Collisionless Unmagnetized Plasma Research Articles

Relativistic and Heavy Ion Effects on Single‐ and Multi‐Soliton Structures of Ion‐Acoustic Waves

ABSTRACTThe fundamental characteristics of ion‐acoustic waves (IAWs) due to the relativistic effects are investigated in a collisionless unmagnetized plasma system consisting of relativistic positively charged inertial heavy ions, kappa‐distributed electrons, and Maxwellian light ions. The reductive perturbation method (RPM) is used to derive the nonlinear evolution equation like the Korteweg‐de Vries (KdV) equation. The production of single‐, double‐, and triple‐IAW solitons (IAWSs) is also investigated. It is found that for the effects of concerned parameters only rarefactive (IAWSs) are produced. The results obtained in this study are useful not only to understand the space plasma phenomena such as plasma sheet boundary layer of earth's magnetosphere, laser‐plasma interaction, but also to validate the laboratory experiments.

Bifurcation analysis of Van der Pol–Mathieu equation for the dust grain charge with regularized (κ)-distributed electron-ion

This paper presents a novel viewpoint on nonlinear dust-acoustic waves (DAWs) in an unmagnetized collisionless plasma containing regularized [Formula: see text] distributed electrons and ions (ei) and negative dust grain. The nonlinear oscillatory system based on hybridization of the Van der Pol–Mathieu equation (VdPME) is derived by a new technique. By bifurcation analysis of the planar dynamical system (DS), the effects of parameters with the assistance of phase planes and time series of VdPME are studied. After analyzing the equation to identify the resonance region, a fourth-order Runge–Kutta method is used to solve it numerically. We explained the behavior of DA periodic, stable limit cycle, and chaotic limit cycle wave solutions with different parameters. These types of numerical solutions are illustrated in two-dimensional and three-dimensional graphics by changing the rate at which charged dust grain is produced [Formula: see text], as well as waste [Formula: see text] and comparing the results with those of earlier research. A novel bifurcation analysis of VdPE and VdPME is obtained with the effects of the cut-off factor [Formula: see text] of regularized [Formula: see text]-distribution (RKD) distributed ei, the superthermality of ei particles [Formula: see text], the ratio of ion to electron temperature [Formula: see text], and the ratio of dust to electron density [Formula: see text] illustrated. It is noticed that the DAW shows promotion in width and amplitude as the frequency [Formula: see text] increases and it becomes rarefaction as the cut-off parameter [Formula: see text] increases. On the contrary, it becomes compressive under the impact of superthermality [Formula: see text] and [Formula: see text]. The obtained conclusions may help explain and comprehend a variety of applications in experimental plasma containing highly energy regularized [Formula: see text] dispersed ei, as well as in the interstellar medium.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

Formation and interaction of multi-dimensional electrostatic ion-acoustic solitons in two-electron temperature plasmas

Ion-acoustic waves are investigated in an unmagnetized collisionless plasma comprising dynamical ions and inertialess cold and hot (C–H) electrons expressed by Maxwellian, kappa, and (r, q) distributions. The reductive perturbation theory is applied for deriving a modified Kadomtsev–Petviashvili (mKP) equation to examine the characteristics of ion-acoustic structures (solitary waves, IASWs). The Hirota bilinear formalism is used to investigate the propagation of a single soliton and the interaction of two solitons with special reference to space plasmas. It is found that ratio of number density of cold to hot electrons and non-Maxwellian nature of cold electrons not only affect the propagation characteristics of single mKP solitons but also alter the interaction time of the IASWs. It is found that the swiftness of the interaction of solitons for flat-topped distribution surpasses both kappa and Maxwellian distributions. It is also found that the bipolar and tripolar structures depend on the ratio of the propagation vectors. The ranges of electric field amplitude for the IASWs are calculated for C–H electron distributions corresponding to Saturn's B-ring and the region just beyond terrestrial magnetopause, and are shown to agree with Cassini wideband receiver observational data and wideband plasma wave instrument's waveform data.

