Nonlinear dust acoustic waves in a charge varying complex plasma with nonthermal ions featuring Tsallis distribution

The concept of ion nonthermality is generalized within the theoretical framework of the Tsallis thermostatistics. In this connection, a physically meaningful ion distribution function is outlined. As the nonextensive character of the nonthermal ions increases, the distribution shoulders may become less or more prominent and high energy states are less or more probable than in the extensive nonthermal case. Variable charge dust acoustic waves are then addressed. We first consider the case of adiabatic dust charge variation and discuss later the case when the nonadiabatic charge variations are self-consistently included. Our results may complement and provide new insight into previously published work in nonthermal space plasmas.     

Formation of obliquely propagating dust-ion-acoustic shock waves due to dust charge fluctuation in magnetized nonthermal dusty plasma

A theoretical investigation is made on the formation as well as basic properties of dust-ion-acoustic (DIA) shock waves in a magnetized nonthermal dusty plasma consisting of immobile charge fluctuating dust, inertial ion fluid and nonthermal electrons. The reductive perturbation method is employed to derive the Korteweg-de Vries-Burgers equation governing the DIA shock waves. The combined effects of external static magnetic field, obliqueness, nonthermal electron distribution and dust charge fluctuation on the DIA shock waves are also investigated. It is shown that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the DIA shock waves. It is also observed that the combined effects of obliqueness, nonthermal electron distribution and dust charge fluctuation significantly modify the basic properties of the DIA shock waves. The implications of our results in space and laboratory dusty plasma situations are briefly discussed.     

Dust acoustic shock waves in suprathermal dusty plasma in the presence of ion streaming with dust charge fluctuations

Dust acoustic (DA) shock waves are investigated in a dusty plasma having a high-energy-tail electron distribution. The effects of ion streaming, charge variation and electron deviation from the Maxwellian distribution on the DA shock wave are then considered. It is shown that as the suprathermal character of the plasma is increased, the potential amplitude enhances. It is also found that the ion temperature may be destructive for the formation of DA shock waves. Their strength decreases with increasing ion streaming speed. Our results may be useful in understanding the basic nonlinear features of the DA wave propagation that may occur in space dusty plasmas, especially those including a relative motion between species (comet tails, solar wind streams, etc.).     

Alternative dust-ion acoustic waves in a magnetized charge varying dusty plasma with nonthermal electrons having a vortex-like velocity distribution

The Kadomtsev-Petviashvili equation in unmagnetized plasma having ions and superthermal electrons and positrons has been derived using the reductive perturbation method. The space-time-fractional Kadomtsev-Petviashvili equation is formulated applying the Euler-Lagrange variational technique and is solved using the sub-equation method. The effects of space time fractional order and superthermal parameters on the properties of obtained soliton have been investigated.     

Evolution of double layers in magnetised plasmas contaminated with dust charge fluctuations

Coherent structures entailing the existence of double layers have been studied in magnetised plasma contaminated with dust charging fluctuations. It has been shown that the dust charging in magnetic plasma leads to complexity in the derivation of the Sagdeev wave equation, but under way new procedure enable one to study the nature of double layers showing the effective role of the constituents of the plasma. A parametric analysis is a subject of interest in laboratory and space plasmas, and it has been explained with the input of various typical plasma numerics. The proposed mathematical mechanism has shown the success to yield plasma acoustic modes in a dusty plasma which, in turn, has been solved convincingly for double layers. Observations have been evaluated in an appropriate model with a view to agree with the observations in astrophysical problems dealing with present new findings.     

Electron-acoustic solitons in plasma with nonthermal electrons

Nonlinear electron-acoustic solitary waves (EASWs) are studied using Sagdeev’s pseudo-potential technique in a collisionless unmagnetized plasma consisting of a cold electron fluid, nonthermal hot electrons and stationary ions. It is shown that the presence of fast nonthermal electrons may modify the parametric region where electron-acoustic solitons may exist. Our investigation is of wide relevance to astronomers and space scientists working on interstellar space plasmas.     

Effects of dust charge fluctuations and deviations from isothermality of electrons on nonlinear dust ion-acoustic waves

The effects of dust charge fluctuations and deviations from isothermality of electrons are incorporated in the study of nonlinear dust ion-acoustic waves. Deviations from isothermality of electrons are included in this model as a result of nonlinear resonant interaction of the electrostatic wave potential with electrons during its evolution. The basic properties of stationary structures are studied by employing the reductive perturbation method, and conditions for the formation of small but finite amplitude dust ion-acoustic solitary waves in the space dusty plasma situations are clearly explained. It is shown that a more depletion of the background free electrons owing to the attachment of these electrons to the surface of the dust grains during the charging process can lead to the formation of solitary waves with smaller amplitude. Furthermore, effects of the dust charge fluctuation and deviations from isothermality of electrons show a non-uniform behavior for the amplitude of solitary waves in transition from the Boltzmann electron distribution to a trapped electron one. It is also found that the dust charge fluctuation caused by trapped as well as free electrons is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves.     

