Nonlinear Plasma Waves Research Articles

Solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili dynamic equation in dust-acoustic plasmas

Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Nonlinear Electrostatic Waves in PIE and PI Plasmas With Field-Aligned Shear Flow

Nonlinear low-frequency ion acoustic (IA) wave and pair plasma convective cell (PPCC) mode are investigated in pair-ion (PI) plasmas with and without electrons in the presence of sheared flows. IA wave forms both KdV solitons and dipolar vortices in PI-electron plasma, and their amplitude depends upon electron density and sheared flow. But when electron density is too low, the structures disappear, because IA does not exist in pure PI plasma. On the other hand, PPCC mode cannot form pulse-type solitary structures in the pair plasma, while it forms dipolar vortices due to finite vorticity. The nonlinear analysis has been performed assuming the presence of electrons in fullerene PI plasma and limit of zero electron density is also considered for a comparison.

Influence of Optical Nonlinearities on Plasma Waves in Graphene

A theory of the nonlinear plasma waves in graphene is developed in the nonperturbative regime. The influence of strong electric fields on the position and linewidth of plasma resonances in the far-infrared transmission experiments, as well as on the wavelength and the propagation length in the scanning near-field optical microscopy experiments is studied. The theory shows that the fields of order of a few to a few tens of kV/cm should lead to a red shift and broadening of plasma resonances in the first type and to a reduction of the wavelength and the propagation length in the second type of experiments.

Excitation of monochromatic and stable electron acoustic wave by two counter-propagating laser beams

The undamped electron acoustic wave is a newly-observed nonlinear electrostatic plasma wave and has potential applications in ion acceleration, laser amplification and diagnostics due to its unique frequency range. We propose to make the first attempt to excite a monochromatic and stable electron acoustic wave (EAW) by two counter-propagating laser beams. The matching conditions relevant to laser frequencies, plasma density, and electron thermal velocity are derived and the harmonic effects of the EAW are excluded. Single-beam instabilities, including stimulated Raman scattering and stimulated Brillouin scattering, on the excitation process are quantified by an interaction quantity, , where γ is the growth rate of each instability and is the characteristic time of the undamped EAW. The smaller the interaction quantity, the more successfully the monochromatic and stable EAW can be excited. Using one-dimensional Vlasov–Maxwell simulations, we excite EAW wave trains which are amplitude tunable, have a duration of thousands of laser periods, and are monochromatic and stable, by carefully controlling the parameters under the above conditions.

Dust acoustic waves in an inhomogeneous plasma having dust size distribution

Propagations of nonlinear dust acoustic solitary waves in an inhomogeneous unmagnetized dusty plasma having power law dust distribution are investigated. Using a reductive perturbation technique, a variable coefficient deformed Korteweg-deVries (VCdKdV) equation is derived from the basic set of hydrodynamic equations. The generalized expansion method is employed to obtain a solitary wave solution for the VCdKdV equation. The different propagation characteristics of the solitary waves are studied in the presence of both plasma inhomogeneity and dust distribution.

Higher order nonlinear dust-acoustic waves in a dusty plasma with dust of opposite polarity

The nonlinear propagation of dust-acoustic (DA) waves in an unmagnetized dusty plasma (containing positive and negatively charged inertial dust grains and nonextensive distributed electrons and ions) have been investigated theoretically. Three different types of nonlinear dynamical equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and Gardner equations have been derived by employing the reductive perturbation method. The basic features (viz., polarity, amplitude, width, etc.) of solitary waves have been also analyzed numerically. It has been observed that the effects of nonextensivity of electrons and ions, mass and charge of positive and negative dust, and different dusty plasma parameters have significantly modified the fundamental properties of the solitary waves.

Effects of Landau damping on finite amplitude low-frequency nonlinear waves in a dusty plasma

The effect of linear ion Landau damping on weakly nonlinear as well as weakly dispersive low-frequency waves in a dusty plasma is investigated. The standard perturbative approach leads to the Korteweg–de Vries (KdV) equation with a linear Landau damping term for the dynamics of the low-frequency nonlinear wave. Landau damping causes the wave amplitude to decay with time and the dust charge variation enhances the damping rate.

