Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

Solar wind driven electrostatic instabilities with generalized (r,q) distribution function

Using Boltzmann–Vlasov kinetic model, a currentless ion acoustic instability driven by stream of solar wind plasma is studied in a non‐thermal distributed electrons and ions. The non‐thermal distribution considered here is the generalized distribution which has low energetic flat‐top and velocity power law tail at higher energies. The instability threshold is found to be affected and depends upon the spectral indices r and q . It is found that the growth rate increases with the decrease in the value of r and increase with q . Moreover, such kinetic instability has also been discussed for three species electron–ion–dust plasma using the generalized (r, q) distribution function. Such case is of interest when the solar wind is streaming through the cometary plasma in the presence of interstellar dust and excites electrostatic instabilities. The dispersion properties and growth rates for ion‐acoustic and dust‐acoustic mode are calculated analytically and plotted for different values of the spectral indices r and q .     

Ion‐ and positron‐acoustic solitons in magnetized dusty plasma with q‐non‐extensive electron and positron velocity distribution

In this study, the properties of ion‐ and positron‐acoustic solitons are investigated in a magnetized multi‐component plasma system consisting of warm fluid ions, warm fluid positrons, q‐non‐extensive distributed positrons, q‐non‐extensive distributed electrons, and immobile dust particles. To drive the Korteweg–de Vries (KdV) equation, the reductive perturbation method is used. The effects of the ratio of the density of positrons to ions, the temperature of the positrons, and ions to electrons, the non‐extensivity parameters q_e and q_p , and the angle of the propagation of the wave with the magnetic field on the potential of ion‐ and positron‐acoustic solitons are also studied. The present investigation is applicable to solitons in fusion plasmas in the edge of tokamak.     

Retrieval of currents of multiply charged ions emitted from laser-produced carbon plasma

The emission of ions from laser-produced carbon plasmas is investigated by a deconvolution of ion collector signals. The deconvolution is based on the use of Kelly and Dreyfus function expressing the time-resolved ion current to recover hidden peaks in an ion collector signal. The parameters of recovered C ^q+ (1?≤?q?≤?6) currents make possible the quantification of properties of laser-produced plasmas. The drift and peak velocities of C ^q+ ions, the abundance of ions and the plasma temperature are presented in the dependence on focused laser beam energy. The carbon plasma was generated employing either single 9-ns pulses of second harmonics (532 nm) of Nd:YAG laser or pulses repeated at a stable repetition rate of 30 Hz.     

Plasmons and their damping in a doped semiconductor superlattice

The complex zeroes of dielectric response function of a doped GaAs superlattice are computed to study the frequencies and damping rates of oscillations in coupled electron-hole plasma. The real part of a complex zero describes the plasma frequency, whereas imaginary part of it yields the damping rate. Strong scattering of charge carriers from random impurity potentials in a doped GaAs superlattice gives rise to a large value of damping rate which causes over-damping of plasma oscillations of coupled electron-hole gas below q_c, a critical value of wave vector component (q) along the plane of a layer of electrons (holes). The plasma oscillations which correspond to electrons gas enter into over-damped regime for the case of weak coupling between layers. Whereas, plasma oscillations which belong to hole gas go to over-damped regime of oscillations for both strong as well as weak coupling between layers. The damping rate shows strongq-dependence forq < q_c, whereas it weakly depends onq forq ≥q _c . The damping rate exhibits a sudden change atq =q _c , indicating a transition from non-diffusive regime (where collective excitation can be excited) to diffusive regime (over-damped oscillations).     

Effects of non‐extensive electrons on the sheath of dusty plasmas with variable dust charge

In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.     

Dust ion‐acoustic solitons with trapped q‐non‐extensive electrons,dissipative processes,and streaming ions

The characteristics of dust ion‐acoustic waves (DIAWs) that are excited because of streaming ions and hot q‐non‐extensive electrons obeying a vortex‐like distribution are investigated. By exploiting a pseudo‐potential technique, we have derived an energy integral equation. The presence of non‐extensive q‐distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton‐like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency β. Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.     

