion method based on the Laplace equation in the sense that approximation to sloped transitions by steps is avoided. It is shown through intensive comparisons and tests that the present analytical model is valid for a trench/channel or shoal/breakwater with the maximal slope being at least 1:1.5.

On linear transformation of waves in a two-dimensional inhomogeneous magnetized plasma with collisional absorption

UDC 537.876 We consider the linear coupling of waves in the electron-cyclotron frequency range in a nonone-dimensional inhomogeneous magnetized plasma in the vicinity of the plasma cutoff surface with allowance for their collisional dissipation. Model wave equations describing the normal wave interaction in the considered case are formulated and solved analytically. Effects of the absorption anisotropy typical of magnetized plasma on the linear mode coupling in two-dimensional inhomogeneous geometry are analyzed.

Long surface wave dynamics along a convex bottom

Long linear wave transformation in a basin of varying depth is studied for a case of a convex bottom profile h(x) ∼ x4/3. This bottom geometry provides the “nonreflecting” wave propagation at least in the framework of the one‐dimensional shallow water equation. In this case, shoaling effects are very strong and wave reflection occurs in the immediate vicinity of the shoreline. The existence of traveling wave solutions (which propagate without reflection) in this geometry is established through construction of a 1:1 transformation of the general 1‐D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two traveling waves propagating in opposite directions and allows a detailed description of the wavefield (vertical displacement and depth‐averaged flow). It is found that generally a zone of weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long‐wave runup on a beach with this profile is studied for the sine pulse, Korteweg‐de Vries soliton, and N wave. It is shown that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the border of a shallow coastal area of constant depth and a section with the convex profile shows that a transmitted wave always has a sign‐variable shape. Results of the wave transformation above the convex beach and beaches following a general power law are compared. This simplified model demonstrates the potential importance of the tsunami wave transformation along convex beaches.

Excitation and trapping of lower hybrid waves in striations

The theory of lower hybrid (LH) waves trapped in striations in warm ionospheric plasma in the three-dimensional case is presented. A specific mechanism of trapping associated with the linear transformation of waves is discussed. It is shown analytically that such trapping can take place in elongated plasma depletions with the frequencies below and above the lower hybrid resonance frequency of the ambient plasma. The theory is applied mainly to striations generated artificially in ionospheric modification experiments and partly to natural plasma depletions in the auroral upper ionosphere. Typical amplitudes and transverse scales of the trapped LH waves excited in ionospheric modification experiments are estimated. It is shown that such waves possibly can be detected by backscattering at oblique sounding in very high frequency (VHF) and ultra high frequency (UHF) ranges.

Modelling linear wave transformation induced by dissipative structures—Random waves

The relevant theory is presented and numerical results are compared with the analytical solution for the interaction of non-breaking waves with an array of vertical porous circular cylinders on a horizontal bed. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The influence of the mechanical properties of porous structures and wave irregularity on wave transformation is analysed. Results for unidirectional and multidirectional wave spectra are compared to those obtained for regular waves. The model presented reproduces well the analytical results and provides a tool for analysing several engineering problems.

Modelling linear wave transformation induced by dissipative structures—Regular waves

A numerical model of the modified time-independent mild-slope equation for linear waves over a rapidly changing finite porous bed is presented. In this solution the reflection and phase coefficient shift are solved implicitly. Boundaries are assumed to be open, partially reflecting, or fully absorbing through the second-order parabolic approximation. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The model has been validated and the numerical predictions are in excellent agreement with analytical solutions.

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.

Effect of coupling and linear transformation of waves in shear flows

A new linear mechanism of reciprocal transformation of waves and a corresponding energy transfer in shear flows is discovered. The effect is demonstrated on the simplest example --- the two-dimensional waves in unbounded, parallel hydromagnetic flow with uniform velocity shear. The phenomenon discovered is of importance for magnetohydrodynamics and fusion plasma devices and for various terrestrial and astrophysical shear flows. Grasping the result became possible thanks to the nonmodal analyses of the perturbation evolution in the flow. \textcopyright{} 1996 The American Physical Society.

