Nonlinear Plasma Waves Research Articles

Electrostatic Korteweg-deVries solitary waves in a plasma with Kappa-distributed electrons

The Korteweg-deVries (KdV) equation that describes the evolution of nonlinear ion-acoustic solitary waves in plasmas with Kappa-distributed electrons is derived by using a reductive perturbation method in the small amplitude limit. We identified a dip-type (negative) electrostatic KdV solitary wave, in addition to the hump-type solution reported previously. The two types of solitary waves occupy different domains on the κ (Kappa index)-V (propagation velocity) plane, separated by a curve corresponding to singular solutions with infinite amplitudes. For a given Kappa value, the dip-type solitary wave propagates faster than the hump-type. It was also found that the hump-type solitary waves cannot propagate faster than V = 1.32.

Energy of electron acoustic solitons in plasmas with superthermal electron distribution

The propagation of nonlinear waves in plasmas consisting of cold electron fluid and superthermal hot electrons and stationary ions is studied. The Korteweg-de Vries (KdV) equation is derived using the reductive perturbation theory. It is found that only the rarefractive solitons can be created. Moreover, the linear dispersion relation and energy of solitary waves in the presence of hot superthermal electrons are derived. Our investigation is of wide relevance to astronomers and space scientists working on interstellar space plasmas.

Coherent relativistic wake wave of a charged object moving steadily in a plasma

Nonlinear electron plasma waves driven by a finite-charged particle pulse or rigid object moving at relativistic speeds are investigated. Quasi-stationary smooth and spiky wake waves comoving with the object are found. Localized soliton-like solutions are also shown to exist. Relativistic effects tend to prevent their formation because of the electron mass increase. The application of the very-large-amplitude wake density waves as a source of ultrahigh-energy cosmic-ray events is discussed.

Effect of nonthermal electrons on the propagation characteristics and stability of two-dimensional nonlinear electrostatic coherent structures in relativistic electron positron ion plasmas

Two-dimensional propagation of nonlinear ion acoustic shock and solitary waves in an unmagnetized plasma consisting of nonthermal electrons, Boltzmannian positrons, and singly charged hot ions streaming with relativistic velocities are investigated. The system of fluid equations is reduced to Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili (KP) equations in the limit of small amplitude perturbation. The dependence of the ion acoustic shock and solitary waves on various plasma parameters are explored in detail. Interestingly, it is observed that increasing the nonthermal electron population increases the wave dispersion which enervates the strength of the ion acoustic shock wave; however, the same effect leads to an enhancement of the soliton amplitude due to the absence of dissipation in the KP equation. The present investigation may be useful to understand the two-dimensional propagation characteristics of small but finite amplitude localized shock and solitary structures in planetary magnetospheres and auroral plasmas where nonthermal populations of electrons have been observed by several satellite missions.

Propagation of ion-acoustic waves in a warm dusty plasma with electron inertia

The KdV equation is derived for weakly nonlinear ion-acoustic waves in an unmagnetized warm dusty plasma with electron inertia. It has been shown that the inclusion of electron inertia and pressure variation of the species not only significantly modifies the basic features (width and amplitude) of dust ion-acoustic solitions, but also introduces a new parametric regime for the existence of positive and negative solitons.

Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics

In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons β and the temperature ratio σ (= Ti/Te) on the stability, where the stability for Burger’s equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of σ and β. We usa a reductive perturbation technique, where the nonlinear evolution of an IAW is governed by the driven Burger equation. This equation is solved exactly by using two methods: the tanh-function method and the Cole–Hopf transformation. Both methods produce shock wave solutions, their results compared, and good agreement exists in most predictions. The analytical calculations show that an IAW propagates as a shock wave with subsonic speed. The flow velocity, pressure, number density, electrostatic potential, and thermodynamic characteristics are estimated and illustrated as functions of time t and the distance x. It is found via the tanh-function method that the amplitudes of the sought-for functions of the system are suppressed and move towards an equilibrium state at the highest value of β. The tanh-function method reveals an advantage over the Cole–Hopf method in the viscous and collisional cases of IAWs, where it satisfies the stability conditions at the highest value of β with the chosen σ values when applied to evaluate the Onsager relation.