Attenuation of electromagnetic waves in an unmagnetized collisionless plasma by particle-in-cell method

Attenuation of electromagnetic waves in an unmagnetized collisionless plasma by particle-in-cell method

Collisional positron acoustic soliton and double layer in an unmagnetized plasma having multi-species

This paper explores the head-on collision between two-counter propagating positron acoustic solitons and double layers (DLs) in an unmagnetized collisionless plasma having mobile cold positrons fluid, immobile positive ions and (r,;q)-distributed hot positrons, and hot electrons. By employing the extended Poincaré–Lighthill–Kuo method, the coupled Korteweg–de Vries (KdV), modified KdV (mKdV) and Gardner equations are derived to archive this goal. The effect of dimensionless parameters on the propagation characteristics of interacting KdV solitons (KdVSs), mKdV solitons (mKdVSs), Gardner solitons (GSs) and DLs are examined in detail by considering the limiting cases of (r,;q)-distribution. It is noted that the interaction of GSs and DLs are reported for the first time. The outcomes might be comprehended and beneficial not only in space and astrophysical environments but also in laboratory studies.

Dispersion and damping rate of Langmuir wave in space plasma with regularized Kappa distributed electrons

The dispersion of Langmuir wave (LW) in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory. The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a type III solar radio burst. It is found that the linear behavior of LW is greatly modified by the suprathermal index κ and the exponential cutoff parameter α. In the region κ < 1.5, the damping rate of LW will be much larger than the one with Maxwellian distributed electrons. Hence, the nonlinear process of LW in low κ region may exhibit different properties in comparison with the one in large κ region.

On the dynamics of nonlinear propagation and interaction of the modified KP solitons in multicomponent complex plasmas

Dust-acoustic waves (DAWs) are analyzed in the small amplitude limit in a collisionless unmagnetized dusty plasma whose constituents are inertial dust grains, massless ions expressed by the generalized (r,q) distribution and inertialess Maxwellian electrons using the fluid theory of plasmas. The modified Kadomtsev-Petviashvili (mKP) equation is derived at a critical plasma condition for which the quadratic nonlinearity vanishes. The propagation of single soliton and interaction of two solitons are analyzed for the mKP equation in the context of plasma physics by employing Hirota bilinear formalism. The effects of the flatness parameter r and tail parameter q of the ions on the frequency of the DAWs are studied and the comparison with Maxwellian and kappa distributions is drawn. Using the plasma parameters corresponding to the Saturn’s E-ring, the range of electric field amplitude for dust-acoustic solitary waves (DASWs) for different ion distributions is calculated and is shown to agree very well with the Cassini Wideband Receiver (WBR) observations. The interaction time of two DASWs for non-Maxwellian ion distributions is estimated and shown to be fastest for the (r,q) distributed ions. The interesting feature of the interaction between compressive solitons with their rarefactive counterparts is also discussed in detail.

Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.

In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahony (BBM) equation, etc.) are reported in detail using different techniques. The single and periodic peakons are investigated by studying the stability analysis of the gDP equation. The novel compacton solutions to the equations under consideration are derived in the form of Weierstrass elliptic function. Also, the periodicity of these solutions is obtained. The cnoidal wave solutions are obtained in the form of Jacobi elliptic functions. Moreover, both soliton and trigonometric solutions are covered as a special case for the cnoidal wave solutions. Finally, a new form for the peakon solution is derived in details. As an application to this study, the fluid basic equations of a collisionless unmagnetized non-Maxwellian plasma is reduced to the equation under consideration for studying several nonlinear structures in the plasma model.

Nonlinear coherent structures of electron acoustic waves in unmagnetized plasmas

The propagation dynamics of nonlinear electron acoustic waves (EAW) are explored analytically and numerically in collisionless unmagnetized plasmas. The dynamics of the nonlinear wave is shown to be governed by a Boussinesq equation. In the supersonic range, the wave becomes unstable in the short wave limit. In the nonlinear stage, this unstable mode reaches a maximum values and after that it damps. Different limiting cases of the general solutions are discussed. Analytical and computational results predict that the nonlinear EAW possesses breather structures apart from the usual solitary wave solutions. The results are discussed in the context of astrophysical plasmas.

