Propagation of hydromagnetic waves in a semi-infinite plasma

The generation and propagation of hydromagnetic waves in a semi-infinite plasma bounded by an oscillating flat boundary of arbitrary electrical conductivity is analysed. The resistive and ion-cyclotron terms are retained in the governing equations. The two-dimensional plasma flow is permeated by four distinct modes of wave propagation, two of which are modified shear waves and the remaining modes penetrate through the inviscid region of the plasma. It is found that, a perfectly conducting bounding surface is able to generate all the four wave modes whereas the effect of an insulating boundary is confined within the modified viscous layer of the plasma.I thank Prof. S. S. Chawla for his guidance and advice. It is a pleasure to acknowledge the numerous valuable suggestions made by the referee.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

On the momentum of quasi-monochromatic waves in a plasma

The formulae for the momentum of quasi-monochromatic wave packets of transverse and longitudinal waves in a plasma without a magnetic field are derived including the terms of the second order in the amplitude of the electromagnetic field. The well-known increase of the momentum of the transverse wave penetrating into the plasma is given by the momentum (transported with the group velocity of the wave) of the averaged motion of the plasma. The laws of energy and momentum conservation lead simply to some results of the theory of the wave decay.Nademlýnská 600, Praha 9, Czechoslovakia.The authors thank K. Jungwirth for valuable discussions.     

A study of plasma filled parallel plate waveguide with one boundary corrugated

Warm plasma theory is used to investigate the propagation of electromagnetic waves in a plasma filled parallel plate waveguide with one boundary plate corrugated. Dispersion relations for TE- and TM-modes are derived and it is found that the propagation of TE-modes is unaffected by corrugation of one boundary plane while the propagation of TM-modes is affected by it. For TM-modes the wave numberk depends on the frequency ta as well as on the distance through which the wave is propagated.The authors take the opportunity to thank Professor M. L. Ghosh, Department of Mathematics, North Bengal University for suggesting the problem and one of the authors (S. K. Ghosh) wishes to express his thanks to the University of North Bengal for financial support.     

Nonlinear resonance of plasma waves in the thermal irregularities of ionospheric plasma

We study the effect of striction plasma density disturbances on the generation intensity of longitudional cold and plasma oscillations due to polarization of the magnetic field-aligned ionospheric plasma irregularities with δN_o<0 by a powerful radio wave. It is assumed that the plasma density level inside the irregularity intersects the upper-hybrid resonance level, in the vicinity of which the cold oscillations excited directly by a powerful radio wave are transformed to shorter-wave plasma oscillations. We consider the short plasma wave limit to reduce the problem to a system of two coupled equations for the cold wave induction and plasma wave electric field. The first equation is supplemented by a local source equal to the integral of the plasma wave electric field in the resonance region. The second equation involves the cold wave induction at the resonance point and describes the electric field of interacting waves in the resonance vicinity. We use simplifications connected with the small absorption of plasma waves propagating inside the irregularity and weak radiation of these waves outside the irregularity. These conditions correspond to the generation of eigenmodes of plasma oscillations trapped in the irregularity. We have obtained a resonance-type nonlinear equation for the electric field intensity (or energy flux) of eigenmode plasma waves with allowance for striction disturbances of the plasma density profile in the resonance region. It is shown that the striction expulsion of plasma is responsible for the occurrence of coefficients describing the change in the intensity of excitation and radiation of plasma waves at the irregularity boundary. Such an expulsion leads to variations of the efficient generation band of plasma eigenmodes with the total phase increment of the wave in the irregularity. It also leads to a change in the phase shift of the plasma wave reflected from the resonance. These coefficients and the nonlinear phase shift are expressed in terms of real wave functions of the nonlinear Airy equation which describes the electric field of the excited waves in the resonance vicinity when the dissipation is absent. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 270–297, March, 1998.     

Nonlinear gravitational waves in plasma

An exact solution is obtained for the relativistic collisionless kinetic equations describing a test plasma in the field of a strong plane gravitational wave. The gravitational wave induces in the plasma a longitudinal electric current whose amplitude is maximum at temperatures Te ip m_ec². The interaction of gravitational waves with a system consisting of Boltzmann ions and degenerate electrons is also considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 20–24, July 1981.The authors thank G. G. Ivanov for a number of valuable comments.     