Dust acoustic soliton energy in a mixed nonthermal high energy-tail electron distribution

Weak dust acoustic (DA) solitary waves are investigated in a mixed nonthermal high energy-tail electron distribution, focusing on the influence of an interplay between nonthermality and superthermality on the DA soliton energy. It is shown that in a pure superthermal plasma (α=0), electron thermalization (κ→∞) leads to an increase of the energy carried by the soliton. Addition of minute quantities of nonthermal electrons drastically modifies the κ-dependence of the soliton energy E _κ,α . The latter first decreases, then exhibits a local minimum before leveling at a constant value. The energy exchange between the non-Maxwellian electrons and the localized solitary structure depends drastically on the interplay between superthermality and nonthermality.     

Large amplitude double layers in a dusty plasma with nonthermal electrons featuring Tsallis distribution

The problems of large amplitude double layers are discussed using Sagdeev’s pseudo-potential technique for a dusty plasma comprising two temperature isothermal ions and nonextensive nonthermal velocity distributed electron. For different sets of plasma parameter values, the Sagdeev potential V(?) has been plotted. It is found that nonextensive q parameter plays a significant role in determining the shape and size of large amplitude double layers. Also, it is observed that the existence of large amplitude double layers depends on different plasma parameters.     

Nonextensive dust acoustic waves in a charge varying dusty plasma

Our recent analysis on nonlinear nonextensive dust-acoustic waves (DA) [Amour and Tribeche in Phys. Plasmas 17:063702, 2010] is extended to include self-consistent nonadiabatic grain charge fluctuation. The appropriate nonextensive electron charging current is rederived based on the orbit-limited motion theory. Our results reveal that the amplitude, strength and nature of the nonlinear DA waves (solitons and shocks) are extremely sensitive to the degree of ion nonextensivity. Stronger is the electron correlation, more important is the charge variation induced nonlinear wave damping. The anomalous dissipation effects may prevail over that dispersion as the electrons evolve far away from their Maxwellian equilibrium. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar dusty plasmas where nonthermal distributions are turning out to be a very common and characteristic feature.     

Dust acoustic shock waves in a suprathermal dusty plasma with dust charge fluctuation

The properties of small but finite amplitude dust acoustic (DA) shock waves are studied in a charge varying dusty plasma with ions and electrons having kappa velocity distribution. We obtain the global Debye length including the influence of suprathermality effects and dust charge fluctuations. It is shown that the effects of suprathermality of ions/electrons and dust charge fluctuation significantly modify the basic properties of DA shock wave. We observe that only negative DA shock waves will be excited in this model. The amplitude of DA shock wave increases with deviation of electrons or ions from Maxwellian distribution via decrease of spectral index, κ _j (j=i,e denotes, ions and electrons, respectively). Also, it is indicated that the amplitude and steepness of the shock front decreases with an increase in the ion temperature.     

Effects of nonthermal ions of distinct temperatures on dust acoustic shock waves in a dusty plasma

The nonlinear propagation of dust acoustic (DA) waves in an unmagnetized dusty plasma system consisting of negatively charged mobile dust fluid, Boltzmann distributed electrons, and two-temperature nonthermally distributed ions, is rigorously investigated. The reductive perturbation method has been employed to derive the Burgers equation. The hydrodynamic equation for inertial dust grains has been used to derive the Burgers equation. The effects of two temperature nonthermally distributed ions and dust kinematic viscosity, which are found to significantly modify the basic features of DA shock waves, are briefly discussed. Our present investigation can be effectively utilized in many astrophysical situations (e.g. satellite or spacecraft observations, Saturn’s E ring, etc.), which are discussed briefly in this analysis.     

