Electromagnetic Solitary Waves Research Articles

Light bullet passing an array of carbon nanotubes with metallic mesh irregularities

We consider the propagation of 2D solitary electromagnetic waves and their scattering on a lattice of metallic inhomogeneities in the system of carbon nanotubes (CNTs). The electromagnetic field is considered on the basis of Maxwell equations, and the electronic system of carbon nanotubes is treated by the Boltzmann equation in relaxation time approximation. We numerically analyze the derived effective equation and reveal an increase of spectral composition of the last electromagnetic wave. Some possible practical applications of the discovered effect are discussed.

Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.

Relativistic solitary waves modulating long laser pulses in plasmas

This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency ω, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V–ω plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

Solitary waves of laser pulse in a plasma channel

The propagation of a Gaussian laser pulse in a preformed plasma channel is investigated. The conditions for the existence of electromagnetic solitary waves are obtained theoretically by analyzing the differential equation of the pulse spot size including the effects of relativistic self-focusing, ponderomotive self-channeling, and preformed channel focusing. Some solitarylike wave solutions are presented numerically and their possible implications on laser-plasma acceleration are discussed briefly.

Numerical Simulation of Electromagnetic Solitons and Their Interaction with Matter

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.

Density cavities generated by plasma–field interactions in the far wake region of a space vehicle

Under the consideration of non-steady case, a set of equations is derived, which describes the non-steady nonlinear interactions between plasma and field in the far wake region of a space vehicle. Numerical calculations are also made and the numerical results show that density cavities and electromagnetic solitary waves are generated due to the modulation instability, if the envelope of high frequency modulation field is strong enough. This is of great significance to the detection of disguised space vehicles.

Formation and dynamics of relativistic electromagnetic solitons in plasmas containing high-and low-energy electron components

We present theoretical and numerical studies of the nonlinear interactions between intense electromagnetic waves in plasmas containing high-and low-energy electron components. Such plasmas are frequently observed in laser-plasma experiments, where the hot electron component is created by the acceleration of electrons by strong electrostatic waves that are created by the laser-induced Raman forward and backward instabilities. The two-component electron plasma is described by the Vlasov equation for the hot electrons and the hydrodynamic equations for the cold electrons, which are coupled nonlinearly to the electromagnetic wave equation and the Poisson equation for the potential. The present nonlinear system is shown to admit electromagnetic solitary waves correlated with a positive potential and trapped electron islands from the hot electron population.

Electromagnetic solitary waves in the saturation regime of stimulated Brillouin backscattering

Recent particle-in-cell simulations of the stimulated Brillouin backscattering (SBBS) of electromagnetic radiation have shown that even at sub-relativistic intensities (Iλ2 = 1016 Wμm2/cm2) non-drifting solitary waves, “solitons” for short, are easily produced, and remain almost unchanged all along the simulation time, typically for several thousands of optical cycles. They appear in the form of stable local concentrations of electromagnetic radiation trapped inside quasi-neutral density holes. The plasma density inhomogeneity associated with their presence disrupts the resonant SBBS amplification. The cavitation process is accompanied by strong electron and ion heating. The physical characteristics of such solitons are discussed and they are compared with the theoretical predictions of an analytical model for localized solution of the Maxwell equations in warm plasma.

Parallel Propagating Electromagnetic Solitons and Oscillitons in Space Plasmas and in Relativistic Electron-Positron Plasmas

An overview is given of methods to study weak and strong nonlinear modes in multispecies plasmas, with a discussion of how they correspond (or not) for phenomena at not too strong amplitudes. Reductive perturbation analysis leads for weak nonlinear waves to several well known nonlinear evolution equations. In contrast, strong nonlinear phenomena are dealt with by immediately looking for stationary solutions of the model equations. While this works well for electrostatic modes via the Sagdeev pseudopotential technique, large amplitude, parallel propagating solitary electromagnetic waves occur as oscillitons, for which the correct nonlinear evolution equation is still lacking. Electromagnetic modes in (relativistic) electron-positron plasmas are an exception, in that they give pure solitons, both at large and smaller nonlinear amplitudes. The behaviour of the wave magnetic field is expressed through an energy integral that involves the Mach number of the structure, thus yielding the limits on the allowable Mach numbers and soliton amplitudes.

Low-frequency electromagnetic solitary and shock waves in an inhomogeneous dusty magnetoplasma

It is shown that the nonlinear dynamics of one-dimensional Shukla mode [Phys. Lett. A 316, 238 (2003)] is governed by a modified Kortweg–de Vries–Burgers equation. The latter admits stationary solutions in the form of either a solitary wave or a monotonic/oscillatory shock. The present nonlinear waves may help to understand the salient features of localized density and magnetic field structures in molecular dusty clouds as well as in low-temperature laboratory dusty plasma discharges.

Plasma-field interactions in the wake region of a space vehicle

Under the non-steady limit, a set of equations are derived, which describe the non-steady, non-linear interactions between plasma and field in the wake region of a space vehicle. Numerical calculations are also made and the numerical results show that density cavities and electromagnetic solitary waves will be generated due to modulational instability, if the envelope of the high frequency modulation field is strong enough. This will be of great significance for detecting disguised space vehicles.

Stationary Solitary Electomagnetic Waves Generated in Relativistic Laser-Plasma Interaction.

Stationary solitary electromagnetic waves generated in ultraintense relativistic laser-plasma interactions are studied numerically. For one-dimensional stationary propagation with circular polarization, subcycle solitary waves moving with finite velocity are obtained for a given value of wave velocity and nonlinear frequency shift, and it is shown that the solitary-wave amplitude increases for the larger nonlinear frequency shift. A new type of solitary-wave solution, a paired solution of positive and negative solitary waves, is also shown.

