热电子等离子体低频不稳定性的非线性理论

本文分析了热电子等离子体中低频漂移不稳定性和交换不稳定性的非线性性质,导出了扰动幅度随时间变化的非线性耦合方程,得到了等离子体密度扰动的饱和幅度,讨论了热电子成分对饱和幅度的影响。漂移波引起的等离子体密度扰动相对幅度约20％,交换模引起的等离子体密度相对扰动幅度约5％。当热电子成分达到线性稳定条件所要求的阈值时,漂移波和交换模的饱和幅度降为零。 关键词：     

Secondary instabilities of hexagonal patterns in a Bénard-Marangoni convection experiment

We have identified experimentally secondary instability mechanisms that restrict the stable band of wave numbers for ideal hexagons in Bénard-Marangoni convection. We use "thermal laser writing" to impose long wave perturbations of ideal hexagonal patterns as initial conditions and measure the growth rates of the perturbations. For epsilon=0.46 our results suggest a longitudinal phase instability limits stable hexagons at a high wave number while a transverse phase instability limits low wave number hexagons.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.     

Dynamic Instability of Solid Surfaces under Load

The mechanism of dynamic instability of a solid surface under a load, determined by perturbations of the electron density and the change in the interatomic interaction, is considered. This instability is manifested upon the excitation of dynamic displacements of atoms in the surface layer, which can lead to formation of finite-lifetime structures in the form of waves with a large amplitude. Such structures were earlier observed experimentally on a stretched germanium (111) surface.     

在弱相对论条件下哨声波的调制不稳定性

本文在研究哨声波调制不稳定性时,除考虑由有质动力引起的密度变化和流速改变两个非线性效应外,还计及由弱相对论效应引起电子质量变化的非线性效应,得到了在形成孤子的条件、产生不稳定性的条件、和不稳定性增长率等方面与非相对论情况不同的结果。     

Softening induced instability of a stretched cohesive granular layer

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.     

Low-frequency current instabilities in nonisothermal magnetoactive plasma

The excitation of current instabilities in the lower ionosphere is studied for magnetic-field-aligned inhomogeneities of arbitrary length with allowance for electron-temperature perturbations and the dependence of electron collision frequency on electron temperature. It is found that the threshold velocity of Farley-Buneman instability has a minimum for a finite degree of inhomogeneity elongation when the temperature dependence of the electron collision frequency is sufficiently strong.Scientific-Research Radio-Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 1, pp. 25–36, January, 1993.     

Soft fermi surfaces and breakdown of Fermi-liquid behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.     

A slow wave free-electron laser in a longitudinal wiggler field

Linearized Vlasov-Maxwell equations are solved to obtain the growth rate of free electron laser instability from a tenuous relativistic electron beam propagating in a partially dielectric loaded waveguide immersed in combined axial and longitudinal wiggler magnetic fields. The instability appears via cyclotron resonance interactions for wave perturbations very close to w-kV_z-w_c=nk ₀V_Z where n is the general harmonic number. For n=0, the gain is similar to a slow wave cyclotron amplifier. For n⩾1, the growth rate is substantially larger than the standard slow wave free electron laser scheme utilizing a transverse wiggler field     

Drift wave turbulence in a dense semi-classical magnetoplasma

A semi-classical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbations. The relevance to nanoscale turbulence in nonuniform dense magnetoplasmas is discussed.     

Ion velocity shear-induced drift wave and momentum transport in non-Maxwellian magnetoplasma flows

We have investigated the diamagnetic flow in a non-uniform partially ionized plasma with non-Maxwellian electron population to explain the dynamics of ion velocity shear-induced low-frequency drift mode and associated instabilities. The dispersion relations are found, and instability threshold conditions are pointed out along with ion-parallel momentum transport due to drift motion with relative phase shift of fluctuating quantities in a non-conservative system. The real frequencies and instability growth rates are studied numerically and illustrated for typical space and laboratory plasmas. This study should be useful in understanding some aspects of low-frequency time-delayed perturbations with sheared flow leading to drift instabilities and cross-field parallel ion momentum transport in nonuniform magnetoplasmas containing a non-Maxwellian electron population.     

Generalized equations for the dynamics of the resistive firehose instability of an REB with time-dependent radius and current

Generalized equations are derived that describe the linear stage of the resistive firehose instability of a relativistic electron beam whose radius and current change along the pulse. Such factors as reverse current, the perturbations of the plasma channel, and the evolution of the plasma conductivity due to impact ionization, avalanche ionization, and recombination are taken into account.     

