Incoherent Scattering of Electromagnetic Waves by Langmuir Fluctuations Trapped in a Plasma Density Well

Incoherent scattering of a probing wave by Langmuir fluctuations trapped and enhanced near a local minimum of the electron density (plasma density well) in plasma with a parabolic density profile is considered. Steady-state amplitudes of fluctuations are calculated for arbitrary velocity distribution functions of plasma particles with allowance for electron collisions. It is shown that quasi-periodic oscillations with two characteristic scales can be present in the spectrum of the plasma line. The smaller scale is due to the wellknown effect of discretization of the spectrum of Langmuir fluctuations in a plasma density well. The larger scale is associated with the generation of scattered waves in two spatial regions and subsequent interference of these waves at the exit from the density well. Oscillations with this scale are more stable under unsteady plasma conditions and can be more often observed in experiments. The results of this work can be used to experimentally determine the plasma parameters, such as the electron collision frequency and the size and lifetime of the plasma density well.     

Exact solutions for oblique solitary Alfvén waves in plasma

The properties of solitary Alfvén waves are studied for different ratios between the thermal plasma pressure and the magnetic pressure. It is shown that the wave propagation is accompanied by the generation of a nonlinear ion current along the magnetic field, the contribution of which to the Sagdeev potential was previously ignored. An expression for the quasi-potential of Alfvén waves with allowance for this effect is derived. It is found that Alfvén waves are compression waves in the inertial limit, whereas kinetic Alfvén waves are rarefaction waves. In a high-pressure plasma, a solitary wave has the form of either a well or a hump in the plasma density, depending on the relations between the Mach number, angle between the wave propagation direction and the magnetic field, and the value of the plasma beta.     

On the theory of Cherenkov emission in a plasma

The Cherenkov emission of transverse-longitudinal waves in an anisotropic plasma is considered by applying a Hamiltonian method and by drawing an analogy between the equations for the Cherenkov emission of purely transverse and purely longitudinal waves in isotropic media and the equations for the emission of transverse-longitudinal electromagnetic waves in a highly anisotropic medium (a magnetized plasma). A formula for the emitted power is derived, as well as an expression for the directional pattern of the emitted waves in an anisotropic plasma.     

Wavespeed in reaction–diffusion systems, with applications to chemotaxis and population pressure

We present a method based on the Melnikov function used in dynamical systems theory to determine the wavespeed of travelling waves in perturbed reaction–diffusion systems. We study reaction–diffusion systems which are subject to weak nontrivial perturbations in the reaction kinetics, in the diffusion coefficient, or with weak active advection. We find explicit formulæ for the wavespeed and illustrate our theory with two examples; one in which chemotaxis gives rise to nonlinear advection and a second example in which a positive population pressure results in both a density-dependent diffusion coefficient and a nonlinear advection. Based on our theoretical results we suggest an experiment to distinguish between chemotactic and population pressure in bacterial colonies.     

Traveling waves in cross-diffusion models of population dynamics

"Traveling wave"--type solutions of some models with cross-diffusion were considered. It was shown that "cross-diffusion" terms, as opposed to "diffusion" terms, do not increase the dimensionality of the automodel system. The bifurcation approach was used to study the dependence of the wave solutions on the parameters of the models being considered, and the waves were classified. It was shown that, at the same parameter values, both "fast" and "slow" waves can exist and that these waves are described by different automodel systems.     

Generation of solar microwave bursts at the second harmonic of the plasma frequency

The nonlinear interaction between upper hybrid waves is simulated numerically for conditions corresponding to the sources of solar microwave bursts (at a frequency of about 5.7 GHz). The source of plasma waves is considered to be an electron beam with a loss-cone-type distribution. It is shown that, for a symmetric double-sided loss cone, the degree of polarization of the radiation generated in a direction transverse to the magnetic field can reach 100% and corresponds to an extraordinary wave. For a one-sided loss cone, in accordance with the previous results, the degree of polarization is found to be low. The efficiency of the plasma mechanism for the radiation generation is estimated.     

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.     

