The instability of current-driven ion-acoustic waves in the collisionless magnetic-field-free space plasma is investigated by using a nonextensive approach. The ions and the electrons are thought of in the power-law distributions that can be described by the generalized q-Maxwellian velocity distribution and are considered with the different nonextensive q-parameters. The generalized q-wave frequency and the generalized instability q-growth rate for the ion-acoustic waves are derived. The numerical results show that the nonextensive effects on the ion-acoustic waves are not apparent when the electron temperature is much more than the ion temperature, but they are salient when the electron temperature is not much more than the ion temperature. As compared with the electrons, the ions play a dominant role in the nonextensive effects.
We investigate the dispersion relation and Landau damping of ion acoustic waves in the collisionless magnetic-field-free plasma if it is described by the nonextensive q-distributions of Tsallis statistics. We show that the increased numbers of superthermal particles and low velocity particles can explain the strengthened and weakened modes of Landau damping, respectively, with the q-distribution. When the ion temperature is equal to the electron temperature, the weakly damped waves are found to be the distributions with small values of q.
The low-frequency acoustic-like modes in a pair plasma (electron-positron or pair-ion) is studied by employing a kinetic theory model based on the Vlasov and Poisson's equation with emphasizing the Tsallis's nonextensive statistics. The possibility of the acoustic-like modes and their properties in both fully symmetric and temperature-asymmetric cases are examined by studying the dispersion relation, Landau damping and instability of modes. The resultant dispersion relation in this study is compatible with the acoustic branch of the experimental data [W. Oohara, D. Date, and R. Hatakeyama, Phy…
We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale technique, a nonlinear Schr{ö}dinger (NLS) equation is derived which governs the dynamics of modulated wave packets. It is shown that in nonextensive plasmas, the IAW envelope is always stable for long-wavelength modes $(k\rightarrow0)$ and unstable for short-wavelengths with $k \gtrsim1$. However, the envelope can be unstable at an intermediate scale of perturba…
We study the ion acoustic solitary waves in the four-component complex plasma consisting of cold inertial ions, positrons, cold and hot (two-temperature) electrons, where the electrons and positrons are the Cairns-Tsallis distribution and have different nonthermal and nonextensive parameters. Base on the plasma hydrodynamic equations and Sagdeev pseudo-potential theory, we derive the conditions of the solitary waves to exist in the plasma, such as the Sagdeev pseudo-potential, the normalized electrostatic potential, the lower and upper limits of Mach number, and the compressive/rarefactive sol…
The small amplitude ion-acoustic solitary waves in the magneto-rotating plasma consisting of cold fluid ions, hot positrons, and the two-temperature electrons (cold and hot electrons) are investigated when the electrons obey a modified Cairns-Tsallis distribution. By using the reductive perturbation method, we derive the Korteweg-de Vries equation and the modified Korteweg-de Vries equation and obtain the small amplitude ion-acoustic solitary wave solutions. The dependences of solitary wave solutions on the nonextensive q-parameter, the nonthermal alpha-parameter and the plasma physical quanti…
The dust-acoustic waves and their stability driven by a flowing dusty plasma when it cross through a static (target) dusty plasma (the so-called permeating dusty plasma) are investigated when the components of the dusty plasma obey the power-law q-distributions in nonextensive statistics. The frequency, the growth rate and the stability condition of the dust-acoustic waves are derived under this physical situation, which express the effects of the nonextensivity as well as the flowing dusty plasma velocity on the dust-acoustic waves in this dusty plasma. The numerical results illustrate some n…
A quantitative analysis is presented of the dust acoustic wave instability driven by the solar and stellar winds. This is a current-less kinetic instability which develops in permeating plasmas, i.e.., when one quasi-neutral electron-ion wind plasma in its propagation penetrates through another quasi-neutral plasma which contains dust, electrons and ions.
