On a characteristic surface Ω of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Ω. This result can be interpreted also as a transport equation along rays of the wavefront Ωt in x-space associated with Ω. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

We study the existence of stable axially and spherically symmetric plasma structures on the basis of the new nonlinear Schrödinger equation (NLSE) accounting for non-local electron nonlinearities. The numerical solutions of NLSE having the form of spatial solitions are obtained and their stability is analyzed. We discuss the possible application of the obtained results to the theoretical description of natural plasmoids in the atmosphere.

In this paper, we investigated the output characteristics of the electron bunch accelerated by a chirped femtosecond laser pulse in vacuum using linear, elliptical and circular polarization states. To examine the features of the energy and angular spectra, emittances and position distribution of the electron bunch numerically, 105 electrons are used. It is found that the initial emittances of the electron bunch together with a proper choice of the polarization state of the laser pulse could lead to the efficient electron bunch acceleration.

The study, being on two-dimensional modelling of low pressure discharges, suggests an approach to the nonlinear inertia term in the momentum equation of the positive ions needed to be accounted for in the free-fall regime of the discharge maintenance. On the basis of conclusions that the inertia term acts in the wall sheath, where the ions fly perpendicularly to the walls, it is shown that (i) the parallel – to the walls – velocity component can be neglected, and (ii) the rest of the convective derivative can be determined by using the energy conservation law in the collisionless case. In a way, the inertia term acting as a retarding force is joined to the momentum loss term by introducing effective collision frequencies. The validity of the procedure is proved in a model of a low pressure argon discharge by comparison with the exact solutions for the two-dimensional spatial distribution of the discharge characteristics (ion velocity, electron density and temperature and DC electric field and its potential). The conclusion is that (i) ignoring the velocity component that is parallel to the walls does not cause deviation from the exact solution, and (ii) the approximation of using the energy conservation law in the collisionless case is good enough.

Through particle-in-cell simulations, the evolution of the bump-on-tail instability (BoTI) is studied for plasma subject to one-dimensional mechanical compression. It is shown that the final state of BoTI differs from that described by quasilinear theory for stationary bulk plasma and can depend on the compression history. The transformation of thermal energy into wave energy increases the plasma compressibility, thereby decreasing the amount of mechanical work required to compress the plasma to a specified size. Also, the energy spectrum of the excited modes can be tailored by choosing a particular compression scenario, offering a new technique for manipulating plasmas mechanically.

A theory of two-stream free-electron laser in a combined electromagnetic wiggler and an ion-channel guiding is developed. In the analysis, the electron trajectories and the small signal gain are derived by considering the effects of self-fields. Numerical calculations show that there are seven group's trajectories rather than nine groups reported in Mehdian and Saviz (2010 Chin. Phys. B 19(1), 014214). The comparison of the normalized gains and their corresponding normalized frequencies by employing the axial magnetic field and ion-channel guiding, with and without self-fields, in FEL has been studied numerically. The results show that the normalized maximum gain in FEL with axial magnetic is larger than that for using ion-channel guiding except in small region, but the results for their corresponding normalized frequencies are opposite.

Plasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vector-potential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instability.

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ϕ, which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ϕ. This leads to an implicit equation for the phase function and a generalization of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure, and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigenequations require that the rate of change of the magnetic induction B with ϕ throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ϕ) or B(ϕ) are developed.

It is shown that sheared/zonal flows (ZFs) can be nonlinearly excited by incoherent drift waves (DWs) in a strongly magnetized non-uniform plasma composed of electrons, positrons and ions. The dynamics of incoherent DWs in the presence of ZFs is governed by a wave-kinetic equation. The governing equation for ZFs in the presence of nonlinear forces (associated with nonlinear ion polarization and nonlinear ion-diamagnetic drifts) of the DWs is deduced by combining the Poisson equation, as well as the e-p-i continuity equations, together with appropriate plasma particle velocities in the DW and the ZF fields. Standard techniques are used to derive a nonlinear dispersion relation, which depicts two classes of the modulational instability of the DWs against the ZFs. Non-thermal ZFs can reduce the turbulent cross-field particle transport in non-uniform, strongly magnetized e-p-i plasmas.

A neodymium-doped yttrium aluminum garnet laser of wavelength 0.532 μm with the maximum energy of 900 mJ creates plasmas at a focal point in air in the path of a 1 kW continuous wave fiber laser of wavelength 1.08 μm. We find that there is an unexpected influence on a standard set of turbulent parameters in these laser-induced plasmas. Specifically, the continuous wave laser increased the complexity in the turbulent fluctuations. The continuous wave laser reduces the characteristic fluctuation frequencies in the neutral lines. Furthermore, the continuous wave laser enhances turbulence energies in ions while it diminishes turbulence energies in neutrals.

A paraxial-like approach has been invoked to understand the nature of propagation of a hollow Gaussian beam (HGB) propagating in plasma under the influence of relativistic non-linearity. In this approach, the parameters are expanded in terms of the radial distance from the maximum of irradiance rather than that from the axis. This paper investigates the excitation of plasma wave in a hot collision less plasma by HGB. On account of the × force, a plasma wave at 2ω0 (here, ω0 is the pump laser frequency) is generated. The solution of the HGB has been obtained within the paraxial ray approximation. Filamentary structures of the laser beam are observed due to relativistic non-linearity.

