Collisionless Unmagnetized Plasma Research Articles

Kinetic theory of dust ion acoustic waves in a kappa-distributed plasma

Using a kinetic theory approach, dust ion acoustic (DIA) waves are investigated in an unmagnetized collisionless plasma with kappa-distributed electrons and ions, and Maxwellian dust grains of constant charge. Both analytical and numerical results, the latter following from the full solution of the associated dispersion relation, are presented, and a comparison is made. The effects of the ion and electron spectral indices, as well as the species' density (ne/ni) and temperature (Te/Ti) ratios, on the dispersion and damping of the waves are considered. In the long wavelength regime, increases in both the electron spectral index (κe) and the dust density fraction (reduced f=ne/ni) lead to an increase in phase velocity. The range in wavelength over which modes are weakly damped increases with an increase in Te/Ti. However, the ion spectral index, κi, does not have a significant effect on the dispersion or damping of DIA waves.

Roles of Superthermal Electrons and Adiabatic Heavy Ions on Heavy-Ion-Acoustic Solitary and Shock Waves in a Multi-Component Plasma

Heavy-ion-acoustic (HIA) waves in an unmagnetized collisionless plasma system comprising superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions have been investigated both numerically and analytically. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV) and Burgers (BG) equations. The parametric regimes for the existence of both the positive and negative solitary and shock waves have been obtained. The effects of adiabaticity of heavy ions and superthermality of electrons, which are found to notably modify the fundamental features (viz. polarity, amplitude, phase speed, etc.) of HIA solitary and shock waves, are precisely studied. The results of our theoretical investigation can be applicable to understand the characteristics and basic nonlinear structures of HIA waves both in space and laboratory plasma situations.

Landau damping of Gardner solitons in a dusty bi-ion plasma

The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold, and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely, the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids 12, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV), or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures (σ) and the number densities (μ) of hot and cold ions as well as the cold to hot ion mass ratio m. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV, and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn), in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.

Nonlinear Dust Acoustic Waves in Strongly Coupled Quantum Dusty Plasmas

Using a set of fluid equations to describe the inertial dust grain component in dense collisionless unmagnetized quantum dusty plasmas, where the electrons and ions obey the Thomas-Fermi density distribution, the propagation characteristics of dust acoustic solitary waves (DASWs) are studied. First, a linear dispersion of dust acoustic wave (DAW) is obtained, and it is shown that the DAW is modified by a strongly coupled parameter. Then for small amplitude solitary waves, the Korteweg-de Vries equation is obtained by applying the reductive perturbation technique. For arbitrary amplitude solitary waves, the Sagdeev potential method is employed and the Sagdeev potential is analyzed. In both cases, the effect of dust coupling parameters on the characteristics of DASWs in our system are analyzed.

Effect of nonthermal electrons and positrons on ion-acoustic solitary waves in a plasma with warm drifting ions

Using Sagdeev potential technique, ion-acoustic solitary waves have been theoretically studied in collisionless unmagnetized plasma consisting of nonthermal electrons, nonthermal positrons and warm drifting positive ions. Ion-acoustic solitary wave solutions have been obtained and its profiles have been numerically analyzed with respect to plasma parameters. The nonthermal parameters and temperatures are shown to play significant role on the formation and nature of solitary waves. It is shown that the nature, amplitude and width of lower- and higher-order solitons depend sensitively on these plasma parameters. The dependence of Sagdeev potential profile on different plasma parameters has also been examined. We have found that stronger nonthermality leads to shorter and wider solitons.

Large amplitude ion-acoustic rarefactive and compressive solitons and double layers in a dusty plasma with finite ion temperature

Large amplitude ion-acoustic solitons and double layers are studied using Sagdeev’s pseudo potential technique in a collisionless unmagnetized plasma consisting of hot and cold Maxwellian electrons, warm adiabatic ions, and heavily charged massive dust grains. It is found that for the selected set of plasma parameters, the system can support both solitons and double layers in the presence of negative as well as positive dust in the plasma. Further we have also investigated the ranges of parameters for simultaneous existence of both rarefactive and compressive supersonic solitons. The effects of dust concentration and ion temperature on the amplitude and Mach number of the double layer have also been studied. Our findings may be helpful in understanding the formation of non-linear structures, specially the solitons and double layers in space plasma, such as: in interstellar clouds, circumstellar clouds, planetary rings, comets, cometary tails, asteroid zones, auroral plasma, magnetospheric plasma, pulsars, and other astronomical environments and laboratory plasmas.