In plasmas with electron drift (current) relative to static ions, the ion acoustic wave is subject to the kinetic instability which takes place if the directed electron speed exceeds the ion acoustic speed. The instability threshold becomes different in the case of one quasi-neutral electron-ion plasma propagating through another static quasi-neutral (target) plasma. The threshold velocity of the propagating plasma may be well below the ion acoustic speed of the static plasma. Such a current-less instability may frequently be expected in space and astrophysical plasmas.
The instability of the dust-acoustic waves driven by drifting electrons and ions in a dusty plasma is investigated by the kinetic theory. All the plasma components (electrons, ions and dust particles) are assumed to be the Lorentzian kappa-distributions. The spectral indexes kappa of the kappa-distributions for the three plasma components are different from each other. The obtained instability growth rate depends on the physical quantities of the plasma not only, but on the spectral indexes. The numerical results for the kappa-effect on the instability growth rate show that, if the normalized …
The propagation characteristics and interactions between the dust acoustic (DA) one and multi solitons in an unmagnetized dusty plasmas composing negatively charged mobile dust, Boltzmann distributed electrons, nonextensive distributed cold and nonthermal distributed hot ions are studied. The well known extended Poincar Lighthill Kuo (PLK) method is employed to derive the two sided Korteweg de Vries (KdV) equations. The solutions of KdV equations are constructed using the Hirota method both for one and multi solitons. The phase shifts are determined for the interaction of one, two and three DA…
We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have derived a nonlinear Schr{ö}dinger equation using the standard reductive perturbation method to describe the nonlinear amplitude modulation of ion acoustic wave satisfying the dispersion relation of ion acoustic wave propagating at an arbitrary angle to the direction of the external uniform static magnetic field. We have investigated the correspondence between t…
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Phys. Rev. E {\bf87}, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schr{ö}dinger (NLS) equation with a nonlocal nonlinear term $\propto {\cal{P}}…
We use the exponential parametrization of the nonextensive distribution to calculate the dielectric constant in an electron gas obeying the nonextensive statistics. As we show, the exponential parametrization allows us to make such calculations in a straightforward way, bypassing the use of intricate formulas obtained from integral tables and/or numerical methods. For illustrative purposes, we apply first the method to the calculation of the permittivity and the corresponding dispersion relation in the ultrarelativistic limit of the electron gas, and verify that it reproduces in a simple way t…
A generalized plasma model having warm ions, iso-thermal electrons, super-thermal electrons and positrons is considered to theoretically investigate the modulational instability (MI) of ion-acoustic waves (IAWs). A standard nonlinear Schrödinger equation is derived by applying reductive perturbation method to study the MI of IAWs. It is observed that the MI criteria of the IAWs are significantly modified by various plasma parameters. The present results should be useful in understanding the conditions for MI of IAWs which are relevant to both space and laboratory plasma system.
The nonlinear thin-shell instability (NTSI) may explain some of the turbulent hydrodynamic structures that are observed close to the collision boundary of energetic astrophysical outflows. It develops in nonplanar shells that are bounded on either side by a hydrodynamic shock, provided that the amplitude of the seed oscillations is sufficiently large. The hydrodynamic NTSI has a microscopic counterpart in collisionless plasma. A sinusoidal displacement of a thin shell, which is formed by the collision of two clouds of unmagnetized electrons and protons, grows and saturates on timescales of the…
The kinetic theory for the cylindrical plasma, produced by the cylindrically symmetric (azimuthal mode number m=0) helicon wave, is developed with accounting for the cylindrical geometry and the radial inhomogeneity of the helicon wave and plasma. This theory reveals macroscale effect of the azimuthal steady rotation of electrons with a radially inhomogeneous angular velocity, caused by radial inhomogeneity of the helicon electric field. It is found that this sheared rotation as well as the electron density and temperature inhomogeneity are responsible for the development of the high frequency…
Nonlinear Saturation of the Acoustic Resonant Drag Instability
Weizmann Institute of Science（魏茨曼科学研究所）；Princeton University（普林斯顿大学）；University of Otago（奥塔哥大学）；Kavli Institute for Particle Astrophysics & Cosmology (KIPAC), Stanford University（斯坦福大学卡弗里粒子天体物理与宇宙学研究所）
The basic features of nucleus-acoustic (NA) envelope bright and dark solitons, which exist in degenerate quantum plasmas, have been theoretically investigated by deriving the nonlinear Schrödinger (NLS) equation. The reductive perturbation method, which is valid for a small but finite amplitude limit, is employed. It is found that the bright envelope solitons are modulationally unstable, whereas the dark ones are stable. It is also observed that the fundamental properties (viz. Modulational instability (MI) growth rate, width and energy concentration of NA waves, etc.) of NA unstable bright en…
The stability theory of the inductively coupled plasma (ICP) is developed for the case when the electron quiver velocity in RF wave is of the order of or is larger than the electron thermal velocity. The theory predicts the existence the instabilities of the ICP which are driven by the current formed in the skin layer by the accelerated electrons, which move relative ions under the action of the ponderomotive force.
