Nonlinear excitations in ferromagnetic chains with nearest and next nearest neighbor exchange interactions

Weakly nonlinear excitations in one-dimensional isotropic Heisenberg ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions are considered. Based on the properties of modulational stability of corresponding linear spin waves, the existence regions of bright and dark magnetic solitons of the system are discussed in the whole Brillouin zone. The antidark soliton mode which is convex soliton super-imposed with a plane wave component is obtained near the zero-dispersion points of the spin wave frequency spectrum. The analytical results are checked by numerical simulations. [S0163;1829(98)01838-4].

Nonlinear electrostatic excitations of charged dust in degenerate ultra-dense quantum dusty plasmas

The linear and nonlinear properties of low-frequency electrostatic excitations of charged dust particles (or defects) in a dense collisionless, unmagnetized Thomas-Fermi plasma are investigated. A fully ionized three-component model plasma consisting of electrons, ions, and negatively charged massive dust grains is considered. Electrons and ions are assumed to be in a degenerate quantum state, obeying the Thomas-Fermi density distribution, whereas the inertial dust component is described by a set of classical fluid equations. Considering large-amplitude stationary profile travelling-waves in a moving reference frame, the fluid evolution equations are reduced to a pseudo-energy-balance equation, involving a Sagdeev-type potential function. The analysis describes the dynamics of supersonic dust-acoustic solitary waves in Thomas-Fermi plasmas, and provides exact predictions for their dynamical characteristics, whose dependence on relevant parameters (namely, the ion-to-electron Fermi temperature ratio, and the dust concentration) is investigated. An alternative route is also adopted, by assuming weakly varying small-amplitude disturbances off equilibrium, and then adopting a multiscale perturbation technique to derive a Korteweg–de Vries equation for the electrostatic potential, and finally solving in terms for electric potential pulses (electrostatic solitons). A critical comparison between the two methods reveals that they agree exactly in the small-amplitude, weakly superacoustic limit. The dust concentration (Havnes) parameter h = Zd0nd0/ne0 affects the propagation characteristics by modifying the phase speed, as well as the electron/ion Fermi temperatures. Our results aim at elucidating the characteristics of electrostatic excitations in dust-contaminated dense plasmas, e.g., in metallic electronic devices, and also arguably in supernova environments, where charged dust defects may occur in the quantum plasma regime.

Oblique propagation of arbitrary amplitude electron acoustic solitary waves in magnetized kappa-distributed plasmas

The linear and nonlinear properties of large-amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modeled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential-type analysis reveals the existence of large-amplitude electrostatic solitary waves and allows for an investigation of their propagation characteristics and existence domain, in terms of the soliton speed (Mach number). The effects of the key plasma configuration parameters, namely the superthermality index and the cold electron density, on the soliton characteristics and existence domain, are studied. The role of obliqueness and magnetic field is discussed.

Electron-acoustic solitary waves in the presence of a suprathermal electron component

The nonlinear dynamics of electron-acoustic localized structures in a collisionless and unmagnetized plasma consisting of “cool” inertial electrons, “hot” electrons having a kappa distribution, and stationary ions is studied. The inertialess hot electron distribution thus has a long-tailed suprathermal (non-Maxwellian) form. A dispersion relation is derived for linear electron-acoustic waves. They show a strong dependence of the charge screening mechanism on excess suprathermality (through ?). A nonlinear pseudopotential technique is employed to investigate the occurrence of stationary-profile solitary waves, focusing on how their characteristics depend on the spectral index ?, and the hot-to-cool electron temperature and density ratios. Only negative polarity solitary waves are found to exist, in a parameter region which becomes narrower as deviation from the Maxwellian (suprathermality) increases, while the soliton amplitude at fixed soliton speed increases. However, for a constant value of the true Mach number, the amplitude decreases for decreasing ?.

Electrostatic waves in superthermal dusty plasmas: review of recent advancement

Real plasmas are often caracterized by the presence of excess energetic particle populations, resulting in a long-tailed non-Maxwellian distribution. In Space plasma physics, this phenomenon is usually modelled via a kappa-type distribution. This presentation is dedicated to an investigation, from first principles, of the effect of superthermality on the characteristics of dusty plasma modes. We employ a kappa distribution function to model the superthermality of the background components (electrons and/or ions). Background superthermality is shown to modify the charge screening mechanism in dusty plasmas, thus affecting the linear dispersion laws of both low- and higher frequency DP modes substantially. Various experimentally observed effects may thus be interpreted as manifestations of superthermality. Focusing on the features of nonlinear excitations (solitons) as they occur in different dusty plasma modes, we investigate the role of superthermality in their propagation dynamics (existence laws, stability profile) and characteristics (geometry).

Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-distributed non-thermal plasmas: an overview

Space plasmas provide abundant evidence of highly energetic particle population, resulting in a long-tailed non-Maxwellian distribution. Furthermore, the first stages in the evolution of plasmas produced during laser-matter interaction are dominated by nonthermal electrons, as confirmed by experimental observation and computer simulations. This phenomenon is efficiently modelled via a kappa-type distribution. We present an overview, from first principles, of the effect of superthermality on the characteristics of electrostatic plasma waves. We rely on a fluid model for ion-acoustic excitations, employing a kappa distribution function to model excess superthermality of the electron distribution. Focusing on nonlinear excitations (solitons), in the form of solitary waves (pulses), shocks and envelope solitons, and employing standard methodological tools of nonlinear plasmadynamical analysis, we discuss the role of excess superthermality in their propagation dynamics (existence laws, stability profile), geometric characteristics and stability. Numerical simulations are employed to confirm theoretical predictions, namely in terms of the stability of electrostatic pulses, as well as the modulational stability profile of bright- and dark-type envelope solitons.