Electromagnetic plasma waves in the nonextensive statistics

This paper presents theoretical findings of new electromagnetic plasma waves in nonextensive and Maxwellian plasma below and above plasma frequency. The new waves are observed among the solutions of general and exact nonextensive dispersion relations for electromagnetic waves in unmagnetized collisionless plasma. The solutions for all values of nonextensive q parameter are also containing a light mode. The exact dispersion relations are obtained via calculation of kinetic dispersion integral using nonextensive distributions and hypergeometric function properties. Finally the effects of q parameter on the oscillation modes and damps are discussed.

Compressive and rarefactive dust-ion-acoustic Gardner solitons in a multi-component dusty plasma

The linear and nonlinear propagations of dust-ion-acoustic solitary waves (DIASWs) in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated theoretically. The linear properties are analyzed by using the normal mode analysis and the reductive perturbation method is used to derive the nonlinear equations, namely, the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. The basic features (viz., polarity, amplitude, width, etc.) of Gardner solitons (GS) are found to exist beyond the K-dV limit and these dust-ion-acoustic GS are qualitatively different from the K-dV and mK-dV solitons. It is observed that the basic features of DIASWs are affected by various plasma parameters (viz., electron nonextensivity, negative-to-positive ion number density ratio, electron-to-positive ion number density ratio, electron-to-positive ion temperature ratio, etc.) of the considered plasma system. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear structures and the characteristics of DIASWs propagating in both space and laboratory plasmas.

Dust ion acoustic rogue waves in superthermal warm ion plasma

The properties of dust ion acoustic rogue waves (DIARWs) in an unmagnetized collisionless plasma system composed of charged dust grains, superthermal electrons and warm ions as a fluid are studied. The multiple scale perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for DIARWs. From the coefficients of nonlinearity and dispersion, we have determined the critical wave number threshold kcr at which modulational instability sets in. This critical wave number depends on the various plasma parameters, viz. superthermality of electrons, ion temperature and dust concentration. Within the modulational instability region, a random perturbation of amplitude grows and thus, creates DIARWs. It is found that DIARWs are significantly affected by electron superthermality (via κ), ion temperature (via σ) and dust concentration (via f). In view of the crucial importance of DIARWs in space environments, our results may be useful in understanding the basic features of DIARWs that may occur in space plasmas.

Theoretical description based on general and exact nonextensive dispersion relations of plasma oscillation data and verification of new acoustic plasma waves

In this paper, first we represent the differences between spatial and temporal dispersions and their dependence on the measurement techniques for electrostatic waves in unmagnetized collisionless plasma. Then, three different experimental data are compared to the solutions of exact nonextensive dispersion relations for electron-ion and pair plasma. The results confirm the existence of new acoustic plasma waves. Furthermore, these comparisons yield a Maxwellian and a nonextensive plasma with nonextensive parameter q larger than one, and a Maxwellian plasma with some abnormal dispersion properties.

Large amplitude ion-acoustic double layers in warm dusty plasma

Large amplitude ion-acoustic double layer (IADL) is studied using Sagdeev's pseudo-potential technique in collisionless unmagnetized plasma comprising hot and cold Maxwellian population of electrons, warm adiabatic ions, and dust grains. Variation of both Mach number (M) and amplitude |φm| of large amplitude IADL with charge, concentration, and mass of heavily charged massive dust grains is investigated for both positive and negative dust in plasma. Our numerical analysis shows that system supports only rarefactive large amplitude IADL for the selected set of plasma parameters. Our investigations for both negative and positive dust grains reveal that ion temperature increases the mobility of ions, resulting in increase in the Mach number of IADL. The larger mobility of ions causes leakage of ions from localized region, resulting into decrease in the amplitude of IADL. Other parameters, e.g. temperature ratio of hot to cold electrons, charge, concentration, mass of heavily charged massive dust grains also play significant role in the properties and existence of double layers. Since it is well established that both positive and negative dust are found in space as well as laboratory plasma, and double layers have a tremendous role to play in astrophysics, we have included both positive and negative dust in our numerical analysis for the study of large amplitude IADL. Further data used for negative dust are close to experimentally observed data. Hence, it is anticipated that our parametric studies for heavily charged (both positive and negative) dust may be useful in understanding laboratory plasma experiments, identifying nonlinear structures in upper part of ionosphere and lower part of magnetosphere structures, and in theoretical research for the study of properties of nonlinear structures.

LINEAR VLASOV THEORY IN THE SHEARING SHEET APPROXIMATION WITH APPLICATION TO THE MAGNETO-ROTATIONAL INSTABILITY

We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low frequency guiding center (or "kinetic MHD") approximation, Hall MHD, and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.

Modulation Instability of Ion-Acoustic Waves in Plasma with Nonthermal Electrons

Modulational instability of ion-acoustic waves has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schrödinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons.