Modulational instability (MI) of ion-acoustic waves (IAWs) has been theoretically investigated in a plasma system which is composed of inertial warm adiabatic ions, isothermal positrons, and two temperature superthermal electrons. A nonlinear Schrödinger (NLS) equation is derived by using reductive perturbation method that governs the MI of the IAWs. The numerical analysis of the solution of NLS equation shows the existence of both stable (dark envelope solitons exist) and unstable (bright envelope solitons exist) regimes of IAWs. It is observed that the basic features (viz. stability of the w…
We examine the modulational instability (MI) of ion-acoustic waves (IAWs) in an electronegative plasma containing positive and negative ions as well as electrons that follow the nonextensive statistics proposed by Tsallis [J. Stat. Phys. 52, 479 (1988)]. Using the reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) that governs the modulational instability of the IAWs is obtained. Inspired by the experimental work of Ichiki \emph{et al.} [Phys. Plasmas 8, 4275 (2001)], three types of electronegative plasmas are investigated. The effects of various parameters on the p…
Amplitude modulation of quantum ion-acoustic waves (QIAWs) in a quantum electron-pair-ion plasma is studied. It is shown that the quantum coupling parameter $H$ (being the ratio of the plasmonic energy density to the Fermi energy) is ultimate responsible for the modulational stability of QIAW packets, without which the wave becomes modulational unstable. New regimes for the modulational stability (MS) and instability (MI) are obtained in terms of $H$ and the positive to negative ion density ratio $β$. The growth rate of MI is obtained, the maximum value of which increases with $β$ and decrease…
The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one- and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical plasma clouds, which consist of equally hot electrons and ions with a mass ratio of 250. The Mach number of the collision speed with respect to the initial ion acoustic speed of the plasma is set to 4.6. This high Mach number delays the formation of such structures by tens of inverse ion plasma frequencies. A pair of stable shock-like structures is observed afte…
We study electron heating in collisionless current-driven turbulence due to the nonlinear interactions between electron- and ion-acoustic waves. PIC simulation results show that due to a large difference between the electron and ion mean velocities the Buneman instability excites large-amplitude ion-acoustic waves, which strongly modifies the electron velocity distribution function, leading to a secondary instability that generates fast electron-acoustic waves; and in this process, a giant electron hole is ultimately created. This giant electron hole is responsible for strong electron heating …
We present a linear stability analysis of the perturbation modes in anisotropic MHD flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model, that takes into account not only the effect of pressure anisotropy, but also the effect of anisotropic heat fluxes. In this model the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow e…
The modulational instability (MI) criteria of dust-ion-acoustic (DIA) waves (DIAWs) have been investigated in a four-component pair-ion plasma having inertial pair-ions, inertialess non-thermal non-extensive electrons, and immobile negatively charged massive dust grains. A nonlinear Schrödinger equation (NLSE) is derived by using reductive perturbation method. The nonlinear and dispersive coefficients of the NLSE can predict the modulationally stable and unstable parametric regimes of DIAWs and associated first and second order DIA rogue waves (DIARWs). The MI growth rate and the configuration…
A Two-dimensional Numerical Study of Ion-Acoustic Turbulence
Massachusetts Institute of Technology（麻省理工学院）；Department of Defense（国防部）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Proxima Fusion GmbH（Proxima Fusion有限公司）