Return current and collisional effects in nonthermal electron beams with pulsed injection

The evolution of a pulse of nonthermal electrons, with a truncated power-law spectrum, injected into a uniformly dense coronal plasma, is studied by the 1-D particle simulation of return current and direct collisional effects. The beam pulse injection profile varies gradually enough for total current neutrality, and a steady-state Ohm's law for the return current, to apply at each point and time. Quasi-linear relaxation of the beam is deliberately ignored in order to isolate the modification of return current effects by pulsed injection.When parameters are such that return current losses dominate, the resulting energetic electron trajectories differ very markedly between the pulsed injection case and the continuous injection case for the same beam current at injection. In general, the energy losses to return current dissipation are lower in the pulsed case. This is due to the rapid fall in the local beam current as the pulse disperses in space. Conditions necessary for the beam to comprise a series of pulses sufficiently separated for dispersion effects to be significant are also discussed.On leave from the Astronomical Institute of the Czechoslovak Academy of Sciences, 25165 Ondejov, Czechoslovakia.     

Dust acoustic solitary waves in dusty plasma with nonthermal ions

In this paper, the characteristics of the dust acoustic solitary waves in dusty plasmas are studied. The distribution of ions is nonthermal, and the nonthermal parameter is treated as a variable. The pseudo-potential method has been used to investigate the possibility of soliton formation. We show that for some values of the nonthermal parameter there is no soliton.     

Dust acoustic solitary and shock waves in coupled dusty plasmas with variable dust charge and vortex-like ion distribution

The modified Kodomtsev-Petviashvili-Burger (mKP-Burger) and Kodomtsev-Petviashvili-Burger equations are derived in strongly coupled dusty plasmas containing iso-nonthermal ions; Boltzmann distributed electrons and variable dust charge. We use reductive perturbation method and discuss on solitary waves and shock waves solutions of these equations.     

Temperature fluctuations in interstellar dust grains

Temperature fluctuations in interstellar dust grains caused by absorption of ultraviolet photons are discussed. Temperature probability distributions are presented for various assumptions about the grain specific heat and far infrared emissivity. Grains smaller than or about 0.01 may suffer large temperature fluctuations and would spend most of their time at very low temperatures. The equilibrium temperature is not a good measure for most average temperatures of such grains. It is shown that, although small grains spend only a small fraction of their time at the higher temperatures, the emitted far infrared spectrum is significantly shifted towards shorter wavelengths than predicted for grains assumed to be at the equilibrium temperature.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

Ion-acoustic rogue waves in a plasma with a q-nonextensive electron velocity distribution

Ion-acoustic rogue waves (IARWs) are addressed in a two-component plasma with a q-nonextensive electron velocity distribution. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries (K-dV) equation with a particular emphasis on its application to the IARWs. This K-dV equation is transformed to a nonlinear Schr?dinger equation, provided that the frequency of the carrier wave is much smaller than the ion plasma frequency. Interestingly, it is found that the IARWs may be drastically affected by electron nonextensivity depending on whether the entropic index q is positive or negative. In view of the crucial importance of RWs in space environments, our results should be useful in understanding the basic features of the nonextensive IARGs that may occur in space plasmas.     

Large-amplitude dust-ion acoustic solitary waves in a dusty plasma with nonthermal electrons

Propagation regimes of large-amplitude dust-ion acoustic solitary wave in a dusty plasma with nonthermal electrons are analyzed by employing the Sagdeev potential technique. Two domains of the Mach numbers are defined depending on the nonthermal and plasma parameters. The two types of soliton solution are found to be exited corresponding to certain values of the nonthermal parameter. Numerical solutions are presented that illustrate the dependence of soliton characteristics on practically interesting plasma and nonthermal parameters. The findings of this investigation could be useful in understanding the detected solitary waves in space plasma in the presence of nonthermal electrons such as electrostatic solitary structures observed in Saturn’s E-ring.     

Planar electron-acoustic solitary waves and double layers in a two-electron-temperature plasma with nonthermal ions

A rigorous theoretical investigation of nonlinear electron-acoustic (EA) waves in a plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) is studied by the reductive perturbation method. The modified Gardner (MG) equation is derived and numerically solved. It has been found that the basic characteristics of the EA Gardner solitons (GSs), which are shown to exist for α around its critical value α _c [where α is the nonthermal parameter, α _c is the value of α corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation, e.g. α _c ≃0.31 for μ=n _h0/n _i0=0.5, σ=T _h /T _i =10, n _h0, n _i0 are, respectively, hot electron and nonthermal ion number densities at equilibrium, T _h (T _i ) is the hot electron (ion) temperature], are different from those of the K-dV solitons, which do not exist for α around α _c , and mixed K-dV solitons, which are valid around α∼α _c , but do not have any corresponding double layers (DLs) solution. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential, are obtained. The present investigations can be observed in various space plasma environments (viz. the geomagnetic tail, the auroral regions, the cusp of the terrestrial magnetosphere, etc.).