Langmuir wave filamentation in the kinetic regime. II. Weak and strong pumping of nonlinear electron plasma waves as the route to filamentation

We consider two kinds of pumped Langmuir waves (LWs) in the kinetic regime, kλD≳0.2, where k is the LW wavenumber and λD is the Debye length, driven to finite amplitude by a coherent external potential whose amplitude is either weak or strong. These dynamically prepared nonlinear LWs develop a transverse (filamentation) instability whose nonlinear evolution destroys the LW's transverse coherence. Instability growth rates in the weakly pumped regime are the same as those of Bernstein-Greene-Kruskal modes considered in Part I (D. A. Silantyev et al., Phys. Plasmas 24, 042104 (2017)), while strongly pumped LWs have higher filamentation grow rates.

Numerical simulation for the solitary wave of Zakharov–Kuznetsov equation based on lattice Boltzmann method

The Zakharov–Kuznetsov equation is considered, which is an equation describing two dimensional weakly nonlinear ion-acoustic waves in plasma. We focus on using the lattice Boltzmann method to study the Zakharov–Kuznetsov equation. A lattice Boltzmann model is constructed. In numerical experiments, the propagation of the single solitary wave and the collision of double solitary waves are simulated. The results with different parameters are investigated and compared.

Nonlinear oscillations and waves in multi-species cold plasmas

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.

Characteristics of nonlinear dust acoustic waves in a Lorentzian dusty plasma with effect of adiabatic and nonadiabatic grain charge fluctuation

In this paper, characteristics of small amplitude nonlinear dust acoustic wave have been investigated in a unmagnetized, collisionless, Lorentzian dusty plasma where electrons and ions are inertialess and modeled by generalized Lorentzian Kappa distribution. Dust grains are inertial and equilibrium dust charge is negative. Both adiabatic and nonadiabatic fluctuation of charges on dust grains have been taken under consideration. For adiabatic dust charge variation reductive perturbation analysis gives rise to a KdV equation that governs the nonlinear propagation of dust acoustic waves having soliton solutions. For nonadiabatic dust charge variation nonlinear propagation of dust acoustic wave obeys KdV-Burger equation and gives rise to dust acoustic shock waves. Numerical estimation for adiabatic grain charge variation shows the existence of rarefied soliton whose amplitude and width varies with grain charges. Amplitude and width of the soliton have been plotted for different electron Kappa indices keeping ion velocity distribution Maxwellian. For non adiabatic dust charge variation, ratio of the coefficients of Burger term and dispersion term have been plotted against charge fluctuation for different kappa indices. All these results approach to the results of Maxwellian plasma if both electron and ion kappa tends to infinity.

Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation

In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the \((3+1)\)-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the \((3+1)\)-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas.

Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma

This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries (KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influence of plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequency waves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.

Collapse of nonlinear electron plasma waves in a plasma layer

The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region.

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number kλ_{De} is small, such as kλ_{De}=0.1, the fluid NFS dominates in the total NFS and will reach as large as nearly 15% when the wave amplitude |eϕ/T_{e}|∼0.1, which indicates that in the condition of small kλ_{De}, the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

A theoretical study for parallel electric field in nonlinear magnetosonic waves in three-component plasmas

The electric field parallel to the magnetic field in nonlinear magnetosonic waves in three component plasmas (two-ion-species plasma and electron-positron-ion plasma) is theoretically studied based on a three-fluid model. In a two-ion-species plasma, a magnetosonic mode has two branches, high-frequency mode and low-frequency mode. The parallel electric field E∥ and its integral along the magnetic field, F=−∫E∥ds, in the two modes propagating quasiperpendicular to the magnetic field are derived as functions of the wave amplitude ϵ and the density ratio and cyclotron frequency ratio of the two ion species. The theory shows that the magnitude of F in the high-frequency-mode pulse is much greater than that in the low-frequency-mode pulse. Theoretical expressions for E∥ and F in nonlinear magnetosonic pulses in an electron-positron-ion plasma are also obtained under the assumption that the wave amplitudes are in the range of (me/mi)1/2<ϵ<1, where me/mi is the electron to ion mass ratio.

