A rigorous and most general covariant kinetic formalism is developed to study the nonlinear-wave interaction in relativistic Vlasov plasmas. The typical nonlinear plasma reaction is a nonlinear current measured by the nonlinear plasma conductivity, and these quantities are derived here on the basis of relativistic Vlasov–Maxwell equations. Knowing the nonlinear plasma conductivity allows us to determine all plasma modes nonlinearly excited in plasma. The general covariant form of nonlinear conductivity is provided first for any value of plasma temperature and for the whole complex frequency plane by a correct analytical continuation. The further analysis is restricted to a correct relativistic particle distribution, which is vanishing for particle speeds greater than the speed of light. In the limit of non-relativistic plasma temperatures, the covariant nonlinear conductivity is significantly different from the standard non-covariant non-relativistic results, which are reached only in the formal limit of an infinitely large speed of light $c \to \infty$.

The coupling of shear and fast Alfvén waves in the vicinity of a magnetic X-point is studied for the case in which a weak longitudinal guide field $B_{z0}$ is present, with variations in the longitudinal direction and plasma pressure effects neglected. It is shown that an analytical solution for the shear wave in the limit of ideal magnetohydrodynamics (MHD) and $B_{z0}\,{=}\,0$ exhibits phase mixing and equilibration of the field and kinetic energy at a rate that increases with the spatial extent of the initial disturbance. Equations describing perturbatively the pumping of fast waves by shear waves in the presence of finite $B_{z0}$ are derived and solved numerically, taking into account resistivity and electron inertial effects. It is shown that shear wave energy is most rapidly and efficiently converted to plasma kinetic energy when the collisionless skin depth exceeds the resistive scale length. The conversion of incompressible MHD modes to compressible modes at X-points provides a possible mechanism for solar coronal heating, and mode conversion processes of this type are also likely to occur in tokamak plasmas with X-points.

We report here on the expansion dynamics of a non-equilibrium plasma produced by an excimer laser interaction with a Cu solid target. Its characteristics were investigated in the fast and slow time regime by two Faraday cups of different diameter. The larger cup had an 8 cm diameter collector and was fixed along a drift tube at a distance of 20 cm from the plasma source; the smaller cup had a 3.3 cm diameter collector and was fixed transversally to the target at a distance of about 6 cm. During the experiments the target support signal was also recorded. The laser beam was focused onto the target and the spot dimensions were analysed by scanning it on the lens focal plane. An average power density on the target of 0.3 GW cm$^{-2}$ was achieved with a 15 cm focal length lens. Using signals from the Faraday cups we obtained information on the overall plasma evolution in the slow and fast time regimes. Fitting the plasma current waveform by a ‘shifted’ Maxwell–Boltzmann distribution, a Knudsen-layer temperature of $5.3 \times 10^{5}$ K ($\sim$50 eV) and a drift velocity of 5300 m s$^{-1}$ resulted. The system efficiency in ablation yield and ion production was 0.235 $\mu$g pulse$^{-1}$ and $5 \times 10^{13}$ ion pulse$^{-1}$, respectively.

Collisionless time evolutions of geodesic acoustic modes (GAMs) in tokamaks are investigated by the gyrokinetic theory and simulation. It is shown that the collisionless damping of the GAM oscillations is enhanced when the ratio of the typical drift orbit width of passing ions to the radial wavelength of the zonal flow increases.

SPECTOR3D is a magnetohydrodynamic (MHD) code designed to study the resistive stability and mode spectrum of stellarators. It finds the spectrum of the linearized, compressible, resistive MHD equations. Some typical results are given for a tokamak model with toroidal field ripple and a 17-period Heliotron.

