The nonlinear interaction of intense linearly polarized electromagnetic waves (EMWs) with longitudinal electron density perturbations is revisited in relativistic degenerate plasmas. The nonlinear dynamics of the EMWs and the longitudinal field, driven by the EMW ponderomotive force, is governed by a coupled set of nonlinear partial differential equations. A numerical simulation of these coupled equations reveals that the generation of wakefields is possible in weakly relativistic degenerate plasmas with $R_0\equiv p_F/mc\ll1$ and $v_g/c\sim1$, where $p_F$ is the Fermi momentum, $m$ is the mass of electrons, $c$ is the speed of light in vacuum, and $v_g$ is the EMW group velocity. However, when the ratio $v_g/c$ is reduced to $\sim0.1$, the wakefield generation is suppressed, instead the longitudinal fields get localized to form soliton-like structures. On the other hand, in the regimes of moderate $(R_0\lesssim1)$ or strong relativistic degeneracy $(R_0>1)$ with $v_g/c\sim0.1$, only the EM solitons can be formed.
It is well known that when a short laser pulse propagates in an underdense plasma, it induces longitudinal plasma oscillations at the plasma frequency after the pulse, typically referred to as the 'wakefield'. However, for plasma densities approaching the critical density wakefield generation is suppressed, and instead the EM-pulse undergoes nonlinear self-modulation. In this article we have studied the transition from the wakefield generation to formation of quasi-solitons as the plasma density is increased. For this purpose we have applied a one dimensional (1D) relativistic cold fluid model…
The existence of standing high frequency electromagnetic (EM) solitons in a fully degenerate overdense electron plasma is studied applying relativistic hydrodynamics and Maxwell equations. The stable soliton solutions are found in both relativistic and nonrelativistic degenerate plasmas.
The excitation of a non-linear ion-wake by a train of ultra-relativistic electron bubble wake [1]-[8] is modeled. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton [11]-[14]. The phases of the oscillating radial electric fields of the slowly-propagating [21] electron bubble is asymmetric in time and excites time-averaged inertial ion motion radially. The electron compression in the back of the bubble sucks-in the ions and the space-charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure with on-axis and b…
The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron-positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown.
The evolution of electromagnetic (EM) solitons due to nonlinear coupling of circularly polarized intense laser pulses with low-frequency electron-acoustic perturbations is studied in relativistic degenerate dense astrophysical plasmas with two groups of electrons: a sparse population of classical relativistic electrons and a dense population of relativistic degenerate electron gas. Different forms of localized stationary solutions are obtained and their properties are analyzed. Using the Vakhitov-Kolokolov stability criterion, the conditions for the existence and stability of a moving EM solit…
The existence and the basic features of ion-acoustic (IA) envelope solitons in a self-gravitating degenerate quantum plasma system (SG-DQPS), containing inertial non-relativistically degenerate light and heavy ion species as well as inertialess non-relativistically degenerate positron and electron species, have been theoretically investigated by deriving the nonlinear Schrödinger (NLS) equation. The NLS equation, which governs the dynamics of the IA waves, has disclosed the modulationally stable and unstable regions for the IA waves. The unstable region allows to generate bright envelope solit…
The basic features of nucleus-acoustic (NA) envelope bright and dark solitons, which exist in degenerate quantum plasmas, have been theoretically investigated by deriving the nonlinear Schrödinger (NLS) equation. The reductive perturbation method, which is valid for a small but finite amplitude limit, is employed. It is found that the bright envelope solitons are modulationally unstable, whereas the dark ones are stable. It is also observed that the fundamental properties (viz. Modulational instability (MI) growth rate, width and energy concentration of NA waves, etc.) of NA unstable bright en…
High-density low-temperature plasmas with degenerate species are considered in the limit of high Fermi velocities close to the speed of light. The small amplitude ion-acoustic solitons are studied in this regime. Presented analysis is based on the relativistic hydrodynamic model with the average reverse gamma factor evolution consists of the equations for evolution of the following functions the concentration, the velocity field, the average reverse relativistic gamma factor, and the flux of the reverse relativistic gamma factor, which are considered as main hydrodynamic variables. Justificati…
The dynamical behaviors of electromagnetic (EM) solitons formed due to nonlinear interaction of linearly polarized intense laser light and relativistic degenerate plasmas are studied. In the slow motion approximation of relativistic dynamics, the evolution of weakly nonlinear EM envelope is described by the generalized nonlinear Schr{ö}dinger (GNLS) equation with local and nonlocal nonlinearities. Using the Vakhitov-Kolokolov criteria, the stability of an EM soliton solution of the GNLS equation is studied. Different stable and unstable regions are demonstrated with the effects of soliton velo…