A proper theoretical research has been carried out to explore the modulational instability (MI) conditions of dust-ion-acoustic (DIA) waves (DIAWs) in a three-component dusty plasma system containing inertialess $κ$-distributed electrons, and inertial warm positive ions and negative dust grains. The novel nonlinear Schrödinger equation (NLSE) has been derived by employing the reductive perturbation method. The analysis under consideration demonstrates two types of modes, namely, fast and slow DIA modes. The dispersion and nonlinear properties of the plasma medium, as well as the MI conditions …
The nonlinear propagation of heavy-ion-acoustic (HIA) waves (HIAWs) in a four component multi-ion plasma (containing inertial heavy negative ions and light positive ions, as well as inertialess nonextensive electrons and positrons) has been theoretically investigated. The nonlinear Schrödinger (NLS) equation is derived by employing the reductive perturbation method. It is found that the NLS equation leads to the modulational instability (MI) of HIAWs, and to the formation of HIA rogue waves (HIARWs), which are due to the effects of nonlinearity and dispersion in the propagation of HIAWs. The c…
The theory of the nonmodal ion-acoustic instability in the skin layer of the inductively coupled plasma (ICP) is developed. This instability has time dependent growth rate and is driven by the current formed in the skin layer by the accelerated motion of electrons relative to ions under the action of the ponderomotive force. It is found that the development of the ion acoustic turbulence (IAT) in the skin layer and the scattering of electrons by IAT are basic nonlinear channels of the nonlinear absorption of the RF energy in the skin layer.
A theoretical investigation has been made to understand the mechanism of the formation of both bright and dark envelope soltions associated with dust-ion-acoustic waves (DIAWs) propagating in an unmagnetized three component dusty plasma medium having inertial warm positive ions and negative dust grains, and inertialess non-thermal Cairns' distributed electrons. A nonlinear Schrödinger equation (NLSE) is derived by employing reductive perturbation method. The effects of plasma parameters, viz., $γ_2$ (the ratio of the positive ion temperature to electron temperature times the charge state of io…
The equations governing the interaction between incoherent light and electron-acoustic waves are presented. The modulational instability properties of the system are studied, and the effect of partially coherent light is discussed. It is shown that partial coherence of the light suppresses the modulational instability. However, short wavelength perturbations are less affected, and will therefore dominate in, e.g. pulse filamentation. The results may be of importance to space plasmas and laser-plasma systems.
We theoretically and numerically investigate the ion-acoustic features of collective Thomson scattering (CTS) in two-stream plasmas. When the electron distribution functions of two (stationary and moving) components overlap with each other at the phase velocities corresponding to the two resonant peaks of the ion-acoustic feature, the theoretical spectrum shows asymmetry because the rate of electron Landau damping is different for the two peaks. The results of numerical simulations agree well with the theoretical spectra. We also demonstrate the effect of a two-stream-type instability in the i…
The Damping and Instability of Ion-acoustic Waves in the Solar Wind: Solar Orbiter Observations
Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德太空科学实验室）；Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学月球与行星实验室）
Dust-ion-acoustic damped solitary waves and shocks in laboratory and Saturn's E-ring magnetized nonthermal dusty plasmas with anisotropic ion pressure and dust-charge fluctuation
A new mechanism for Geodesic acoustic mode (GAM) excitation by a not fully slowed down energetic particle (EP) beam is analysed to explain experimental observations in Large Helical Device. It is shown that the positive velocity space gradient near the lower-energy end of the EP distribution function can strongly drive GAM unstable. The new features of this EP-induced GAM (EGAM) are: 1. no instability threshold in the pitch angle; 2. the EGAM frequency can be higher than the local GAM frequency; and 3. the instability growth rate is much larger than that driven by a fully slowed down EP beam.