Linear transformation of waves in the ionosphere and the formation of ion whistlers

Linear transformation of waves in the ionosphere and the formation of ion whistlers

Electron Landau damping of lower hybrid waves

The role of electron Landau damping (ELD) in the lower hybrid resonance region is reviewed. First, it is shown that good matching of waves with parallel index n∥ large enough for efficient ELD from a finite-length antenna is possible only if the antenna is facing a tenuous plasma such that . This situation appears to prevail in recent experiments using phased waveguide arrays as launching structures. Moreover, it is shown that the relevant portion of the spectrum will be depleted by linear wave transformation before suffering appreciable ELD, unless the frequency is at least 1.5 times higher than the resonant frequency in the core of the plasma. Thus, in the case of a phased waveguide array designed for efficient ion heating in the resonance region, hardly more than a few per cent of the power will be absorbed by the electrons through ELD. On the other hand, provided that the antenna design is appropriate, ELD itself can be regarded as a simple and efficient method of heating large plasmas up to thermonuclear temperatures.

Linear mode conversion in an inhomogeneous iterative network

An LC lattice with nearest- and second-neighbor inductive coupling between the capacitors is described and shown to exhibit linear wave transformation properties when the capacitor values vary iteratively down the lattice structure. Possible applications as a device for selectively delaying, transmitting, or storing pulses of slightly differing frequencies are suggested.

Problems of the theory of linear and nonlinear transformation of waves in inhomogeneous media

The review is devoted to effects that occur when waves propagate in inhomogeneous media. The types of linear transformation of waves by the inhomogeneities of the medium are classified, and the conditions under which they are realized are indicated. Linear transformation of oscillations in a non-equilibrium medium, leading to wave amplification, is investigated. The linear transformation is consistently analyzed on the basis of a fourth-order differential equation. Attention is called to the singularities of linear wave transformation in a plasma-beam system, particularly the anisotropy of the radiation of transverse waves following passage of a modulated beam through an inhomogeneous plasma. The generation of the second harmonic of an electromagnetic wave in an inhomogeneous plasma and decay processes in inhomogeneous media are considered. Kinetic nonlocal effects (of the echo type) in an inhomogeneous plasma, wherein the focusing action of the inhomogeneity makes possible linear nonlocal effects as well as echo at the summary frequency are described. The indicated nonlinear and kinetic nonlocal effects lead to transparentization of the inhomogeneous media. Certain experimental studies dealing with the problems touched upon in the review are discussed.

Investigation of two types of collisionless linear dampings of electromagnetic waves in a non-homogeneous magnetized plasma

The space damping of EM waves in a magnetoactive plasma caused by the electron cyclotron resonance (ECR-damping) and the damping as a result of linear transformation of waves (LTW-damping) was experimentally measured. It was shown that under identical conditions the ECR-damping is considerably more effective than LTW-damping.

LINEAR TRANSFORMATION AND ABSORPTION OF WAVES IN A PLASMA

CONTENTS Introduction 413 1. Theory of linear wave transformation in a plasma 413 2. Experimental investigations of the absorption of high-frequency waves by a plasma 422 Conclusion 434 Cited literature 435

Effect of the polarization of the electromagnetic wave on wave energy absorption caused by the linear transformation of waves

The paper deals with the experimental verification of the effect of the polarization of the electromagnetic wave on the linear transformation of waves in an inhomogeneous magnetoactive plasma. Experiments were carried out in magnetic field satisfying conditionωce/ω>1, whereωce,ω are the electron cyclotron frequency and the frequency of the electromagnetic wave. The expressive dependence of the electromagnetic wave energy absorption on its polarization found experimentally is in excellent agreement with the theory.

Linear transformation of waves in a magnetoactive plasma generated by a strong microwave signal

This paper describes the experimental verification of the linear transformation of the (left-hand circularly polarized) wave in a magnetoactive plasma, in which the electron density surpasses the critical value. The study is carried out for magnetic fields satisfying the condition omega ce/ omega <1; omega ce is the electron cyclotron frequency, and omega is the frequency of the wave generating the plasma.