Nonplanar double layers in plasmas with opposite polarity dust

Nonplanar (cylindrical and spherical) double layers (DLs) in a four-component dusty plasma (composed of inertial positively and negatively charged dust, Boltzmann electrons and ions) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the dust-acoustic (DA) waves is derived, and its nonplanar double layer solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential only, are obtained. The basic features of nonplanar DA DLs, which are found to be different from planar ones, are also identified. The implications of our results to different space and laboratory dusty plasma situations, where opposite polarity dust are observed, are discussed.     

Arbitrary amplitude solitary waves and double layers in an ultra-relativistic degenerate dense dusty plasma

Arbitrary amplitude solitary waves (SWs) and double layers (DLs) in an ultra-relativistic degenerate dense dusty plasma (containing ultra-relativistic degenerate ultra-cold electron fluid, inertial ultra-cold ion fluid, and negatively charged static dust) have been investigated by the pseudo-potential approach. It has been found that for δ=1 (where δ is the ratio of nonlinear wave speed to linear wave phase speed) extremely large amplitude DLs with negative potential exist for μ=0.537 (where μ is the ratio of dust charge density to ion charge density) and SWs with negative potential exist for 1>μ>0.537. It is also shown that for δ>1 only SWs with positive potential exist for 0?μ<0.537, but SWs with positive potential coexist with SWs or DLs with a negative potential for 0.537>μ>0.851. The implications of our results in some compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.     

Modulational instability of dust-ion-acoustic waves in pair-ion plasma having non-thermal non-extensive electrons

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 of the DIARWs are examined, and it is found that the MI growth rate increases (decreases) with increasing the number density of the negatively charged dust grains in the presence (absence) of the negative ions. It is also observed that the amplitude and width of the DIARWs increase (decrease) with the negative (positive) ion mass. The implications of the results to laboratory and space plasmas are briefly discussed.     

Roles of positively charged dust in the formation of ion-acoustic subsonic solitary waves in electron-ion-positively charged dust plasmas

The electron-ion-positively charged dust plasma system containing Boltzmann distributed electron species, cold inertial ion species, and stationary positively charged dust (pcd) species are considered. The roles of pcd species in the formation of ion-acoustic (IA) subsonic solitary waves (SWs) are investigated by the pseudo-potential approach, which is valid for arbitrary amplitude time-independent subsonic SWs, as well as by the reductive perturbation method, which is valid for the time-dependent small amplitude subsonic SWs. It is observed that the presence of the pcd species reduces the phase speed of the IA waves, and consequently supports the IA subsonic SWs with the positive wave potential in such electron-ion-pcd plasmas. This is due to the reduction of the space charge electric field by the presence of the pcd species. The applications of the work in space environments (viz. Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc.), where pcd species have been detected, are briefly discussed.     

Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic （DIA） shock waves in an unmagnetized dusty plasma （containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains） are investi- gated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.     

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Kadomtsev-Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili-Burgers (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.     

Cylindrical and spherical electron-acoustic Gardner solitons and double layers in a two-electron-temperature plasma with nonthermal ions

Cylindrical and spherical Gardner solitons (GSs) and double layers (DLs) in a two-electron-temperature plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the electron-acoustic (EA) waves is derived, and its nonplanar GS and DL solutions are numerically analyzed. The parametric regimes for the existence of GSs, which are associated with both positive and negative potential, and DLs which are associated with positive potential, are obtained. The basic features of nonplanar EA GSs, and DLs, which are found to be different from planar ones, are also identified. The implications of our results in space and laboratory plasmas are briefly discussed.     

Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves

The nonlinear propagation of dust-ion-acoustic (DIA) waves in an adiabatic dusty plasma (containing adiabatic inertial-less electrons, adiabatic inertial ions, and negatively charged static dust) is investigated by the pseudo-potential approach. The combined effects of adiabatic electrons and negatively charged static dust on the basic properties (critical Mach number, amplitude, and width) of small as well as arbitrary amplitude DIA solitary waves are explicitly examined. It is found that the combined effects of adiabatic electrons and negatively charged static dust significantly modify the basic properties (critical Mach number, amplitude, and width) of the DIA solitary waves. It is also found that due to the effect of adiabaticity of electrons, negative DIA solitary waves [which are found to exist in a dusty plasma (containing isothermal electrons, cold ions, and negatively charged static dust) for α=zdnd0/ni0>2/3, where zd is the number of electrons residing onto a dust grain surface, nd0 is the constant (static) dust number density and ni0 is the equilibrium ion number density] disappears, i.e. due to the effect of adiabatic electrons, one cannot have negative DIA solitary waves for any possible set of dusty plasma parameters [0?α<1 and 0?σ=Ti0/Te0?1, where Ti0 (Te0) is electron (ion) temperature at equilibrium].     

Current-driven dust ion-acoustic instability in a collisional dustyplasma

A fluid analysis of the excitation of dust ion-acoustic (DIA) waves in a collisional dusty plasma is presented. The DIA waves are excited by a relative drift of the electrons and ions produced by a steady-state electric field applied to the plasma. The DIA instability is more easily excited if the relative concentration of negatively charged dust is increased     

Nonplanar dust ion-acoustic solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution

Properties of nonplanar (viz. cylindrical and spherical) dust ion-acoustic (DIA) solitary and shock waves propagating in a dusty plasma containing charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following a vortex-like distribution, are investigated by the reductive perturbation method. It has been shown that all the basic features of the DIA solitary and shock waves are significantly modified by the effects of vortex-like electron distribution, dust charge fluctuation, and nonplanar cylindrical and spherical geometries. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.     