Superluminal electromagnetic solitary waves in electron-positron plasmas

The propagation of an electromagnetic wave packet in an electron-positron plasma, in the form of coupled localized electromagnetic excitations, is investigated, from first principles. By means of the Poincare section method, a special class of superluminal localized nonlinear stationary solutions, existing along a separatrix curve, are proposed as intrinsic electromagnetic modes in a relativistic electron-positron plasma. The ratio of the envelope time scale to the carrier wave time scale of these envelope solitary waves critically depends on the carrier's phase velocity. In the strongly superluminal regime, v(ph)/c >> 1, the large difference between the envelope and carrier time scales enables us to carry out a multiscale perturbative analysis resulting in an analytical form of the solution envelope. The analytical prediction thus obtained is shown to be in agreement with the solution obtained via a direct numerical integration. Copyright (c) EPLA, 2012

Nonlinear scattering by anisotropic dielectric periodic structures

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. © 2012 O. V. Shramkova and A. G. Schuchinsky.

Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space-particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off-a diagnostic that is in principle accessible to observation.

Electromagnetic rogue waves in beam-plasma interactions

The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid Maxwell equations describing weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schrödinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered as potential candidates for the modeling of rogue waves (freak waves) in beam-plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-)frequency and the plasma frequency. © 2013 IOP Publishing Ltd.

Nonlinear dynamics of multidimensional electrostatic excitations in nonthermal plasmas

Electrostatic solitary waves in plasmas are the focus of many current studies of localized electrostatic disturbances in both laboratory and astrophysical plasmas. Motivated by recent experimental observations, in which electrostatic solitary structures were detected in laser-plasma experiments, we have undertaken an investigation of the nonlinear dynamics of plasma evolving in two dimensions, in the presence of excess superthermal background electrons. We investigate the effect of a magnetic field on weakly nonlinear ion-acoustic waves. Deviation from the Maxwellian distribution is effectively modelled by the kappa model. A linear dispersion relation is derived, and a decrease in frequency and phase speed in both parallel and perpendicular modes can be seen, which is due to excess superthermal electrons, and which is stronger in the upper mode, and hardly noticeable in the lower (acoustic) mode. We show that ion-acoustic solitary waves can be generated during the nonlinear evolution of a plasma fluid, and their nonlinear propagation is governed by a Zakharov-Kuznetsov (ZK) type equation. A multiple scales perturbation technique is used to derive the ZK equation. Shock excitations can be produced if we allow for dissipation in the model, resulting in a Zakharov-Kuznetsov Burgers type equation. Different types of shock solutions and solitary waves are obtained, depending on the relation between the system parameters, and the effect of these on electrostatic shock structures is investigated numerically. A parametric investigation is conducted into the role of plasma nonthermality and magnetic field strength. © 2013 IOP Publishing Ltd.

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron-positron-ion plasmas:Modulational instability and rogue waves

A fluid model is used to describe the propagation of envelope structures in an ion plasma under the influence of the action of weakly relativistic electrons and positrons. A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude. Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed. © Cambridge University Press 2013.

Freak waves and electrostatic wavepacket modulation in a quantum electron-positron-ion plasma

The occurrence of rogue waves (freak waves) associated with electrostatic wavepacket propagation in a quantum electron-positron-ion plasma is investigated from first principles. Electrons and positrons follow a Fermi-Dirac distribution, while the ions are subject to a quantum (Fermi) pressure. A fluid model is proposed and analyzed via a multiscale technique. The evolution of the wave envelope is shown to be described by a nonlinear Schrödinger equation (NLSE). Criteria for modulational instability are obtained in terms of the intrinsic plasma parameters. Analytical solutions of the NLSE in the form of envelope solitons (of the bright or dark type) and localized breathers are reviewed. The characteristics of exact solutions in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather are proposed as candidate functions for rogue waves (freak waves) within the model. The characteristics of the latter and their dependence on relevant parameters (positron concentration and temperature) are investigated. © 2014 IOP Publishing Ltd.

Frequency Filtering of Torsional Alfvén Waves by Chromospheric Magnetic Field

In this Letter, we demonstrate how the observation of broadband frequency propagating torsional Alfvén waves in chromospheric magnetic flux tubes can provide valuable insight into their magnetic field structure. By implementing a full nonlinear three-dimensional magnetohydrodynamic numerical simulation with a realistic vortex driver, we demonstrate how the plasma structure of chromospheric magnetic flux tubes can act as a spatially dependent frequency filter for torsional Alfvén waves. Importantly, for solar magnetoseismology applications, this frequency filtering is found to be strongly dependent on magnetic field structure. With reference to an observational case study of propagating torsional Alfvén waves using spectroscopic data from the Swedish Solar Telescope, we demonstrate how the observed two-dimensional spatial distribution of maximum power Fourier frequency shows a strong correlation with our forward model. This opens the possibility of beginning an era of chromospheric magnetoseismology, to complement the more traditional methods of mapping the magnetic field structure of the solar chromosphere.