Relativisitic longitudinal non-Abelian oscillations in quark-antiquark plasma

We study the relativistic version of the non-Abelian, longitudinal wave in quark-antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian field as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark-antiquark plasma, relevant to the study of quark gluon plasma. We find that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modified for relativistic or large amplitude waves. Further more, the above results are based on just four first-order equations for gauge invariant quantities derived from gauge covariant twelve first-order equations.     

Effects of Schwarzschild black hole horizon on isothermal plasma wave dispersion

The 3 + 1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number k. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature of the waves and their characteristics. These provide interesting information about the black hole magnetosphere near the horizon. There are cases of normal and anomalous dispersion. We find a case of normal dispersion of waves when the plasma admits the properties of Veselago medium. Our results agree with those of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.     

Photon dynamics in plasma waves

In this Letter the evolution of a single photon and collective effect of a photon system in background plasma waves are uniformly described in the framework of photon dynamics. In a small-amplitude plasma wave the modulation of photon dynamical behavior by the plasma wave can be treated as perturbation, and photon acceleration effect and photon Landau damping are investigated in linear theory. In an arbitrary-amplitude plasma wave, photon evolution trajectories in phase space are obtained by solving dynamical equations, and photon trapping effect and motion equations in the given plasma wave are also discussed.     

The nonlinear theory of plasma instability in an oscillating discharge

An analysis is presented of the nonlinear effects caused by plasma instability in an oscillating discharge [V'aclavík J.: Czech. J. Phys.B 15 (1965), 832]. An estimate is made of the energy of unstable oscillations and of the coefficient of turbulent diffusion of plasma using equations of the theory of weak turbulence [Kadomcev B. B.: Problemy teorii plazmy, Vol. IV. Atomizdat, Moskva 1964, 188; Galeev A. A., Karpman V. I., Sagdeev R. Z.: Nucl. Fusion5 (1965), 20].In conclusion the author wishes to thank V. Kopecký and J. Preinhaelter for their valuable discussions of the problem.     

Nonlinear waves in a plasma cylinder

Nonlinear electron plasma waves in a cold plasma bounded by a cylindrical dielectric are investigated using the exact electron fluid equations. After the spatial wave structure is determined, a set of nonlinear equations governing the temporal behavior of the field quantities is solved. It is shown that finite amplitude waves and explosively unstable behavior can occur     

Rogue waves: Classification,measurement and data analysis,and hyperfast numerical modeling

The last twenty years has seen the birth and subsequent evolution of a fundamental new idea in nonlinear wave research: Rogue waves, freak waves or extreme events in the wave field dynamics can often be classified as coherent structure solutions of the requisite nonlinear partial differential wave equations (PDEs). Since a large number of generic nonlinear PDEs occur across many branches of physics, the approach is widely applicable to many fields including the dynamics of ocean surface waves, internal waves, plasma waves, acoustic waves, nonlinear optics, solid state physics, geophysical fluid dynamics and turbulence (vortex dynamics and nonlinear waves), just to name a few. The first goal of this paper is to give a classification scheme for solutions of this type using the inverse scattering transform (IST) with periodic boundary conditions. In this context the methods of algebraic geometry give the solutions of particular PDEs in terms of Riemann theta functions. In the classification scheme the Riemann spectrum fully defines the coherent structure solutions and their mutual nonlinear interactions. I discuss three methods for determining the Riemann spectrum: (1) algebraic-geometric loop integrals, (2) Schottky uniformization and (3) the Nakamura-Boyd approach. I give an overview of several nonlinear wave equations and graph some of their coherent structure solutions using theta functions. The second goal is to discuss how theta functions can be used for developing data analysis (nonlinear Fourier) algorithms; nonlinear filtering techniques allow for the extraction of coherent structures from time series. The third goal is to address hyperfast numerical models of nonlinear wave equations (which are thousands of times faster than traditional spectral methods).     

The resonance state for the induction acceleration of a cylindrical plasma cluster

The resonance conditions for maximum attainable velocity of a cylindrical plasma cluster (theta pinch) were found by solving magnetohydrodynamic equations. A relation is given for the maximum kinetic energy of the cylindrical cluster which it can obtain from the external discharging circuit. Calculation is performed by means of methods of numerical calculation on a computing machine.In conclusion the author would like to thank Professor J. Kracík, Dr.Sc, for valuable suggestions and discussion of this paper.     