We investigate the steepening of the magnetic fluctuation power law spectra observed in the inner Solar wind for frequencies higher than 0.5 Hz. This high frequency part of the spectrum may be attributed to dispersive nonlinear processes. In that context, the long-time behavior of weakly interacting waves is examined in the framework of three-dimensional incompressible Hall magnetohydrodynamic (MHD) turbulence. The Hall term added to the standard MHD equations makes the Alfvén waves dispersive and circularly polarized. We introduce the generalized Elsässer variables and, using a complex helicity decomposition, we derive for three-wave interaction processes the general wave kinetic equations; they describe the nonlinear dynamics of Alfvén, whistler and ion cyclotron wave turbulence in the presence of a strong uniform magnetic field $B_0 \^{e}_{\Vert}$. Hall MHD turbulence is characterized by anisotropies of different strength: (i) for wavenumbers $\textit{kd}_{\rm i}\,{\gg}\,1$ ($d_{\rm i}$ is the ion inertial length) nonlinear transfers are essentially in the direction perpendicular ($\perp$) to ${\bf B}_0$; (ii) for $\textit{kd}_{\rm i}\,{\ll}\,1$ nonlinear transfers are exclusively in the perpendicular direction; (iii) for $\textit{kd}_{\rm i} \sim 1$, a moderate anisotropy is predicted. We show that electron and standard MHD turbulence can be seen as two frequency limits of the present theory but the standard MHD limit is singular; additionally, we analyze in detail the ion MHD turbulence limit. Exact power law solutions of the master wave kinetic equations are given in the small- and large-scale limits for which we have, respectively, the total energy spectra $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-5/2} |k_{\Vert}|^{-1/2}$ and $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-2}$. An anisotropic phenomenology is developed to describe continuously the different scaling laws of the energy spectrum; one predicts $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-2} |k_{\Vert}|^{-1/2} (1+k_{\perp}^2d_{\rm i}^2)^{-1/4}$. Non-local interactions between Alfvén, whistler and ion cyclotron waves are investigated; a non-trivial dynamics exists only when a discrepancy from the equipartition between the large-scale kinetic and magnetic energies happens.

The surface dust-acoustic wave is investigated in a semi-bounded dusty plasma containing elongated and rotating dust grains. The dispersion relation of the low-frequency surface ion plasma wave is obtained by the plasma dielectric function with the specular reflection boundary condition. The results show that the phase and group velocities of the surface dust-acoustic wave propagating along the plasma–vacuum interface decrease with an increase of the rotation frequency. However, for long wavelengths it is found that the phase and group velocities of the surface wave are independent of the magnitude of the rotation frequency.

The Korteweg–de Varies–Zakharov–Kuznetsov (KdV–ZK) equation describes the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external magnetic field in a non-thermal plasma consisting of warm adiabatic ions. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion-acoustic wave is described by a modified KdV–ZK (MKdV–ZK) equation. A combined MKdV–KdV–ZK equation more efficiently describes the nonlinear behaviour of ion-acoustic waves at points in the neighbourhood of the curve in the parametric plane along which the coefficient of the nonlinear term of the KdV–ZK equation vanishes. This combined MKdV–KdV–ZK equation admits both double-layer and alternative solitary-wave solutions having profile different from sech$^{2}$ or sech. In this paper the three-dimensional stability of the alternative solitary-wave solution having profile different from sech$^{2}$ or sech has been investigated by the recently developed multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of instability have been derived at the lowest order. The correct expression of the growth rate of instability at the lowest order has been obtained for a limiting case and the stability analysis has been carried out numerically from our model as presented in this paper for arbitrary values of the parameters involved in the system.

The adaptive nonlinear filtering approach for shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows adopted in our previous work is employed in conjunction with compact high-order methods as the spatial base scheme. The objective is to compare the performance of nonlinear filtering in compact high-order schemes with nonlinear filtering in standard central (non-compact) schemes for multiscale problems containing shock waves.