Effect of q-non-extensive distribution of electrons on the plasma sheath floating potential

In this paper, a collisionless unmagnetized plasma sheath consisting of electrons following non-extensive q-distribution, and cold mobile inertial ions is studied in the stationary state. In this type of plasma with non-Maxwellian electron distribution (Tsallis statistical mechanics), the effective electron temperature (Te, eff) and electron screening temperature (Te,*) are evaluated. The other plasma sheath phenomena such as the Bohm sheath criterion, Debye shielding, floating potential, and sheath length are investigated in the presence of q-non-extensive velocity-distributed electrons. It is observed that above-mentioned phenomena depend significantly on the non-extensive parameter q.

Overtaking collision of two ion acoustic soliton in a plasma with a q-nonextensive electron and thermal positrons

Theoretically the propagation of two ion acoustic soliton interaction in a three component collisionless unmagnetized plasma which consists of electrons, positrons and cold ions, has been investigated here by employing reductive perturbation technique. In this study, q distributed electrons and Maxwell-Boltzmann distributed positrons are considered and Korteweged-de Vries (KdV) equation is derived. The KdV equation is solved to get two soliton solution by using Hirota bilinear method. The effects of the q distributed electrons on the profiles of two soliton structures and the corresponding phase shifts are investigated. It is observed that both the nonextensive parameter (q) and the ratio of positrons density and electron density (p=n p0/n e0), play a significant role in the formation and existence of two soliton and also in the nature of their phase shifts.

Three dimensional electromagnetic wavepackets in a plasma: Spatiotemporal modulational instability

The nonlinear interaction of an intense electromagnetic beam with relativistic collisionless unmagnetized plasma is investigated by invoking the reductive perturbation technique, resting on the model of three-dimensional nonlinear Schrödinger (NLS) equation with cubic nonlinearity which incorporates the effects of self-focusing, self-phase modulation, and diffraction on wave propagation. Relying on the derived NLS equation, the occurrence of spatiotemporal modulational instability is investigated in detail.

Space Charge and Ponderomotive Force Effects in Interaction of High-Power Microwave With Plasma

The interaction between a high-power microwave beam and a collisionless unmagnetized plasma is investigated by taking into account the ponderomotive force and space charge effects. The electromagnetic wave equation coupled with Poisson and momentum transfer equations are solved for obtaining the space charge field and plasma density profiles. It is shown that the increase of microwave energy flux causes steepening of the electron density profiles, sawtooth lines in the curves of space charge field, and modulation of wavelength. In addition, the effect of wave frequency, initial electron density and electron temperature on space charge field, and electron density profiles are studied. It is indicated that the behavior of space charge field is very much influenced by the initial electron density. Furthermore, the result of the research shows that the increase of the electron temperature and microwave frequency cause the decrease of steepening of the electron density profiles.

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Nonlinear ion acoustic excitations in relativistic degenerate, astrophysical electron–positron–ion plasmas

AbstractThe dynamics and propagation of ion acoustic (IA) waves are considered in an unmagnetized collisionless plasma, whose constituents are the relativistically degenerate electrons and positrons as well as the inertial cold ions. At a first step, a linear dispersion relation for IA waves is derived and analysed numerically. For nonlinear analysis, the reductive perturbation technique is used to derive a Korteweg–deVries equation, which admits a localized wave solution in the presence of relativistic degenerate electrons and positrons. It is shown that only compressive IA solitary waves can propagate, whose amplitude, width and phase velocity are significantly modified due to the positron concentration. The latter also strongly influences all the relativistic plasma parameters. Our present analysis is aimed to understand collective interactions in dense astrophysical objects, e.g. white dwarfs, where the lighter species electrons and positrons are taken as relativistically degenerate.

Nonplanar Ion Acoustic Waves with Nonthermal Electrons

Using the standard reductive perturbation technique, nonlinear cylindrical and spherical Kadomtsev-Petviashvili (KP) equations are derived for the propagation of ion acoustic solitary waves in an unmagnetized collisionless plasma with nonthermal electrons and warm ions. The influence of nonthermally distributed electrons and the effects caused by the transverse perturbation on cylindrical and spherical ion acoustic waves (IAWs) are investigated. It is observed that the presence of nonthermally distributed electrons has a significant role in the nature of ion acoustic waves. In particular, when the nonthermal distribution parameter β takes certain values the usual cylindrical KP equation (CKPE) and spherical KP equation (SKPE) become invalid. One then has to have recourse to the modified CKPE or SKPE. Analytical solutions of both CKPE and SKPE and their modified versions are discussed in the present paper. The present investigation may have relevance in the study of propagation of IAWs in space and laboratory plasmas.