In the present research paper, the nonlinear propagation of dust ion acoustic solitary waves in a collisional dusty plasma, which consists of negatively charged small dust grains, positively charged ions and isothermal electrons with background neutral particles, is investigated. The low rates compared to the ion oscillation frequency, of the charge-fluctuation dynamics of the dust grains, the ionization, ion-neutral and dust-neutral collisions (i.e. weak dissipations) are considered. Using the reductive perturbation theory, a damped Korteweg-de Vries (DKdV) equation is derived. On the other hand, the dynamics of solitary waves at a critical phase velocity is governed by a damped modified Korteweg-de Vries (DMKdV) equation. The nonlinear properties of dust ion acoustic waves in the presence of weak dissipations in the two cases are discussed.

On the basis of two magneto-fluid model for two time-scales, the evolution of double layer in the downward current region of the aurora is numerically simulated under the non-static limit case. The results show that localized drop in density owing to collapsed high-frequency field can lead to the formation of double layer. The amplitude of the double layer is the order of the electron temperature, and the ramp potential is up to 36 V localized to tens of Debye lengths, which is around 100–200 m. These are consistent with the measurements in both the ramp potential and thickness by the Fast Auroral SnapshoT satellite in the downward current region of the aurora.

We investigate under which parameter regimes the magnetohydrodynamic (MHD) Rankine–Hugoniot conditions, which describe discontinuous solutions to the MHD equations, allow for slow, intermediate and fast shocks. We derive limiting values for the upstream and downstream shock parameters for which shocks of a given shock-type can occur. We revisit this classical topic in nonlinear MHD dynamics, augmenting the recent time reversal duality finding by in the usual shock frame parametrization.

The theoretical study of microwave characteristics of a thin film of hydrogen plasma in carbon nanotubes, which were grown by iron-catalyzed high-pressure carbon monoxide disproportionation, is presented. The system is assumed to be illuminated by either a transverse magnetic (TM) or a transverse electric (TE) waves at an arbitrary angle of incidence to the film. By considering the interference effects because of multiple reflections between thin plasma layer interfaces, the reflectance, transmittance, and absorptance of microwave radiation at the plasma film are deduced and their functional dependence on the continuous changing of the angle of propagation and plasma thickness with fixed parameters of the system are studied. The simulation results show that for the present system, the interference effects lead to a sinusoidal variation of the reflected intensity and can greatly reduce the amount of reflection power, but the absorption power increases. In addition, it is found that the TE and TM waves have largely indistinguishable microwave absorption and transmission spectrums.

This paper is devoted to the theory of surface waves propagating across axis of symmetry in non-uniform cylindrical metal waveguides with plasma filling. The presented results are devoted to: first, studying an influence of plasma density non-uniformity on the features of these waves; second, studying an influence of an external magnetic fields' non-uniformity on their dispersion properties; third, studying possibility to sustain gas discharge by propagation of these waves under different operating regimes. The problems have been solved both analytically and numerically. Plasma particles are described in the framework of hydrodynamics; fields of the studied waves are determined by a set of Maxwell equations. Analytical research of the obtained equations is carried out by the method of successive approximation; adequacy of such approach is proved here as well. Numerical evaluations of the possibilities to observe experimentally the phenomena, which accompany propagation of these waves, are carried out.

The generalized dispersion equation for superluminal transverse oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma with non-extensive q-distribution is derived. The analytical dispersion relation is obtained in an ultra-relativistic regime, which is related to q-parameter and temperature. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. Using the numerical method, we obtain the full dispersion curve that cannot be given by an analytic method. It is shown that the numerical solution is in good agreement with the analytical result in the long-wavelength and short-wavelength region for ultra-relativistic plasmas.

We theoretically investigate conditions for the refraction of long-wavelength dust acoustic waves by arrays of periodic cylinders in a dusty plasma. This is based on a recent analysis of the refraction of shallow water waves by periodic cylinder arrays (Hu and Chan, Phys. Rev. Lett.95 (2005), 154501). In the dusty plasma case, however, the boundary conditions involve the formation of voids around the cylinders. Possible experimental conditions are discussed.

We derive a generalized linear dispersion relation of waves in a strongly magnetized, compressible, homogeneous and isotropic quasi-neutral plasma. Starting from a two-fluid model, describing distinguishable electron and ion fluids, we obtain a six-order linear dispersion relation of magnetized waves that contains effects due to electron and ion inertia, finite plasma beta and angular dependence of phase speed. We investigate propagation characteristics of these magnetized waves in a regime where scale lengths are comparable with electron and ion inertial length scales. This regime corresponds essentially to the solar wind plasma, where length scales, comparable with ion cyclotron frequency, lead to dispersive effects. These scales in conjunction with linear waves present a great deal of challenges in understanding the high-frequency, small-scale dynamics of turbulent fluctuations in the solar wind plasma.

The backward symplectic DIII-D map and continuous symplectic analog of the map for magnetic field line trajectories in the DIII-D [10] (Luxon, J. L. and Davis, L. E. 1985 Fusion Technol.8, 441) in natural canonical coordinates are used to calculate the magnetic footprint on the outboard collector plate of the DIII-D tokamak from the field errors and internal topological noise. The equilibrium generating function for the DIII-D used in the map very accurately represents the magnetic geometry of the DIII-D. The step-size of the map is kept considerably small so that the magnetic perturbation added from symplectic discretization of the Hamiltonian equations of the magnetic field line trajectories is very small. The natural canonical coordinates allow inverting to the real physical space. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size then together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The footprint is in the form of toroidally winding helical strips. The area of footprint scales as 1st power of amplitude. The physical parameters as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near X-point for lines that strike and that do not strike differs by about four orders of magnitude. The flux loss decreases for high values of amplitude of perturbation.