Excitation of surface waves at a plasma boundary by a short laser pulse

The excitation of surface waves by a laser pulse as it crosses a vacuum-plasma interface is considered. Surface waves are excited by a vortex electric current that is generated at the plasma boundary by the ponderomotive force of the pulse. The question is considered of how the duration and transverse dimensions of the pulse affect the spatiotemporal distribution and the spectral and energy parameters of the excited surface waves.     

Effects of finite heat conductivity on instabilities in a rotating plasma

Analytical theory of magnetorotational and convective instabilities in a rotating cylindrical plasma with finite heat conductivity is developed and discussed. The heat conductivity is incorporated into the standardized equations of the regular magnetohydrodynamic approach to studying these instabilities. A case of high-β plasma (β is the ratio of plasma pressure to the magnetic field pressure) and the modes with parallel phase velocity much smaller than the sound velocity is particularly emphasized and considered in the quasi-incompressible approximation. It is shown that this approximation is more adequate than the Boussinesq approximation. Both these approximations lead to the same results for aperiodical instabilities of the axisymmetric modes which are hybrids of the magnetorotational and convective instabilities. On the other hand, the Boussinesq approximation overlooks the heat-conductivity-induced instabilities predicted by the quasi-incompressible approximation describing the dissipative excitation of the slow magnetoacoustic and Alfvén waves. Non-axisymmetric aperiodical instabilities are considered. It is shown that, for such modes, the role of convective instabilities is greater than for the magnetorotational instability.     

Small-scale Alfvén waves localized near an extremum in the finite-amplitude perturbation of the radial plasma density profile

A study is made of electromagnetic waves localized in the region where the radial plasma density profile has an extremum between two local Alfvén resonances. Analytic expressions for the eigenfrequencies and eigenmodes are obtained. It is shown that kinetic and inertial Alfvén waves can propagate in the vicinity of a maximum and a minimum in the density profile, respectively. Passage to the limiting case in which the plasma density is nonuniform and has a parabolic profile is considered.     

Low-frequency electromagnetic instabilities caused by a rotating dust flow

Low-frequency electromagnetic waves propagating obliquely to an external magnetic field in a plasma with an anisotropic dust component are considered. The cold dust is assumed to have considerable longitudinal and transverse velocity components with respect to the magnetic field. A dispersion relation demonstrating that both fast and slow waves can be unstable is derived in the framework of kinetic theory. Mechanisms and consequences of these instabilities are discussed in the context of the problem of plasma transition into a turbulent state behind the shock front of a supernova.     

Thin current sheets in collisionless plasma: Equilibrium structure,plasma instabilities,and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.     

Low-frequency resonances of the refractive index in weakly ionized plasma with an admixture of dust

The propagation of low-frequency electromagnetic waves along the magnetic field in weakly ionized plasma with an admixture of dust is studied in the framework of the Hall magnetohydrodynamics. Explicit expressions for the coefficients of magnetic field diffusion in plasma are derived. The resonance of the refractive index is found to occur for either right- or left-hand polarized waves. A quantitative criterion is obtained that allows one to determine the polarization of waves that experience resonance at given plasma parameters. The physical mechanism of the resonance is discussed, and the obtained results are compared with the available literature data.     

Excitation of waves in an inhomogeneous plasma

The evolution of initial perturbations in a spatially inhomogeneous cold electron plasma in the absence of an external magnetic field is considered. The excitation of both continuous-spectrum bulk plasma waves and surface plasma waves with a discrete frequency spectrum is investigated. Analytic solutions are obtained in the long-wavelength limit, and the excitation of waves of arbitrary length is analyzed numerically. The local, integral, and spatial spectra are calculated, as well as the field structures and dispersion properties of waves in waveguides filled nonuniformly with a plasma. It is shown that, in a plasma with a smooth boundary, there also exist surface waves with a discrete spectrum (although with somewhat different properties as compared to those in a plasma with a sharp boundary), which are excited together with continuous-spectrum bulk waves during the evolution of the initial perturbation.     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

High-frequency surface waves at a plasma-metal interface: I. Linear model

A study is made of the dispersion properties of surface waves at a plasma-metal interface under thermodynamically nonequilibrium conditions such that a space charge sheath forms at the plasma boundary. In the simplest model, the sheath is described as a dielectric with a given permittivity. The wave parameters in a highly collisional plasma are discussed. The effect of interaction between waves propagating near the opposite plasma boundaries is considered, in particular, for space charge sheaths of different thicknesses. Conditions are determined under which the parameters of surface waves are substantially altered by the plasma-sheath geometric resonance.     

Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.     

Transmission characteristics of axial waves in blood vessels

The elastic behavior of blood vessels can be quantitatively examined by measuring the propagation characteristics of waves transmitted by them. In addition, specific information regarding the viscoelastic properties of the vessel wall can be deduced by comparing the observed wave transmission data with theoretical predictions. The relevance of these deductions is directly dependent on the validity of the mathematical model for the mechanical behavior of blood vessels used in the theoretical analysis. Previous experimental investigations of waves in blood vessels have been restricted to pressure waves even though theoretical studies predict three types of waves with distinctly different transmission characteristics. These waves can be distinguished by the dominant displacement component of the vessel wall and are accordingly referred to as radial, axial and circumferential waves. The radial waves are also referred to as pressure waves since they exhibit pronounced pressure fluctuations. For a thorough evaluation of the mathematical models used in the analysis it is necessary to measure also the dispersion and attenuation of the axial and circumferential (torsion) waves.

To this end a method has been developed to determine the phase velocities and damping of sinusoidal axial waves in the carotid artery of anesthetized dogs with the aid of an electro-optical tracking system. For frequencies between 25 and 150 Hz the speed of the axial waves was between 20 and 40 m/sec and generally increased with frequency, while the natural pressure wave travelled at a speed of about 10 m/sec. On the basis of an isotropic wall model the axial wave speed should however be approximately 5 times higher than the pressure wave speed. This discrepancy can be interpreted as an indication for an anisotropic behavior of the carotid wall. The carotid artery appears to be more elastic in the axial than in the circumferential direction.     

Effect of dust charge fluctuations on dust acoustic structures in magnetized dusty plasma containing nonextensive electrons and two-temperature isothermal ions

Effect of dust electrical charge fluctuations on the nature of dust acoustic solitary waves (DASWs) in a four-species magnetized dusty plasma containing nonextensive electrons and two-temperature isothermal ions has been investigated. In this model, the negative dust electric charge is considered to be proportional to the plasma space potential. The nonlinear Zakharov–Kuznetsov (ZK) and modified Zakharov–Kuznetsov (mZK) equations are derived for DASWs by using the standard reductive perturbation method. The combined effects of electron nonextensivity and dust charge fluctuations on the DASW profile are analyzed. The different ranges of the nonextensive q-parameter are considered. The results show that solitary waves the amplitude and width of which depend sensitively on the nonextensive q-parameter can exist. Due to the electron nonextensivity and dust charge fluctuation rate, our dusty plasma model can admit both positive and negative potential solitons. The results show that the amplitude of the soliton increases with increasing electron nonextensivity, but its width decreases. Increasing the electrical charge fluctuations leads to a decrease in both the amplitude and width of DASWs.     

Magnetosonic oscillations of thin plasma columns

Oscillations of a plasma column in a longitudinal magnetic field are considered. It is found that eigenmodes with frequencies close to the ion cyclotron frequency can be excited in columns the radii of which are smaller than the characteristic wavelength of magnetosonic oscillations predicted by the theory of homogeneous plasma. The eigenmodes have the form of waves running around the column axis in the direction of electron gyration in the magnetic field. Magnetosonic oscillations can be excited as a side effect when using helical antennas for ion cyclotron resonance heating of plasma. These oscillations should enhance electron heating in the plasma core, as well as both electron and ion heating at the periphery of the plasma column. The spectrum of eigenmodes of inhomogeneous plasma columns includes oscillations of different nature. Comparative analysis of their properties performed in the present paper is useful for understanding the full picture of the physical processes occurring during ion cyclotron resonance heating and clarifying the characteristic features of the magnetosonic oscillations under study.