The effect of exchange-correlation coefficient in quantum semiconductor plasma in presence of electron-phonon collision frequency

The influence of exchange-correlation potential, quantum Bohm term, and degenerate pressure on the nature of solitary waves in a quantum semiconductor plasma is investigated. It is found that an amplitude and a width of the solitary waves change with variation of different parameters for different semiconductors. A deformed Korteweg-de Vries equation is obtained for propagation of nonlinear waves in a quantum semiconductor plasma, and the effects of different plasma parameters on the solution of the equation are also presented.

Solitonic and chaotic behaviors for the nonlinear dust-acoustic waves in a magnetized dusty plasma

A model for the nonlinear dust-ion-acoustic waves in a two-ion-temperature, magnetized dusty plasma is studied in this paper. Via the symbolic computation, one-, two- and N-soliton solutions are obtained. It is found that when μeμi<2Ti2Te2+TiTe, the soliton amplitude is positively related to μe, μi, Ti, Zd, and B0, but inversely related to Te and md, with Te, Ti, μe, and μi as the temperature of an electron, temperature of a positive ion, normalized initial density of electrons, and normalized initial density of positive ions, respectively, Zd, B0, and md as the charge number of a dust particle, strength of the static magnetic field, and mass of a dust particle, respectively. It is also found that the two solitons are always parallel during the propagation on the x − y, x − t, and y − t planes, where x, y, and z are the scaled spacial coordinates, and t is the retarded time. Upon the introduction of the driving force Γ(t), both the developed and weak chaotic motions as well as the effect of Γ(t) are explored. Via the phase projections and power spectra, we find the difference between the two chaotic motions roots in the relative magnitude of nonlinearity and external force. Increasing the frequency of the external force or the strength of the damped term can weaken the chaotic motions of such a forced model.

Generation of acoustic rogue waves in dusty plasmas through three-dimensional particle focusing by distorted waveforms

Rogue waves have been observed in fluids and other wave contexts. Experiments now show the formation of 3D acoustic rogue waves in dusty plasmas; they result from wave–particle interactions driving the dust particles into high-amplitude dynamics. Rogue waves—rare uncertainly emerging localized events with large amplitudes—have been experimentally observed in many nonlinear wave phenomena, such as water waves1,2,3,4,5,6, optical waves7,8, second sound in superfluid He II (ref. 9) and ion acoustic waves in plasmas10. Past studies have mainly focused on one-dimensional (1D) wave behaviour through modulation instabilities1,3,4,5,7,11, and to a lesser extent on higher-dimensional behaviour5,6,8,11,12. The question whether rogue waves also exist in nonlinear 3D acoustic-type plasma waves, the kinetic origin of their formation and their correlation with surrounding 3D waveforms are unexplored fundamental issues. Here we report the direct experimental observation of dust acoustic rogue waves in dusty plasmas and construct a picture of 3D particle focusing by the surrounding tilted and ruptured wave crests, associated with the higher probability of low-amplitude holes for rogue-wave generation.

Injection of electrons by colliding laser pulses in a laser wakefield accelerator

To improve the stability and reproducibility of laser wakefield accelerators and to allow for future applications, controlling the injection of electrons is of great importance. This allows us to control the amount of charge in the beams of accelerated electrons and final energy of the electrons. Results are presented from a recent experiment on controlled injection using the scheme of colliding pulses and performed using the Lund multi-terawatt laser. Each laser pulse is split into two parts close to the interaction point. The main pulse is focused on a 2mm diameter gas jet to drive a nonlinear plasma wave below threshold for self-trapping. The second pulse, containing only a fraction of the total laser energy, is focused to collide with the main pulse in the gas jet under an angle of 150°. Beams of accelerated electrons with low divergence and small energy spread are produced using this set-up. Control over the amount of accelerated charge is achieved by rotating the plane of polarization of the second pulse in relation to the main pulse. Furthermore, the peak energy of the electrons in the beams is controlled by moving the collision point along the optical axis of the main pulse, and thereby changing the acceleration length in the plasma.