Evolution of ion acoustic solitary waves in pulsar wind

ABSTRACT We have studied the evolution of ion acoustic solitary waves (IASWs) in pulsar wind. The pulsar wind is modelled by considering a weakly relativistic unmagnetized collisionless plasma comprised of relativistic ions and superthermal electrons and positrons. Through fluid simulations, we have demonstrated that the localized ion density perturbations generated in the polar wind plasma can evolve the relativistic IASW pulses. It is found that the concentration of positrons, relativistic factor, superthermality of electrons, and positrons have a significant influence on the dynamical evolution of IASW pulses. Our results may provide insight to understand the evolution of IASW pulses and their role in astrophysical plasmas, especially in the relativistic pulsar winds with supernova outflow, which is responsible for the production of superthermal particles and relativistic ions.

Overtaking Collisions of Ion Acoustic N-Shocks in a Collisionless Plasma with Pair-Ion and (α,q) Distribution Function for Electrons

In this work, the effects of plasma parameters on overtaking collisions of ion acoustic multi-shocks are studied in an unmagnetized collisionless plasma with positive and negative ions, and (α,q)-distributed electrons. To investigate such phenomena, the reductive perturbation technique is implemented to derive the Burgers equation. The N-shock wave solution is determined for this equation by directly implementing the exponential function. The result reveals that both the amplitudes and thicknesses of overtaking collisions of N-shock wave compressive and rarefactive electrostatic potential are significantly modified with the influences of viscosity coefficients of positive and negative ions. In addition, the density ratios also play an essential role to the formation of overtaking collisions of N-shocks. It is observed from all theoretical and parametric investigations that the outcomes may be very useful in understanding the dynamical behavior of overtaking collisions of multi-shocks in various environments, especially the D- and F-regions of the Earth’s ionosphere and the future experimental investigations in Q-machine laboratory plasmas.

The generalized criterion for collisionless plasma sheaths with kappa distributed electrons

In this paper, by analytical estimation and numerical analysis of the ions Mach number domain in an unmagnetized collisionless plasma sheath, the formation condition of a stable sheath has been examined and formulated in the context of kappa distribution formalism. In this study, by theoretical investigation of the normalized variables with respect to well-defined parameters that enclose recent findings of kappa distribution formalism, a generalized Bohm criterion is derived in terms of an extended Mach number, , and a generalized polytropic index, γe, which characterizes different thermodynamic states with a general flexibility from near-thermal equilibrium states to the far-from-thermal equilibrium states. In our formulation, the allowed domains of isothermal and extended Mach number with respect to the connection between the polytropic index and the kappa distribution has been examined. By definition of the extended Mach number, the necessity of supersonic ions at the edge of sheath remains unchanged, but its appearance is different in the terms of the isothermal Mach number. It is shown that the threshold of extended Mach number in far-from-thermal equilibrium states is a sensitive function of the generalized polytropic index and it decreases by closing to the asymptotic limit of anti-equilibrium state (). Moreover, the threshold of isothermal Mach number decreases in the sub-isothermal regions with γe < 1 and so, by closing to the far-from-thermal equilibrium states, the Mach number domain is extended. Specially, it is shown that the thickness of the plasma sheaths reduces for the kappa distributed plasmas with smaller polytropic indices γe. Finally, the possibility for formation of stable plasma sheaths in different thermodynamic sates is discussed, where the validity of the generalized sheath criterion has been confirmed and given by or equivalently .

Symmetric Airy electron plasma wave

A symmetric Airy electron plasma (SAiEP) wave, which is caused by launching four Airy beams symmetrically in the initial plane in an unmagnetized collisionless plasma, is analytically investigated in this paper. In addition to intensity distributions, evolutions, and the potential of the SAiEP wave with different parameters, the difference between the SAiEP wave and the Airy-like electron plasma wave is studied as well. The results show that the SAiEP wave with different distances between the main lobes in the initial plane behaves differently as the decay factor changes. When the decay factor increases, the frequency and the amplitude of the potential become smaller. Besides, the SAiEP wave has the autofocusing property, while the Airy-like electron plasma wave has the weak diffraction property.

Momentum-exchange current drive by electrostatic waves in an unmagnetized collisionless plasma

For a planar electrostatic wave interacting with a single species in a collisionless plasma, momentum conservation implies current conservation. However, when multiple species interact with the wave, they can exchange momentum, leading to current drive. A simple, general formula for this driven current is derived. As examples, we show how currents can be driven for Langmuir waves in electron–positron–ion plasmas, and for ion-acoustic waves in electron–ion plasmas.