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of one-dimensional solitons in the long-wavelength limit is considered using the expansion for the corresponding spectral problem. It is shown that the KP instability also takes place for two-dimensional solitons in the framework of the three-dimensional KP equation with positive dispersion. According to B.B. Kadomtsev this instability belongs to the self-focusing ty…
The modulational instability (MI) of the dust-acoustic waves (DAWs) in an electron-positron-ion-dust plasma (containing super-thermal electrons, positrons and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the nonlinear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method has been employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super-thermal electrons, positrons and ions significantly modifies both the stable and unstable regions. The critical wave number $k_c$ (at …
The modulational instability of dust-ion-acoustic (DIA) mode and associated rogue waves in a three component dusty plasma system (containing inertial warm ion and negatively charged dust fluids along with inertialess $q$-distributed electrons) has been theoretically investigated. A nonlinear Schrödinger equation (NLSE) has been derived by employing the reductive perturbation method. It is observed that the dusty plasma system under consideration supports the fast and slow DIA modes, and that the dispersion and nonlinear coefficients of the NLSE determine the parametric regimes not only for the…
Perpendicular electron dynamics and the associated collisions are discussed in relation to the collisional drift wave instability. In addition, the limit of small parallel wave numbers of this instability is studied and it is shown to yield a reduced wave frequency. It is also shown that in this case the growth rate in fact {\em decreases} for smaller parallel wave numbers, instead of growing proportional to $1/k_z^2$. As a result, the growth rate appears to be angle dependent and to reach a maximum for some specific direction of propagation. The explanation for this strange behavior is given.…
In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation of the Z dispersion function, previously published, and valid for the entire range. A careful analysis of the solutions spectra of this kind of polynomial equation permits us to calculate easily the growth rate of the drift instability for the ion-dust and dust acoustic mode. The value of the parallel to magnetic field wavelength for which the …
The basic features of linear and nonlinear quantum electron-acoustic (QEA) waves in a degenerate quantum plasma (containing non-relativistically degenerate electrons, superthermal or $κ$-distributed electrons, and stationary ions) are theoretically investigated. The nonlinear Schödinger (NLS) equation is derived by employing thereductive perturbation method. The stationary solitonic solution of the NLS equation are obtained, and examined analytically as well as numerically to identify the basic features of the QEA envelope solitons. It has been found that the effects of the degeneracy and exch…
The standard nonlinear Schrödinger equation (NLSE) is one of the elegant equations to find the information about the modulational instability criteria of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium having inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that under the consideration of inertial warm ions along with inertial negatively charged dust grains, the plasma system supports both fast and slow DIA modes. The charge state and number dens…
Linear analysis of the stability of diffuse clouds in the cold neutral medium with uniform magnetic field is performed. We consider that gas in equilibrium state is heated by cosmic rays, X-rays and electronic photoeffect on the surface of dust grains, and it is cooled by the collisional excitation of fine levels of the CII. Ionization by cosmic rays and radiative recombinations is taken into account. A dispersion equation is solved analytically in the limiting cases of small and large wave numbers, as well as numerically in the general case. In particular cases the dispersion equation describ…
Evolution of the parametric decay instability (PDI) of a circularly polarized Aflvén wave in a turbulent low-beta plasma background is investigated using 3D hybrid simulations. It is shown that the turbulence reduces the growth rate of PDI as compared to the linear theory predictions, but PDI can still exist. Interestingly, the damping rate of ion acoustic mode (as the product of PDI) is also reduced as compared to the linear Vlasov predictions. Nonetheless, significant heating of ions in the direction parallel to the background magnetic field is observed due to resonant Landau damping of the …
For more than 12 hours beginning on January 18, 2021, continuous narrowband electrostatic emissions were observed on Parker Solar Probe near 20 solar radii. The observed <1000 Hz frequencies were well below the local ion plasma frequency. Surprisingly, the emissions consisted of electrostatic wave packets with shock-like envelopes, appearing repetitively at a ~1.5 Hz rate. This repetitiveness correlated and was in phase with low frequency electromagnetic fluctuations. The emissions were associated with simultaneously observed ion beams and conditions favorable for ion-acoustic wave excitation,…
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