Stimulated Brillouin scattering in a plasma with ion-acoustic turbulence

A theory of stimulated Brillouin scattering (STBS) in a plasma with ion-acoustic turbulence is developed using concepts of parametric instability under conditions when equations of two-temperature hydrodynamics can be used to describe ion-acoustic perturbations of the electron density. The temporal growth rate of the absolute instability and the spatial gain of the scattered wave are determined. The dependence of the threshold density of the radiation flux on the angle between the scattering wave vector and the direction of anisotropy of the turbulent noise is described. A new effect of STBS forbiddenness caused by anomalous turbulent heating of the ions is predicted for a plasma with a high level of turbulent noise.     

The instability of streaming fluids with fine dust in porous medium

The instability of the plane interface between two uniform, superposed, and streaming fluids permeated with suspended particles through porous medium is considered. The effect of a uniform horizontal magnetic field on the problem is also studied. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The instability of the system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities and the Alfvén velocity. The suspended particles do not affect the above results.     

Dynamical instability of collapsing radiating fluid

We take the collapsing radiative fluid to investigate the dynamical instability with cylindrical symmetry. We match the interior and exterior cylindrical geometries. Dynamical instability is explored at radiative and non-radiative perturbations. We conclude that the dynamical instability of the collapsing cylinder depends on the critical value γ < 1 for both radiative and nonradiative perturbations.     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

EHD kelvin-helmholtz instability in viscous porous medium permeated with suspended particles

The electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform, superposed viscous and streaming dielectric fluids permeated with suspended particles through porous medium is considered under the influence of a tangential electric field. In the absence of surface tension, it is found that perturbations transverse to the direction of streaming are unaffected by the presence of both streaming and the tangential electric field, if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. In the presence of surface tension, it is found that the instability of this system is suppressed by the presence of the tangential electric field. Both the tangential electric field and the surface tension have stabilizing effects and they are able to suppress Kelvin-Helmholtz instability for small wavelength perturbations. The medium porosity reduces the stability range given in terms of a difference in streaming velocities and the electric field effect, while the suspended particles do not affect the above results.     

Stability of the collisional plasma flow in a magnetic field

A collisional plasma flow moving along a magnetic field at a velocity lower than the speed of sound is considered. It has been found that stationary small perturbations increase downstream in the flow. The mechanism of the increase is related to the fact that subsonic ideal-plasma flows respond to external perturbations primarily by a change in the pressure of the plasma. As a result, the pressure under perturbation of the velocity changes so that the stationary flow is decelerated and accelerated if the force is directed along and against the velocity, respectively. This phenomenon can be explained under the assumption that the effective mass of the plasma is negative. If the velocity of the flow is inhomogeneous in the transverse direction, the viscosity force plays a role of the external perturbing force. In this case, the effective transverse viscosity coefficient, which should be treated as negative, can be renormalized instead of the effective mass. The sign of the effective specific heat or the effective transverse thermal conductivity coefficient changes similarly if the velocity of the flow is lower than the speed of sound but is higher than the thermal velocity of ions calculated from the sum of the ion and electron temperatures. A downstream increase in the stationary perturbations is called in this work spatial instability. The downstream growth rate has been determined. The numerical analysis of the evolution of perturbations illustrates the development of the spatial instability of subsonic collisional plasma flows moving along the magnetic field.     

Zakharov equations with zeroth harmonic and a new type of modulation instability

It has been shown that the system of Zakharov equations for the amplitudes of the first and zeroth harmonics of the waves on the surface of an ideal liquid describes not only the known type of the modulation instability of the envelope of the main harmonic with respect to harmonic perturbations with small wave vectors κ (Benjamin-Feier modulation instability), but also the modulation instability of a combination of the main and zeroth harmonics at κ values on the order of the wave vector k ₀ of the main harmonic. In contrast to the Benjamin-Feier modulation instability typical for large depths, the described modulation instability does not disappear at k ₀ h < 1.363.     

Stability analysis of the Luttinger liquid fixed-point in metallic nanotubes

We study the stability of a Luttinger liquid in a metallic single-walled nanotube against generic backscattering and Umklapp perturbations. Analizing the renormalization group equations we identify nontrivial particular solutions that lay in the same universality class of the Luttinger liquid. We describe in detail the mechanism of instability generation in that electron liquid and discuss under which conditions it governs the physical properties in the presence of low frequency or temperature cutoffs.