The non-linear evolution of spin-electron acoustic, positron-acoustic, and spin-electron-positron acoustic waves is considered. It is demonstrated that weakly nonlinear dynamics of each wave leads to the soliton formation. Altogether, we report on existence of three different solitons. The spin-electron acoustic soliton known for electron-ion plasmas is described for electron-positron-ion plasmas for the first time. The existence of the spin-electron-positron acoustic soliton is reported for the first time. The positron-acoustic soliton and the spin-electron-positron acoustic soliton arise as …
The basic features of linear and nonlinear quantum electron-acoustic (QEA) waves in a degenerate quantum plasma (containing non-relativistically degenerate electrons, superthermal or $κ$-distributed electrons, and stationary ions) are theoretically investigated. The nonlinear Schödinger (NLS) equation is derived by employing thereductive perturbation method. The stationary solitonic solution of the NLS equation are obtained, and examined analytically as well as numerically to identify the basic features of the QEA envelope solitons. It has been found that the effects of the degeneracy and exch…
In the present paper we consider the nonlinear interaction of high frequency intense electromagnetic (EM) beam with degenerate electron plasmas. In a slowly varying envelop approximation the beam dynamics is described by the couple of nonlinear equations for the vector and scalar potentials. Numerical simulations demonstrate that for an arbitrary level of degeneracy the plasma supports existence of axially symmetric 2D solitons which are stable against small perturbations. The solitons exist if the power trapped in the structures, being the growing function of soliton amplitude, is above a cer…
The spin-electron-acoustic waves (sometimes called the spin-plasmons) can be found in degenerate electron gas if the spin-up electrons and spin down electrons move relatively each other. Here, we suggest relativistic hydrodynamics with the separate spin evolution which allows us to study linear and nonlinear spin-electron-acoustic waves, including the spin-electron-acoustic solitons. Presented hydrodynamic model is the corresponding generalization of the relativistic hydrodynamic model with the average reverse gamma factor evolution which consists of the equations for evolution of the followin…
We present a novel one-dimensional nonlinear evolution equation governing the dynamics short-wavelength longitudinal waves in a nonrelativistic fully degenerate quantum plasma using kinetic equation for the Wigner function. The linear dispersion of the equation has a form of "zero sound" $\sim k\exp (-k^{2})$, where $k$ is the wave number, and it strongly differs from previously known nonlinear evolution equations. We numerically find the corresponding soliton solutions and demonstrate that the collisions between three solitons turn out to be elastic resulting only in phase shifts.
The interaction of coherent nonlinear structures (such as sub-cycle solitons, electron vortices and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultra-short electromagnetic pulses. The electromagnetic field of a coherent nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the coherent nonlinear structure. This process is illustrated wi…
A model for the excitation of a non-linear ion-wake mode by a train of plasma electron oscillations in the non-linear time-asymmetric regime is developed using analytical theory and particle-in-cell based computational solutions. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton. The near-void and radially-outwards propagating ion-wake channel of a few plasma skin-depth radius, is explored for application to "Crunch-in" regime of positron acceleration. The coupling from the electron wakefield mode to the ion-mode dictates the long-term e…
The basic properties of the nucleus-acoustic (NA) solitary waves (SWs) are investigated in a super-dense self-gravitating magnetized quantum plasma (SDSGMQP) system in the presence of an external magnetic field, whose constituents are the non-degenerate light (heavy) nuclei, and non/ultra-relativistically degenerate electrons. The Korteweg-de Vries (KdV) equation has been derived by employing the reductive perturbation method. The NA SWs are formed with negative (positive) electrostatic (self-gravitational) potential. It is also observed that the effects of non/ultra-relativistically degenerat…
Using the extended Poincaré-Lighthill-Kuo (PLK) reductive perturbation method to study the small-amplitude ion acoustic solitary wave (IASW) dynamics (propagation and interaction), it is shown that in Thomas-Fermi magneto-plasma consisting of inertial-less degenerate electrons and positrons and isothermal ions, distinctive features emerge when the ultra-relativistic degeneracy pressure applies to electrons and positrons. Calculations show that ion-acoustic solitary waves may interact differently in such plasmas under ultra-relativistic degeneracy pressure.