A one-soliton solution of the [formula omitted] equation with generalized evolution and time-dependent coefficients

We consider a nonlinear dispersive Zakharov–Kuznetsov (for short, Z K ( m , n , k ) ) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. A special form of this model with time-dependent coefficients of the nonlinear terms as well as the nonlinear dispersion terms is studied. Further, there are time-dependent linear attenuation and generalized evolution terms. The solitary wave ansatz is used to carry out the integration and an exact one-soliton solution is obtained. The parameters of the soliton envelope (amplitude, widths, velocity) are explicitly calculated in the course of the derivation of the exact solution, as functions of the varying model coefficients. The constraint relation between these time-dependent coefficients for the one-soliton solution to exist is established.

Two-dimensional Vlasov simulation of electron plasma wave trapping, wavefront bowing, self-focusing, and sideloss

Two-dimensional Vlasov simulations of nonlinear electron plasma waves are presented, in which the interplay of linear and nonlinear kinetic effects is evident. The plasma wave is created with an external traveling wave potential with a transverse envelope of width Δy such that thermal electrons transit the wave in a “sideloss” time, tsl~Δy/ve. Here, ve is the electron thermal velocity. The quasisteady distribution of trapped electrons and its self-consistent plasma wave are studied after the external field is turned off. In cases of particular interest, the bounce frequency, ωbe=keϕ/me, satisfies the trapping condition ωbetsl>2π such that the wave frequency is nonlinearly downshifted by an amount proportional to the number of trapped electrons. Here, k is the wavenumber of the plasma wave and ϕ is its electric potential. For sufficiently short times, the magnitude of the negative frequency shift is a local function of ϕ. Because the trapping frequency shift is negative, the phase of the wave on axis lags the off-axis phase if the trapping nonlinearity dominates linear wave diffraction. In this case, the phasefronts are curved in a focusing sense. In the opposite limit, the phasefronts are curved in a defocusing sense. Analysis and simulations in which the wave amplitude and transverse width are varied establish criteria for the development of each type of wavefront. The damping and trapped-electron-induced focusing of the finite-amplitude electron plasma wave are also simulated. The damping rate of the field energy of the wave is found to be about the sideloss rate, νe~tsl-1. For large wave amplitudes or widths Δy, a trapping-induced self-focusing of the wave is demonstrated.

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev–Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.

Evolution of nonlinear waves in compressing plasma

Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.

Nonlinear Pulse Propagation and Phase Velocity of Laser-Driven Plasma Waves

Laser evolution and plasma wave excitation by a relativistically intense short-pulse laser in underdense plasma are investigated in the broad pulse limit, including the effects of pulse steepening, frequency redshifting, and energy depletion. The nonlinear plasma wave phase velocity is shown to be significantly lower than the laser group velocity and further decreases as the pulse propagates owing to laser evolution. This lowers the thresholds for trapping and wave breaking and reduces the energy gain and efficiency of laser-plasma accelerators that use a uniform plasma profile.

Electrostatic solitary waves in a quantum plasma with relativistically degenerate electrons

A model for nonlinear ion waves in an unmagnetized plasma with relativistically degenerate electrons and cold fluid ions is presented here. The inertia is given here by the ion mass while the restoring force is provided by the relativistic electron degeneracy pressure, and the dispersion is due to the deviation from charge neutrality. A nonlinear Korteweg–de Vries equation is derived for small but finite amplitude waves and is used to study the properties of localized ion acoustic solitons for parameters relevant for dense astrophysical objects such as white dwarf stars. Different degrees of relativistic electron degeneracy are discussed and compared.

Spherical Kadomtsev–Petviashvili equation for dust acoustic waves with dust size distribution and two-charges-ions

The nonlinear dust acoustic waves in dusty plasmas with negative as well as positive ions and the combined effects of bounded spherical geometry and the transverse perturbation and the size distribution of dust grains are studied. Using the perturbation method, a spherical Kadomtsev–Petviashvili (SKP) equation that describes the dust acoustic waves is deduced.

The solution for a class of nonlinear solitary waves in dusty plasma

A class of nonlinear solitary waves in dusty plasma is considered. Firstly, a variational iteration is constructed. Then the initial approximate solution is determined. Finally, using the method of the variational iteration, each degree approximation for corresponding model is found.