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Effects of plasma nonextensivity on the nonlinear cnoidal ion‐acoustic wave in unmagnetized electron‐positron‐ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion‐acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron (σ). For all of the acceptable values of q, the cnoidal ion‐acoustic wave is compressive. Results show that ion‐acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and σ on the characteristics of the ion‐acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency.     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.     

Ion‐Acoustic Waves Instability in a Three Components Magneto‐Plasma with Nonthermal Electrons

A theoretical investigation has been made on obliquely propagating ion‐acoustic (IA) solitary structures in a three components magneto‐plasma containing cold inertial ions, Boltzmann distributed positrons, and hot non‐thermal electrons. The Zakharov‐Kuznetsov equation has been derived by the reductive perturbation method, and its solitary wave solution has been analyzed. Multi‐dimensional instability has also studied by the small‐k (long wave‐length plane wave) perturbation expansion technique, which is found to exist in such a plasma. The effects of the external magnetic field, nonthermal electrons, obliqueness and temperature ratio have significantly modified the basic properties of small but finite‐amplitude IA solitary waves, such as amplitude, width, instability criterion and the growth rate. The present investigation contributes to the physics of the nonlinear IA waves in space and laboratory electron‐positron‐ion magneto‐plasmas in which wave damping produces an electron tail. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geodesic mode spectrum modified by the energetic particles in tokamak plasmas

Effect of a minor concentration of the energetic particles on GAM spectrum in a tokamak is analyzed by drift kinetic theory taking into the account the electron current and diamagnetic drift. A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles in the limit of high bounce frequency in comparison with the GAM frequency. Using the Q-asymptotic of Jacobi function, it is shown that the energetic minority ions can form the continuum minimum/maximum at the NB or ICR power deposition maximum where the geodesic eigenmode may be excited. In this case, the electron current modeled by shifted Maxwell distribution overcomes the ion Landau damping threshold thus resulting in the GAM instability.     

Stability of electrostatic ion cyclotron waves in a multi-ion plasma

We have studied the stability of the electrostatic ion cyclotron wave in a plasma consisting of isotropic hydrogen ions (H⁺) and temperature-anisotropic positively (O⁺) and negatively (O⁻) charged oxygen ions, with the electrons drifting parallel to the magnetic field. Analytical expressions have been derived for the frequency and growth/damping rate of ion cyclotron waves around the first harmonic of both hydrogen and oxygen ion gyrofrequencies. We find that the frequencies and growth/damping rates are dependent on the densities and temperatures of all species of ions. A detailed numerical study, for parameters relevant to comet Halley, shows that the growth rate is dependent on the magnitude of the frequency. The ion cyclotron waves are driven by the electron drift parallel to the magnetic field; the temperature anisotropy of the oxygen ions only slightly enhance the growth rates for small values of temperature anisotropies. A simple explanation, in terms of wave exponentiation times, is offered for the absence of electrostatic ion cyclotron waves in the multi-ion plasma of comet Halley.     

Kinetic treatment of acoustic waves in a four‐component dusty plasma

A kinetic formulation is developed to investigate low‐frequency dust ion acoustic waves (DIAWs) and dust acoustic waves (DAWs) as well as numerically for a four‐component, collisionless, unmagnetized dusty plasma, using the linearized Vlasov–Poisson model for species obeying the Maxwellian distribution. In particular, the dynamics of low‐frequency DIAWs is investigated by considering two cases. In the first case, ions and positive dust particles are assumed to be dynamically adiabatic while the negative dust particles are static in the background. In second case, the ions are taken adiabatic, while both positive and negative dust particles are static in the background. For DAWs, the ions are assumed to be isothermal, while both positive and negative dust species are considered adiabatic. Electrons are assumed to be isothermal in all cases. The linear characteristics and Landau damping rates for DIAWs and DAWs are investigated with effects of the dust particle concentrations and different temperature ratios. It is noted that for higher values of positive dust concentration, DIAWs (DAWs) are less (more) damped. It is also observed that the damping rate increases (decreases) as T_i approaches T_e for DIAWs (DAWs). It is worth adding here that the theoretical results presented here are supported by numerical analyses and illustrations. The relevance of the study to laboratory and cosmic plasmas is also pointed out.     