Coherent Electromagnetic Structures in Relativistic Plasmas

Relativistic electromagnetic low-frequency solitary waves are found to occur in underdense plasmas in regimes where the laser pulse becomes filamented and undergoes energy depletion and frequency downshifting. These slowly propagating “subcycle-solitons” represent one of the channels of conversion of the laser pulse energy. Electron vortices and their associated quasistatic magnetic field represent a different important type of long lived coherent electromagnetic structures. Their generation is related to the dynamics of fast electron currents in the plasma.

Solitary electromagnetic waves in non-Kerr-like nonlinear media

Non-Kerr-like nonlinearity is more general and accurate in simulating practical nonlinear materials. In this paper, transmission of electromagnetic solitary waves in non-Kerr-like media with nonlinearity of n/spl sim/|E|/sup /spl delta// is studied. It is found that for both spatial and temporal solitary waves their governing equations can be generalized with the nonlinear Schrodinger equation. As a result, a solitary solution of the equation is derived in a closed analytic form. The distributions of both temporal and spatial electromagnetic solitons are then obtained in an explicit analytic form.

On the solitary waves in the sine-Gordon model of the two-dimensional Josephson junction

The properties of the possible solitary electromagnetic waves, propagating in two-dimensional SIS Josephson junction without dissipative losses are investigated on the basis of the local theory of the junction. A classification of the waves in the junction with respect to the Swihart velocity is made. It is shown that allowed and forbidden areas for the wave numbers, wave frequency and wave amplitude exist. The cut-off frequency for the solitary waves which velocity is greater than the Swihart velocity can be smaller than the Josephson plasma frequency and moreover these waves can propagate only in a junction that is large in the direction perpendicular to the propagation direction. On the contrary the solitary waves which velocity is smaller than the Swihart velocity request junction size in the above direction to be smaller than a critical one. The investigated two-dimensional solitary waves can be connected with one or two quanta of the magnetic flux.

Interaction between two electromagnetic solitary waves in a plasma

From numerical solutions of two colliding electromagnetic solitary waves, it is shown that their shapes are modified, and a trailing wake of plasma oscillations is produced by the collision. They therefore cannot be classified as solitons. For sufficiently large relative velocities, however, it is shown that the modifications to the vector and scalar potentials, as well as to the wake due to the collision, are small.

One-dimensional, weakly nonlinear electromagnetic solitary waves in a plasma.

The properties of one-dimensional, weakly nonlinear electromagnetic solitary waves in a plasma are investigated. The solution of the resulting eigenvalue problem shows that the solitary waves have amplitudes which are allowed discrete values only and their vector and scalar potentials are proportional to ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$/${\mathrm{\ensuremath{\omega}}}_{0}$ and (${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$/${\mathrm{\ensuremath{\omega}}}_{0}$${)}^{2}$, respectively, where ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ and ${\mathrm{\ensuremath{\omega}}}_{0}$ are the plasma and electromagnetic wave frequencies, respectively. Their widths are comparable to the plasma wavelength ${\ensuremath{\lambda}}_{\mathit{p}}$=2\ensuremath{\pi}c/${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ (where c is the velocity of light), except for the lowest-order solitary wave, whose width is large compared with ${\ensuremath{\lambda}}_{\mathit{p}}$, which is a true wakeless solitary wave only in the limit of vanishing amplitude. Simple analytical solutions are derived for higher-order solitary waves, whose vector-potential envelope is highly oscillatory, and are shown to consist, in the group-velocity frame, of two trapped, oppositely traveling waves.

Propagation of electromagnetic solitary waves in dispersive nonlinear dielectrics.

We have derived the wave equation of electromagnetic field coupling with TO phonons in second-order nonlinear dielectrics. If the loss of the medium can be ignored, theoretical calculation shows that the propagation of electromagnetic pulses without distortion in the dispersive medium is possible due to the dependence of the index of refraction on the electromagnetic field. This electromagnetic field is governed by a Boussinesq equation that has soliton solutions. If the loss of the medium is sufficiently strong that the damping distance is much smaller than the signal width, we find electromagnetic shock-wave solutions. Possible experiments in ${\mathrm{LiTaO}}_{3}$ are discussed.

Force-free electromagnetic pulses in a laboratory plasma.

A short, intense current pulse (I=150 A, \ensuremath{\Delta}t\ensuremath{\simeq}0.2 \ensuremath{\mu}s, N\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}${10}^{14}$ electrons) is drawn from an electrode immersed in a magnetized afterglow plasma (n\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, ${\mathit{kT}}_{\mathit{e}}$\ensuremath{\simeq}1.3 eV, ${\mathit{B}}_{0}$=10 G). The induced magnetic field B(r,t) assumes the shape of a helical double vortex which propagates along ${\mathbf{B}}_{0}$ through the uniform plasma as a whistler mode. The observations support a prediction of force-free (J\ifmmode\times\else\texttimes\fi{}B+neE=0) electromagnetic fields and solitary waves. Energy and helicity are approximately conserved.

Electromagnetic solitary waves in magnetized plasmas

A Hamiltonian formulation, in terms of a non-canonical Poisson bracket, is presented for a nonlinear fluid system that includes reduced magnetohydro-dynamics and the Hasegawa–Mima equation as limiting cases. The single-helicity and axisymmetric versions possess three nonlinear Casimir invariants, from which a generalized potential can be constructed. Variation of the generalized potential yields a description of exact nonlinear stationary states. The new equilibria, allowing for plasma flow as well as partial electron adiabaticity, are distinct from those found in conventional magnetohydrodynamic theory. They differ from electrostatic stationary states in containing plasma current and magnetic field excitation. One class of steady-state solutions is shown to provide a simple electromagnetic generalization of drift-solitary waves.