The parametric excitation of large-scale convective cells in non-uniform dusty plasmas with non-zero ion temperature is considered. A set of two coupled nonlinear equations (for the variation of the electrostatic potential and the ion pressure) governing the nonlinear dynamics of ion-drift waves in dusty plasmas (IDWDPs) is obtained. The equations are then simplified by using a standard multiscale expansion technique. A nonlinear dispersion relation, which describes the nonlinear electrostatic and thermal convective cells, is obtained. The analysis of our dispersion relation shows that only the electrostatic mode yields a non-zero growth rate. The thermal convective cell is found to be stable. A simple expression for the maximum instability growth rate and the optimal dimension of the convective mode is deduced. The fastest growing wave appears to be a zero-frequency mode, elongated perpendicularly to the plasma inhomogeneity. The electrostatic convective cell growth rate is compared with that for the traditional parametric IDWDP decay.

The influence of self-generated magnetic and electric fields on the transport of relativistic electrons in dense plasmas was studied using a particle-in-cell simulation. For conditions relevant to the fast ignitor, the laser-driven relativistic electrons may have significant energy spread along or perpendicular to the propagation direction of the beams. The effect of electron energy spread on the growth rate, the occurrence threshold of both the Weibel-like filamentation instability and the electrostatic two-stream instability and the competition between them were investigated. The Weibel instability results in the formation of a magnetic channel, which may collimate inward fast electrons without significant deviation, and the excitation of a longitudinal electric field due to two-stream instability is destructive to the stability of the magnetic channel. The generation of relativistic electrons by the interaction of a high-intensity laser beam at the vacuum–dense plasma boundary and propagation of the electrons in the dense plasma were studied using a three-dimensional particle-in-cell code. It is shown that the electron velocity spread owing to transverse collective heating saturates the magnetic field and the longitudinal electrostatic field may play a dominant role in limiting the stable propagation of fast electrons into over-dense plasmas.

We have developed a glassless stereoscopic visualization system for the real-time numerical simulator of the interplanetary space–magnetosphere– ionosphere coupling system, adopting the three-dimensional (3D) magnetohydrodynamical (MHD) simulation code. Our real-time Earth's magnetosphere simulator numerically reproduces the global response of the magnetosphere and the ionosphere at the same time with the real world by using the real-time Solar wind data, and has shown two-dimensional (2D) figures of the global magnetosphere of about 1 hour in advance in virtual reality at every minute on Web since November 2003. We implemented 3D graphical techniques such as volume and iso-surface rendering for visualizing scalar variables and also colored 3D streamlines for representing the magnetic field for standard and glassless stereo-displays. A real-time interpolation method mapping the simulated data to structured uniform rectilinear grids commonly utilized in computer graphics was developed, so that this 3D visualization system is capable of monitoring the real-time Earth's magnetosphere simulated data in on-line mode.

In most practical situations, for multi-component non-ideal complex plasma mixtures in pressure–temperature ($P$–$T$) phase space, the problem of solving the system of coupled nonlinear Saha equations subjected to the constraints of electro-neutrality and conservation of nuclei is found to be effectively a one-dimensional nonlinear problem, i.e. solving a single transcendental equation. Computation of ionization stages and partition functions in the $P$–$T$ phase space is particularly important for non-ideal plasmas generated in devices in which pressure is a reliably measurable parameter while it is difficult to measure the number density of heavy particles. The methodology and algorithm presented herein are based on deriving an equivalent single transcendental equation, for which the solution is eminently trivial. The algorithm takes into account different practical models for non-ideality corrections (lowering of ionization potentials, truncation of partition functions and a corrected equation of state). The ease and efficiency of the introduced algorithm allows, with significant simplicity, the computations of population densities of all plasma species (ionized and excited) up to maximum ionization states equal to the atomic numbers of the involved elements with minimal computational work. It also considers an extensive database of energy levels of the excited states. The algorithm presented herein is analytically known to be safe, fast and efficient. It shows no numerical instabilities, no convergence problems and no accuracy limitations or lack of change problems, which have been reported in the literature. A couple of non-trivial problems are worked out and presented herein showing the effectiveness of the present methodology. For completeness, a criterion for the validity of the assumption of local thermodynamic equilibrium (LTE) is applied to the results from the sample problems, showing the regions of the pressure–temperature phase space over which the assumption is valid.