Dust ion acoustic waves in non-thermal Cairns bi-Maxwellian plasma

Using kinetic theory approach, the dispersion relation ω_r and Landau damping rate γ for dust ion acoustic waves are investigated numerically and analytically in an unmagnetized collisionless dusty plasma considering Cairns distribution for electrons and ions in stationary dust particles background. The phase velocity and Landau damping rate are calculated in the limits v_td∥ < v_ti∥ << ω/k << v_te∥ . The electrons and ions non-thermality effects are incorporated via the non-thermality parameter (0 ≤ α < 1) . The real frequency ω_r and Landau damping rate γ of the mode in Cairns bi-Maxwellian distributed plasma are graphically shown to depend on plasma parameters namely non-thermality index α , ion to electron temperature ratio T_i∥/T_e∥ and the dust concentration parameter δ (=1 − ηZ_d) .     

A Simple Ion Source for Monoenergetic Multiply Charged Ion Beams

A small and inexpensive electron beam ion source for multiply charged ions of noble gases is described. One of its essential characteristics is the low energy spread of the extracted ion beam, which depends on the charge state q of the ions and amounts to ∽q × 50 meV. The total ion current containing ionic states up to q = 6 is in the order of 10 nA. The design, construction and important parameters of the ion source are described.     

Thermally Conducting Partially Ionized Plasma in a Variable Magnetic Field

An infinitely extending homogenous partially ionized plasma endowed with several physical mechanisms and permeated by a variable magnetic field is considered. The combined effect of these parameters, namely, Hall currents, finite conductivity, ion viscosity, collision with neutrals and thermal conductivity on the gravitational instability of the plasma is studied. It is found that the several mechanisms play different physical roles in the perturbed problem. Jeans' Criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q = 1, q being the nonextensive parameter. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-dimensional drift solitary structures in inhomogeneous magnetized O?H ion plasmas with generalized (r,q) distributed electrons

In this paper, the effect of generalized (r, q) distributed electrons on the linear and nonlinear coupling of drift and ion acoustic waves in a nonuniform plasma containing Hydrogen and Oxygen ions is investigated. In the linear regime, it is observed that increasing the percentage of flat-topped (i.e. r > 0) electrons enhances the frequency of the coupled drift-ion acoustic waves, whereas the increasing values of the spectral index q mitigates it. In the nonlinear regime, one- and two-dimensional Korteweg de Vries-like and Kadomtsev-Petviashvili-like equations are derived and their solutions are plotted for different ratios of ion number densities and for different values of double spectral indices r and q of the generalized distribution of electrons. It is found that only rarefactive structures exist for two-dimensional solitons, however, both rarefactive and compressive structures are observed for the one-dimensional case. The limiting cases of kappa and Maxwellian distributions are also discussed and their comparison with the generalized (r, q) distribution is thoroughly investigated. Spatial scales for the formation of rarefactive and compressive solitary structures are also discussed with reference to the changing electron distribution functions. The possible applications of the present study are also spelled out with special reference to space plasmas.     

Variable‐size dust grains with generalized (r,q) electrons in a dusty plasma

The effect of the generalized (r, q) distribution on the non‐linear propagation of dust acoustic waves (DAWs) in a dusty plasma consisting of variable‐size dust grains is discussed. A Korteweg–de Vries (KdV) equation is derived using the reductive perturbation technique (RPT). The dust size obeys the power‐law dust size distribution (DSD). The present results reveal that rarefactive and compressive waves can propagate in the proposed plasma model. It is found that the spectral indices r and q influence the main properties of DAWs. Especially, the velocity, amplitude, and width of the DAW change drastically with r compared to changes in q.