Abstract:
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 Schr？dinger (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. 1. Introduction Electron-positron-ion ( - - ) plasmas occur in many astrophysical environments such as active galactic nuclei [1], pulsar magnetospheres [2], polar regions of neutron stars [3], centres of our galaxy [4], the early universe [5, 6], and the solar atmosphere [7]. For this, over the last two decades there has been a great deal of interest in the study of nonlinear wave phenomena in - - plasmas [8–12]. Positrons are produced by pair production in high energy processes occurring in many astrophysical environments. Popel et al. [9] have reported decrease in soliton amplitude in the presence of positrons. Jehan et al. [13] have shown that solitons become narrower as the concentration of positron increases. The presence of non-Maxwellian electron is common in space and astrophysical plasmas including the magnetosphere [12] and auroral zones [14]. The presence of such non-Maxwellian electrons gives rise to many interesting characteristics in the nonlinear propagation of waves including the ion-acoustic solitons [15, 16]. The solitary structures with density depression in the magnetosphere observed by the Freja satellites [17, 18] have been explained by Cairns et al. [19] by assuming electron distribution to be nonthermal. Nonlinear ion-acoustic solitary waves in - - plasma have been considered by some authors [9, 20, 21] assuming ions to be cold. In practice ions have finite temperature and the ionic temperature can significantly affect the characteristics of nonlinear ion-acoustic structures [10, 22, 23]. Chawla et al. [24] have considered ion-acoustic waves in - - plasma with warm adiabatic ions and isothermal electrons. Baluku and Hellberg [25] have considered ion-acoustic solitary waves in - - plasma with cold ions and nonthermal electrons. Hence it is interesting to study the nonlinear ion-acoustic waves in - - plasma assuming simultaneous presence of nonthermal electrons, warm negative ions, and the positrons. Recently Pakzad [11] has shown that the presence of warm ions and nonthermal electrons

Abstract:
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width) of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region. 1. Introduction Nonlinear evolution equations are widely used as models to describe complex physical phenomena and have a significant role in several scientific and engineering fields [1, 2]. The propagation of solitary waves is important as it describes characteristic nature of the interaction of the waves and the plasmas. In the case where the velocity of particles is much smaller than that of light, ion-acoustic waves present the nonrelativistic behaviors, but in the case where the velocity of particles approaches that of light, the relativistic effect becomes dominant [3]. Actually high-speed and energetic streaming ions with the energy from 0.1 to 100？MeV are frequently observed in solar atmosphere and interplanetary space. Nevertheless, relativistic ion-acoustic waves have not been well investigated. When we assume that the ion energy depends only on the kinetic energy, such plasma ions have to attain very high velocity of relativistic order. Thus, by considering the weakly relativistic effect where the ion velocity is about 1/10 of the velocity of light, we can describe the relativistic motion of such ions in the study of nonlinear interaction of the waves and the plasmas [4]. It appears that the weakly relativistic and ion temperature effects play an important role in energetic ion-acoustic waves propagating in interplanetary space [5, 6]. Washimi and Taniuti [7] were the first to use reductive perturbation method to study the propagation of a slow modulation of quasi-monochromatic waves through plasma. And then the attention has been focused by many authors [8–11]. The evolution of small-but finite-amplitude solitary waves, studied by means

Abstract:
An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr?dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg－de Varies equation, obtained by a reductive perturbation theory, is satisfied.

Abstract:
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.

Abstract:
The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.

Abstract:
Bandyopadhyay and Das [Phys. Plasmas, 9, 465-473, 2002] have derived a nonlinear macroscopic evolution equation for ion acoustic wave in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons including the effect of Landau damping. In that paper they have also derived the corresponding nonlinear evolution equation when coefficient of the nonlinear term of the above mentioned macroscopic evolution equation vanishes, the nonlinear behaviour of the ion acoustic wave is described by a modified macroscopic evolution equation. But they have not considered the case when the coefficient is very near to zero. This is the case we consider in this paper and we derive the corresponding evolution equation including the effect of Landau damping. Finally, a solitary wave solution of this macroscopic evolution is obtained, whose amplitude is found to decay slowly with time.

Abstract:
Satellite measurements show that ion beams above the auroral acceleration region are heated to hundreds of eV in a direction perpendicular to the magnetic field. We show that ion acoustic waves may be responsible for much of this heating. Even in the absence of a positive slope in the velocity distribution of the beam ions, ion acoustic waves can be generated by a fan instability. We present analytical estimates of the wave growth rate and ion beam heating rate. These estimates, which are confirmed by particle simulations, indicate that the perpendicular temperature of the beam ions will increase by 30 eV/s, or by 1 eV in 20–25 km. From the simulations we also conclude that the heating saturates at a perpendicular temperature around 200 eV, which is consistent with observations. Key words. Ionosphere (wave-particle interactions) · Magnetospheric Physics (plasma waves and instabilities) · Space plasma physics (wave-particle interactions).

Abstract:
We present Prognoz-8 observations of low-frequency plasma waves (2-105 Hz) associated with plasma fluxes near the outer boundary of the plasma sheet. These plasma fluxes were different from the regular plasma sheet boundary layer and consisted of tailward flowing warm proton and cold oxygen beams accompanied by rather cold electrons (Te less than 100 eV). Observed plasma characteristics were used in the numerical solution of the dispersion relation for the ion-beam acoustic instability. Detailed analysis shows that this instability can be a source of observed emissions at frequencies up to 25 Hz.

Abstract:
One of the interesting observations from the FAST satellite is the detection of strong spiky waveforms in the parallel electric field in association with ion cyclotron oscillations in the perpendicular electric fields. We report here an analytical model of the coupled nonlinear ion cyclotron and ion-acoustic waves, which could explain the observations. Using the fluid equations for the plasma consisting of warm electrons and cold ions, a nonlinear wave equation is derived in the rest frame of the propagating wave for any direction of propagation oblique to the ambient magnetic field. The equilibrium bulk flow of ions is also included in the model to mimic the field-aligned current. Depending on the wave Mach number M defined by M = V/Cs with V and Cs being the wave phase velocity and ion-acoustic speed, respectively, we find a range of solutions varying from a sinusoidal wave form for small amplitudes and low M to sawtooth and highly spiky waveforms for nearly parallel propagation. The results from the model are compared with the satellite observations.

Abstract:
Models for travelling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron-proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the travelling waves can be reduced to a single first order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron proton or an electron positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton-electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic travelling waves consisting of hot electron and cold proton fluids.