Time-resolved characterization of the formation of a collisionless shock.

We report on the temporally and spatially resolved detection of the precursory stages that lead to the formation of an unmagnetized, supercritical collisionless shock in a laser-driven laboratory experiment. The measured evolution of the electrostatic potential associated with the shock unveils the transition from a current free double layer into a symmetric shock structure, stabilized by ion reflection at the shock front. Supported by a matching particle-in-cell simulation and theoretical considerations, we suggest that this process is analogous to ion reflection at supercritical collisionless shocks in supernova remnants.

Surge of power transmission in flat and nearly flat band lattices.

Flat band systems can yield interesting phenomena, such as dispersion suppression of waves with frequency at the band. While linear transport vanishes, the corresponding nonlinear case is still an open question. Here, we study power transmission along nonlinear sawtooth lattices due to waves with the flat band frequency injected at one end. While there is no power transfer for small intensity, there is a threshold amplitude above which a surge of power transmission occurs, i.e., supratransmission, for defocusing nonlinearity. This is due to a nonlinear evanescent wave with the flat band frequency that becomes unstable. We show that dispersion suppression and supratransmission also exist even when the band is nearly flat.

Dynamics of self-generated, large amplitude magnetic fields following high-intensity laser matter interaction.

The dynamics of magnetic fields with an amplitude of several tens of megagauss, generated at both sides of a solid target irradiated with a high-intensity (~10(19) W/cm(2)) picosecond laser pulse, has been spatially and temporally resolved using a proton imaging technique. The amplitude of the magnetic fields is sufficiently large to have a constraining effect on the radial expansion of the plasma sheath at the target surfaces. These results, supported by numerical simulations and simple analytical modeling, may have implications for ion acceleration driven by the plasma sheath at the rear side of the target as well as for the laboratory study of self-collimated high-energy plasma jets.

Characteristics of plasma sheath in multi-component plasmas with three-ion species.

The plasma sheath of a three ion species plasma is studied numerically, relying on the results of the experiment by Yip et al. (Phys. Plasmas 23:050703 (2016) to measure the positive ion velocities at the sheath edge. The positive ion species ([Formula: see text], [Formula: see text] and [Formula: see text]) are assumed to be singly charged and to be characterized by the same temperature. It is shown that the sheath characteristics, viz. the particle number densities, the electrostatic potential and the space charge density profile in the sheath all depend on the [Formula: see text] concentration that is gradually added to the argon-xenon plasma as the third positive ion species. Also, the effect of ion-neutral collisions on the sheath properties is investigated numerically. Our results may be extended to a multi-ion plasma with more than two species of positive ions.

Generation of a purely electrostatic collisionless shock during the expansion of a dense plasma through a rarefied medium.

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. The shock front develops a filamentary structure which is interpreted as the consequence of the electrostatic ion-ion instability, consistently with published analytical models and experimental results.

Electrostatic wave breaking limit in a cold electronegative plasma with non-Maxwellian electrons.

A one-dimensional multifluid hydrodynamic model has been adopted as basis for an investigation of the role of suprathermal electrons on the wave breaking amplitude limit for electrostatic excitations propagating in an electronegative plasma. A three-component plasma is considered, consisting of two inertial cold ion populations of opposite signs, evolving against a uniform background of (non-Maxwellian) electrons. A kappa-type (non-Maxwellian) distribution function is adopted for the electrons. By employing a traveling wave approximation, the first integral for the fluid-dynamical system has been derived, in the form of a pseudo-energy balance equation, and analyzed. The effect of intrinsic plasma parameters (namely the ion density ratio, the ion mass ratio, and the superthermal index of the nonthermal electrons) on the wave breaking amplitude limit is explored, by analyzing the phase space topology of the associated pseudopotential function. Our results are relevant to particle acceleration in Space environments and to recent experiments based on plasma-based accelerator schemes, where the simultaneous presence of negative ions and nonthermal electrons may be observed.

Discrete breathers in hexagonal dusty plasma lattices.

The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter epsilon in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.

Higher-order effects and ultrashort solitons in left-handed metamaterials.

Starting from Maxwell's equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrödinger equation, describing ultrashort solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.

Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the "hexapole" of alternating phases (0-pi) , as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.