We have developed a parallel rendering software for scientific visualization of large-scale, three-dimensional, time development simulations. The goal of this software, MovieMaker, is to generate a movie, or a series of visualization images from one terabyte-scale data set within one night (or less than 12 h). The isocontouring, volume rendering, and streamlines are implemented. MovieMaker is a parallel program for the shared memory architecture with dynamic load balancing and overlapped disk I/O.

Two methods for identifying the flux of high-energy photons as emitted by ball lightning are proposed. It is assumed that ball lightning has a core consisting of oscillating clouds of electrons and totally ionized ions. A search for tooth enamel changes due to the influence of high-energy photons from ball lightning to reveal the influence of such photons on human beings is also proposed. This diagnostic measure should be taken if after observation of ball lightning symptoms similar to those of radiation sickness arise or ball lightning causes heavy burns.

A parallel three-dimensional electrostatic particle-in-cell Monte Carlo Collision (PIC–MCC) code using an unstructured tetrahedral mesh is developed and validated in this paper. Poisson's equation is discretized by a nodal finite element method using a linear interpolation function. Charged-particle motion is traced cell by cell using a leap-frog method and the Boris scheme. Code is validated using quasi-one-dimensional radiofrequency gas discharge by observing the bi-Maxwellian electron energy probability distribution function at low pressure. Parallel performance of the PIC code is tested using a three-dimensional radiofrequency gas discharge on a PC-cluster system. Results show that parallel efficiency of 83% can be achieved at 32 processors with dynamic domain decomposition.

The classical Pierce model consists of a one-dimensional plasma-filled diode into which a monoenergetic electron beam is injected. Particle-in-cell (PIC) simulations are performed with the BIT1 code, involving a large number of superparticles. The evolution of slightly perturbed uniform equilibria into the related nonlinear attractor states for a broad range of $\alpha$ values, where $\alpha\,=\,\omega_{{\rm pe}}d/u_0$ is the diode control parameter, is investigated. A period-doubling route to chaos in the classical Pierce diode for $\alpha$ slightly below $5\pi$ is analyzed in detail.

Particle-in-cell simulations with full dynamics ions and drift kinetic electrons are essential tools to model kinetic instabilities in strongly magnetized plasmas. In these guiding center models, parallel acceleration of the electrons is retained while their perpendicular velocity is given to lowest order by the ${\bf E} \times{\bf B}$ drift. These simulations are applied to a study of the electrostatic stability of energetic velocity-space ion shells observed in the Earth's plasma sheet boundary layer by the Cluster satellites.

We study numerically the role of mode coupling mechanisms in the generation and growth of sideband modes, during the long time evolution of the nonlinear Landau damping of a large-amplitude wave. The results suggest that a rich variety of wave coupling mechanisms develops during the evolution of the system.

The characteristic features of a two-sign point vortex system in positive and negative temperature states are examined by massive numerical simulations using MDGRAPE-2. The temperature is determined by a density of states for a microcanonical ensemble consisting of randomly generated $10^7$ states. Since the density of states has a single peak, the system has negative temperature states. The distributions of vortices in time-asymptotic equilibrium states in positive and negative temperature are obtained by time-development simulations. In positive temperature, both-sign vortices mix with each other and neutralize. In negative temperature, part of the vortices condense and form clumps exclusively consisting of the same-sign vortices, while the other part of the vortices distribute uniformly outside the clumps. It is found that the vortices inside the clumps gain energy and the vortices outside the clumps lose energy to keep the total energy constant. This suggests the common and essential role of the background vortices in the energy-conserving system that assists the formation of the clumps as well as the crystallization and generation of the symmetric configuration observed in the non-neutral plasma experiments.