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.

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail

Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas

The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted.

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas

The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ?c and the (intrinsic) plasma rotation frequency O0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ?c ? ±2O0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T- ˜ T+) “pure” (n- ˜ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.

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.

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.

Characterisation of nonlinear distortion and intermodulation in passive devices and antennas

The paper presents a conceptual discussion of the characterisation and phenomenology of passive intermodulation (PIM) by the localised and distributed nonlinearities in passive devices and antennas. The PIM distinctive nature and its impact on signal distortions are examined in comparison with similar effects in power amplifiers. The main features of PIM generation are discussed and illustrated by the example of PIM due to electro-thermal nonlinearity. The issues of measurement, discrimination and modelling of PIM generated by nonlinearities in passive RF components and antennas are addressed.

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.

Modelling the nonlinear behaviour and fracture process of AS4/PEKK thermoplastic composite under shear loading

The accurate determination of non-linear shear behaviour and fracture toughness of continuous carbon-fibre/polymer composites remains a considerable challenge. These measurements are often necessary to generate material parameters for advanced computational damage models. In particular, there is a dearth of detailed shear fracture toughness characterisation for thermoplastic composites which are increasingly generating renewed interest within the aerospace and automotive sectors. In this work, carbon fibre (AS4)/ thermoplastic Polyetherketoneketone (PEKK) composite V-notched cross-ply specimens were manufactured to investigate their non-linear response under pure shear loading. Both monotonic and cyclic loading were applied to study the shear modulus degradation and progressive failure. For the first time in the reported literature, we use the essential work of fracture approach to measure the shear fracture toughness of continuous fibre reinforced composite laminates. Excellent geometric similarity in the load-displacement curves was observed for ligament-scaled specimens. The laminate fracture toughness was determined by linear regression, of the specific work of fracture values, to zero ligament thickness, and verified with computational models. The matrix intralaminar fracture toughness (ply level fracture toughness), associated with shear loading was determined by the area method. This paper also details the numerical implementation of a new three-dimensional phenomenological model for carbon fibre thermoplastic composites using the measured values, which is able to accurately represent the full non-linear mechanical response and fracture process. The constitutive model includes a new non-linear shear profile, shear modulus degradation and load reversal. It is combined with a smeared crack model for representing ply-level damage initiation and propagation. The model is shown to accurately predict the constitutive response in terms of permanent plastic strain, degraded modulus as well as load reversal. Predictions are also shown to compare favourably with the evolution of damage leading to final fracture.