Formation of dust-acoustic shock waves in a strongly coupled cryogenic dusty plasma

The nonlinear propagation of ultra-low-frequency dust-acoustic (DA) waves in a strongly coupled cryogenic dusty plasma has been investigated, by using the Boltzmann distributed electrons and ions, as well as modified hydrodynamic equations for strongly coupled charged dust grains. The reductive perturbation technique is used to derive the Burger equation. It is shown that strong correlations among negatively charged dust particles acts like a dissipation, which is responsible for the formation of the DA shock waves. The latter are associated with the negative potential, i.e. with the compression of negatively charged cryogenic dust particle density. It is also found that the effective dust-temperature, which arises from electrostatic interactions among negatively charged dust particles, significantly affects the height of the DA shock structures. New laboratory experiments at cryogenic temperature should be conducted to verify our theoretical prediction.     

Wake potential with mobile positive/negative ions in multicomponent dusty plasmas

We employ the test charge approach to calculate the electrostatic potential for a test charge in a multicomponent dusty plasma, whose constituents are the Boltzmann distributed electrons, mobile positive and negative ions, and immobile positive/negative charged dust particles. By using the modified dielectric constant of the dust-ion-acoustic (DIA) waves, the Debye screening and wake potentials are obtained. It is found that the presence of mobile negative ions significantly modify the DIA speed and the wake potential. The present results are relevant to polar mesosphere and microelectronic in the context of charged particle attraction and repulsion.     

Effect of superthermal electrons on dust-acoustic Gardner solitons in nonplanar geometry

The properties of nonplanar (cylindrical and spherical) dust-acoustic solitary waves (DASWs) in an unmagnetized, collisionless three-component dusty plasma, whose constituents are negatively charged cold dust fluid, superthermal/non-Maxwellian electrons (represented by kappa distribution) and Boltzmann distributed ions, are investigated by deriving the modified Gardner (MG) equation. The well-known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar DA Gardner solitons (GSs) are discussed. It is seen that the properties of nonplanar DAGSs (positive and negative) significantly differ as the value of spectral index κ changes.     

Dust ion-acoustic solitary waves in a hot adiabatic magnetized dusty plasma

The basic features of obliquely propagating dust ion-acoustic (DIA) solitary waves in a hot adiabatic magnetized dusty plasma (containing adiabatic inertia-less electrons, adiabatic inertial ions, and negatively charged static dust) have been investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation which admits a small amplitude solitary wave solution. The combined effects of plasma particle (electron and ion) adiabaticity, ion-dust collision, and external magnetic field (obliqueness), which are found to significantly modify the basic features of the small but finite-amplitude DIA solitary waves are explicitly examined. The implications of our results in space and laboratory dusty plasmas are briefly discussed.     

Effects of Vortex-Like Ion Distribution on Dust-Acoustic Solitary Waves in a Self-Gravitating Opposite Polarity Dusty Plasmas

A self-gravitating opposite polarity dust plasma (SGOPDP) medium (containing both positively and negatively charged dust, vortex-like distributed ions and Maxwellian electrons) has been considered in order to examine the effect of vortex-like (trapped) ion distribution on dust-acoustic (DA) solitary waves (SWs) propagating in SGOPDP medium. The reductive perturbation method, which is valid for small but finite amplitude SWs, is employed to derive a modified Korteweg-de Vries equation having stronger nonlinearity. The basic features of the DA SWs in SGOPDP medium are found to be significantly modified by the combined effect of self-gravitational field and vortex-like ion distribution. The results of this paper have many implications in space and laboratory dusty plasmas.

     

A New Approach to Energy Integral for Investigation of Dust-Ion Acoustic(DIA)Waves in Multi-Component Plasmas with Quantum Effects in Inertia Less Electrons

Dust-ion acoustic waves are investigated in this model of plasma consisting of negatively charged dusts,cold ions and inertia less quantum effected electrons with the help of a typical energy integral.In this case,a new technique is applied formulating a differential equation to establish the energy integral in case of multi-component plasmas which is not possible in general.Dust-ion acoustic(DIA) compressive and rarefactive,supersonic and subsonic solitons of various amplitudes are established.The consideration of smaller order nonlinearity in support of the newly established quantum plasma model is observed to generate small amplitude solitons at the decrease of Mach number.The growths of soliton amplitudes and potential depths are found more sensitive to the density of quantum electrons.The small density ratio r(=1-f) with a little quantized electrons supplemented by the dust charges Z_d and the in-deterministic new quantum parameter C_2 are found responsible to finally support the generation of small amplitude solitons admissible for the model.     

Nonlinear interaction phenomenon of dust acoustic solitary and shock waves in dusty plasma

The effects of head-on collision on dust acoustic (DA) solitary and shock waves in dusty plasma are investigated considering positively charged inertial dust, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and superthermal electrons in the plasma system. The nonlinear Korteweg-de-Vries (KdV) Burger equations are derived taking the extended Poincaré-Lighthill-Kuo method into account to study the characteristic properties of nonlinearity and production of solitary shock due to collisions. The study reveals that the amplitudes and widths of the DA shock waves are decreasing with increasing viscosity, electron to dust density ratio, and dust to ion temperature ratio, while they are increasing due to the presence of superthermal electrons. The nonlinearity of DA waves are enhanced with increasing density ratio of electron to dust and temperature ratio of dust to ion and electron, respectively, but it is reducing with superthermal electrons. The phase shifts of DA solitary waves are found to decrease with rising superthermality of electrons and increase with the density ratio of electron to dust.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.