Ion-acoustic shocklets in F-region of ionosphere with non-Maxwellian electrons

The evolution and propagation characteristics of ion-acoustic (IA) shocklets are examined in an unmagnetized collisionless plasma, comprised of warm ions and non-Maxwellian (Kappa/Cairns) electrons. Solving the fluid equations and using the frameworks of diagonalized-matrix/changing variable techniques, a nonlinear set of two characteristic wave equations is obtained, which admits dispersionless/dissipationless evolution of IA shocklets. Numerical analyses have also confirmed the excitation/deformation of IA shocklets and the wave overtaking/breaking effects at time τ>0 for nonlinear coupling of potential field. It is found that superthermal (Kappa distributed) electrons can enhance the overtaking/breaking of IA perturbations in comparison with nonthermal Cairns distributed electrons that lead to less steepened potential field to stabilize IA excitations against the nonlinear steepening. Finite ion temperature has significant impact on the wave coupling to lead the profiles of IA shocklets ahead. This study is important to understand the physical mechanism for excitation and deformation of IA shocklets relevant to the F-region of Ionosphere.

Dispersion characteristics of terahertz transverse electric mode in a smooth-wall cylindrical waveguide with a degenerate plasma layer

The propagation of transverse electric mode in a cylindrical metallic smooth-wall waveguide contains a dielectric rod and a cold collisionless unmagnetized degenerate plasma layer is analytically investigated in the terahertz frequency region. The dispersion relations of fast and slow waves for this mode are derived and solved numerically. The effects of geometrical and physical parameters such as dielectric, plasma and metal radii, and dielectric permittivity on the dispersion characteristics of terahertz transverse electric mode and its frequency spectrum are studied. It is shown that the decrease of dielectric permittivity and metal radius, and the increase of degenerate plasma radius leads to higher frequency fast waves. It is also indicated that an increase in the dielectric radius results in a decrease in the frequency of fast waves. In addition, it is found that by reducing the dielectric rod radius and with increasing metal radius, the frequency is increased in the slow waves. Finally, it is shown that the increase in dielectric permittivity causes a decrease in the frequency of both fast and slow waves.

Nonlinear ion acoustic solitary waves with dynamical behaviours in the relativistic plasmas

This work investigates the basic features of Nonlinear Ion Acoustic Solitary waves (NIASWs) and their dynamical behaviours in an unmagnetized relativistic collisionless plasma system via the Schamel Korteweg-de Vries (SKdV) equation. Such plasma is composed by the generalized distributed electrons, Boltzmann distributed positrons and relativistic warm ions. The influences of plasma parameters on NIASWs and their dynamical behaviours are investigated by comparing 26−term expansion of relativistic Lorentz factor (RLF) with both of weakly (2−term expansion of RLF) and highly (3−term expansion of RLF) regimes. It is found that the 26−term expansion of RLF are significantly changed NIASWs instead of both weakly and highly relativistic regimes. Therefore, the theoretical results would be very useful for understanding the nature (amplitude, width, polarity, etc.) of wave dynamics not only in astrophysical and space environments but also in further laboratory studies, where the proposed plasma assumptions are existed.

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

We have used the Sagdeev pseudo-potential technique to investigate the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of adiabatic warm ions, isothermal cold electrons and nonthermal hot electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the nonlinear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have also investigated the transition of different solitary structures: soliton (before the formation of double layer) $\rightarrow$ double layer $\rightarrow$ supersoliton $\rightarrow$ soliton (soliton after the formation of double layer) by considering the variation of $\theta$ only, where $\theta$ is the angle between the direction of the external uniform static magnetic field and the direction of propagation of the wave.

Numerical Study of Mach Number on Solutions in a Warm Negative Ion Plasma With Flat-Topped Electron Distribution

The influence of the Mach number on the localized ion acoustic solitons is investigated in a collisionless one-dimensional unmagnetized plasma system. The plasma model used here is a negative ion plasma having electrons complying flat-topped distribution. Using the basic fluid equations and applying proper boundary conditions we derive the energy integral equations containing the Sagdeev potential. The Sagdeev potential obtained, depends on various parameters out of which the effect of Mach number on the highly nonlinear structures is studied. It is found that depth of the Sagdeev potential, amplitude of the solitary structures and bipolar electric field pulses rises with rise in the values of M . Also narrower solitons starts appearing with increase in the solitary speed.