Interaction phenomena of ion‐acoustic quasi‐solitons and classical‐solitons in three component plasma

The space–time evolution of the cnoidal‐soliton solution, characteristics of the quasi‐soliton solution of Korteweg‐de‐Vries (KdV) equation, and the interaction phenomena of ion‐acoustic waves (IAWs) are investigated in a plasma system consisting of positive and negative ions with superthermal electrons. To do this, and (Ar⁺, F^?) plasmas are considered and two‐sided KdV equations (KdVEs) are derived applying the extended Poincaré‐Lighthill‐Kuo (ePLK) method. The effects on wave structures, potential profiles, and propagation characteristics with plasma parameters of the cnoidal‐wave, quasi‐soliton solution, and head‐on collision phenomena of IAWs are presented graphically. It was found that the superthermality parameter and the mass ratio of ions play a significant role in the head‐on collision between soliton and standing cnoidal wave and reveal that the collision is elastic and both waves change their phase shifts due to collision. Moreover, the superthermality parameters are also responsible for the production of compressive and rarefactive phase shifts in overtaking collision processes between right travelling classical soliton (CS) and cnoidal wave (CW) and reduced the amplitudes of IAWs. It was also found that a new wave is created with a high amplitude in the interacting region during collision depending on the plasma parameters.     

The properties of magnetoactive plasma generated by high microwave power with variable polarization

The paper deals with the measurement of the electron densityN and the transverse electron temperatureT _e of a magnetoactive plasma, generated in a circular waveguide by a strong microwave signal with variable polarization. The plasma is generated in a homogeneous magnetic field parallel to the axis of the circular waveguide. The results of the measurements show the great influence of wave polarization upon the properties of the plasma. The results of the penetration of the electromagnetic wave into the plasma as a function of the wave polarization are given, too.The authors wish to thank Dr. J. atlov for his helpful discussions and suggestions concerning the purity of electromagnetic wave polarization.     

Ionization self-channeling of whistler waves in a collisional magnetized plasma

An investigation is made of the self-interaction of whistler waves (whistlers) involving the formation of waveguide channels in a collisional magnetoactive plasma as a result of its additional ionization by the field of the propagating wave. Simplified equations are derived to describe the behavior of the whistler field in a channel of enhanced plasma density in the presence of electron collisions. Self-consistent distributions of the field and the plasma corresponding to steady-state ionization self-channeling of whistlers are obtained by numerically solving the equations for the field together with balance equations for the electron density and energy. Our estimates indicate that this effect can be observed under laboratory conditions. Zh. éksp. Teor. Fiz. 112, 1285–1298 (October 1997)     

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.     

Dust acoustic shock wave generation due to dust charge variation in a dusty plasma

In a dusty plasma, the non-adiabaticity of the charge variation on a dust grain surface results in an anomalous dissipation. Analytical investigation shows that this results in a small but finite amplitude dust acoustic (DA) wave propagation which is described by the Korteweg-de Vries-Burger equation. Results of the numerical investigation of the propagation of large-amplitude dust acoustic stationary shock wave are presented here using the complete set of non-linear dust fluid equations coupled with the dust charging equation and Poisson equation. The DA waves are of compressional type showing considerable increase of dust density, which is of significant importance in astrophysical context as it leads to enhanced gravitational attraction considered as a viable process for star formation. The DA shock transition to its far downstream amplitude is oscillatory in nature due to dust charge fluctuations, the oscillation amplitude and shock width depending on the ratioω _pd/V_ch and other plasma parameters Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Supernonlinear ion-acoustic waves in a dusty plasma

An exact solution is obtained for the equations that describe nonlinear ion-acoustic waves in a dusty plasma. It is shown that the solution can be in the form of nonlinear periodic waves, solitons, and supernonlinear waves whose trajectories envelope one or several separatrices in the phase portrait of the wave. Profiles of physical quantities in the wave are constructed. The supernonlinear waves are shown to be of two types, subsonic (type 1) and supersonic (type 2). Existence regions of supernonlinear waves of both types and solitons are constructed in the plane of the problem parameters.     

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schr?dinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.