In this paper, we consider ionospheric plasma consisting of weakly degenerate electrons and heavy ions. We embrace our hydrodynamic model by including the quantum diffraction term. By employing Sagdeev's pseudo-potential method, we obtain double layers and soliton structure. We have studied the various parametric dependence of solitary structures and double layers. The results thus obtained might be helpful in the studies of many high energy astrophysical phenomena.
A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case - in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.
The propagation of ion-acoustic waves (IAWs) in a collisionless unmagnetized self-gravitating degenerate quantum plasma system (SG-DQPS) has been studied theoretically for the first time. A nonlinear Schrödinger equation is derived by using the reductive perturbation method to study the nonlinear dynamics of the IAWs in the SG-DQPS. It is found that for $k_c > k$ ($k_c < k$) (where $k_c$ is critical value of the propagation constant $k$ which determines the stable and unstable region of IAWs) the IAWs are modulationally unstable (stable), and that $k_c$ depends only on the ratio of the electro…
Linear and nonlinear ion-acoustic waves are studied in a fluid model for non-relativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and apply equally well both to fully degenerate or classical, non-degenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obt…
We derive Quantum Zakharov-Kuznetsov to study ion acoustic solitons propagating in electron positron (hole) ion degenerate plasma with quantized magnetic field and exchange corelation effects.
Nonlinear ion-acoustic waves are analyzed in a non-relativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite temperature quantum kinetic theory in the long wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the c…
In plasma wakefield accelerators, the wave excited in the plasma eventually breaks and leaves behind slowly changing fields and currents that perturb the ion density background. We study this process numerically using the example of a FACET experiment where the wave is excited by an electron bunch in the bubble regime in a radially bounded plasma. Four physical effects underlie the dynamics of ions: (1) attraction of ions toward the axis by the fields of the driver and the wave, resulting in formation of a density peak, (2) generation of ion-acoustic solitons following the decay of the density…
We derive a nonlinear equation governing dynamics of short-wavelength longitudinal waves in ultrarelativistic electron-positron-ion plasmas. In contrast to the recent work by Lashkin [Phys. Plasmas {\textbf{27}}, 102302 (2020)], where a similar equation was suggested in the framework of the Wigner function approach for a nonrelativistic electron-ion degenerate plasma, in our case which is based on the Vlasov kinetic equation all three species of particles (electrons, positrons and ions) should be present. The nonlinearity arises only in the presence of a population of ions. By numerical simula…
For degenerate astrophysical electron-positron plasmas we have considered dynamics of electromagnetic beams carrying angular momentum. It is found for arbitrary level of degeneracy such a beam having the power exceeding a certain critical value breaks up into many filaments, eventually leading to the formation of stable spatial solitons keeping zero field in the center of the structure.
Nonlinear wave--coupling is studied in a multi-species degenerate astrophysical plasma consisting of two electron species (at different temperatures): a highly degenerate main component plus a smaller classical relativistic flow immersed in a static neutralizing ion background. It is shown that the high frequency electromagnetic (HF EM) waves, through their strong nonlinear interactions with the electron--acoustic waves (sustained by a multi-electron component (degenerate) plasma surrounding a compact astrophysical object) can scatter to lower frequencies so that the radiation observed faraway…