Efficient spectral and pseudospectral algorithms for 3D simulations of whistler-mode waves in a plasma

Efficient spectral and pseudospectral algorithms for simulation of linear and nonlinear 3D whistler waves in a cold electron plasma are developed. These algorithms are applied to the simulation of whistler waves generated by loop antennas and spheromak-like stationary waves of considerable amplitude. The algorithms are linearly stable and show good stability properties for computations of nonlinear waves over tens of thousands of time steps. Additional speedups by factors of 10–20 (comparing single core CPU and one GPU) are achieved by using graphics processors (GPUs), which enable efficient numerical simulation of the wave propagation on relatively high resolution meshes (tens of millions nodes) in personal computing environment. Comparisons of the numerical results with analytical solutions and experiments show good agreement. The limitations of the codes and the performance of the GPU computing are discussed.

Dark-current-free petawatt laser-driven wakefield accelerator based on electron self-injection into an expanding plasma bubble

A dark-current-free plasma accelerator driven by a short (⩽150 fs) self-guided petawatt laser pulse is proposed. The accelerator uses two plasma layers, one of which, short and dense, acts as a thin nonlinear lens. It is followed by a long rarefied plasma (∼1017 electrons cm−3) in which background electrons are trapped and accelerated by a nonlinear laser wakefield. The pulse overfocused by the plasma lens diffracts in low-density plasma as in vacuum and drives in its wake a rapidly expanding electron density bubble. The expanding bubble effectively traps initially quiescent electrons. The trapped charge given by quasi-cylindrical three-dimensional particle-in-cell (PIC) simulations (using the CALDER-Circ code) is ∼1.3 nC. When laser diffraction saturates and self-guiding begins, the bubble transforms into a bucket of a weakly nonlinear non-broken plasma wave. Self-injection thus never resumes, and the structure remains free of dark current. The CALDER-Circ modelling predicts a few π mm mrad normalized transverse emittance of electron beam accelerated in the first wake bucket. Test-particle modelling of electron acceleration over 9 cm (using the quasistatic PIC code WAKE) sets the upper limit of energy gain 2.6 GeV with ∼2% relative spread.

Study of near-GeV acceleration of electrons in a non-linear plasma wave driven by a self-guided laser pulse

Electrons are accelerated up to 0.8 GeV in a self-injecting laser wakefield accelerator driven at a plasma density of 5.5 × 1018 cm−3 by a 10 J, 55 fs, 800 nm laser pulse in the blow-out regime. The electron beam stability is correlated with the laser focal spot pointing stability and depends on the target alignment. Variations of the laser pulse energy, focal spot size and energy within the full width at half maximum have little effect on the electron beam profile (stability) but impact the electron energy (stability). The peak electron energy is higher than expected for the initial vacuum intensity. This is evidence for intensity amplification which also explains the observation of polyenergetic beamlets.

Positron acoustic shock waves in planar and nonplanar geometry

The nonlinear positron acoustic shock waves (PASWs) in an unmagnetized plasma consisting of cold positrons, immobile positive ions and Boltzmann-distributed electrons and hot positrons are studied in both unbounded planar geometry and bounded nonplanar geometry. In this regard, with the help of the reductive perturbation method, the cylindrical and spherical Korteweg–de Vries Burger (KdVB) equations are derived for PASWs. Numerically, the effects of several parameters and ion kinematic viscosities on the properties of PASWs in both planar and nonplanar geometry are discussed. It is found that PASWs in nonplanar geometry significantly differ from those in planar geometry.

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.

Influence of superthermal and trapped electrons on oblique propagation of ion-acoustic waves in magnetized plasma

Effects of superthermal and trapped electrons on the oblique propagation of linear and nonlinear ion-acoustic waves in an electron-ion plasma in the presence of a uniform external magnetic field are investigated. In order to model the superthermal electrons, a Lorentzian (kappa) velocity distribution function has been employed. The ions are cold and their dynamics are studied by hydrodynamic equations. First, the linear dispersion relation of the fast and slow modes are obtained. It is shown that the superthermal electrons cause the both modes to propagate with smaller phase velocities. Then, modified Korteweg–de Vries equations describing the propagation of nonlinear slow and fast ion-acoustic waves are derived. It is shown that the presence of superthermal and trapped electrons has great influence on the nature of magnetized ion-acoustic solitons. The dependency of soliton attributes to the parameters associated with the superthermality and trapping mechanism will be shown.