Existence of multisite intrinsic localized modes in one-dimensional Debye crystals.

The existence of highly localized multisite oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The results are applied in the description of vertical (transverse, off-plane) dust grain motion in dusty plasma crystals, by taking into account the lattice discreteness and the sheath electric and/or magnetic field nonlinearity. Explicit values from experimental plasma discharge experiments are considered. The possibility for the occurrence of multibreathers associated with vertical charged dust grain motion in strongly coupled dusty plasmas (dust crystals) is thus established. From a fundamental point of view, this study aims at providing a rigorous investigation of the existence of intrinsic localized modes in Debye crystals and/or dusty plasma crystals and, in fact, suggesting those lattices as model systems for the study of fundamental crystal properties.

Self-focusing and envelope pulse generation in nonlinear magnetic metamaterials.

The self-modulation of waves propagating in nonlinear magnetic metamaterials is investigated. Considering the propagation of a modulated amplitude magnetic field in such a medium, we show that the self-modulation of the carrier wave leads to a spontaneous energy localization via the generation of localized envelope structures (envelope solitons), whose form and properties are discussed. These results are also supported by numerical calculations.

Ion-beam-plasma interaction effects on electrostatic solitary wave propagation in ultradense relativistic quantum plasmas.

Understanding the transport properties of charged particle beams is important not only from a fundamental point of view but also due to its relevance in a variety of applications. A theoretical model is established in this article, to model the interaction of a tenuous positively charged ion beam with an ultradense quantum electron-ion plasma, by employing a rigorous relativistic quantum-hydrodynamic (fluid plasma) electrostatic model proposed in McKerr et al. [M. McKerr, F. Haas, and I. Kourakis, Phys. Rev. E 90, 033112 (2014)PLEEE81539-375510.1103/PhysRevE.90.033112]. A nonlinear analysis is carried out to elucidate the propagation characteristics and the existence conditions of large amplitude electrostatic solitary waves propagating in the plasma in the presence of the beam. Anticipating stationary profile excitations, a pseudomechanical energy balance formalism is adopted to reduce the fluid evolution equation to an ordinary differential equation. Exact solutions are thus obtained numerically, predicting localized excitations (pulses) for all of the plasma state variables, in response to an electrostatic potential disturbance. An ambipolar electric field form is also obtained. Thorough analysis of the reality conditions for all variables is undertaken in order to determine the range of allowed values for the solitonic pulse speed and how it varies as a function of the beam characteristics (beam velocity and density).

Multispecies plasma expansion into vacuum: The role of secondary ions and suprathermal electrons.

The self-similar expansion of multispecies ion plasma is investigated by a two-ion fluid model with adiabatic equation of state for each ionic species. Our aim is to elucidate the effect of secondary ions on a plasma expansion front, in combination with energetic (suprathermal) electrons in the background, modeled by a kappa-type distribution function. The plasma density, velocity, and electric-field profile is investigated. It is shown that energetic electrons have a significant effect on the expansion front dynamics, essentially energizing the front, thus enhancing the ion acceleration mechanism. Different special cases are considered as regards the relative magnitude of the ion mass and/or charge state.

Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma.

The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.

Publisher's Note: Relativistic breather-type solitary waves with linear polarization in cold plasmas [Phys. Rev. E 91, 033102 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.91.033102.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Relativistic breather-type solitary waves with linear polarization in cold plasmas.

Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. Localized structures, in the form of exact numerical nonlinear solutions of the one-dimensional Maxwell-fluid model for a cold plasma with fixed ions, are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breather-type behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finite-differences scheme allows us to compute a branch of solutions within the frequency range Ωmin<Ω<ωpe, where ωpe and Ωmin are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of Ω is presented. Small-amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the Akhiezer-Polovin system. Direct numerical simulations of the Maxwell-fluid model show that these solitary waves propagate without change for a long time.

Electron-acoustic plasma waves: oblique modulation and envelope solitons.

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons, and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schrödinger equation, reveals that the EAW may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.

Modeling relativistic soliton interactions in overdense plasmas: a perturbed nonlinear Schrödinger equation framework.

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.

Dust-acoustic shocks in strongly coupled dusty plasmas.

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.