Heavy ions frequently appear as minor components in space plasmas, for example as charged helium in the solar wind and heavy ions in the vicinity of comets. Both the different components of ions and the associated plasma waves are observed by extraterrestrial in situ measurements. These plasma waves appear as large-amplitude magnetic field fluctuations in space plasmas. They must be described appropriately by means of multifluid equations. Because of the nonlinear nature of these waves, we here investigate nonlinear waves in multi-ion plasmas. Solitary waves that can only exist in a magnetized bi-ion plasma are presented. We employ a perturbation theory at the linear solution of a left-hand circularly polarized, low-frequency (below the proton gyrofrequency) plasma wave and take only the first nonlinear terms into account. Thus the multifluid equations are reduced to a single equation of the type of a nonlinear Schrödinger equation. The derived soliton solution is valid for magnetic field amplitudes lower than 10% of the ambient unperturbed magnetic field. The solutions are discussed for plasma parameters that are typical of the solar wind. A density enhancement can be observed within the soliton, where the helium ion density is more enhanced than the proton density.

The three-dimensional particle-in-cell (PIC) code VLPL (Virtual Laser Plasma Lab) allows, for the first time, direct fully electromagnetic simulations of relativistic laser–plasma interactions. Physical results on relativistic self-focusing in under-dense plasma are presented. It is shown that background plasma electrons are accelerated to multi-MeV energies and 104 T magnetic fields are generated in the process of self-focusing at high laser intensities. This physics is crucial for the fast ignitor concept in inertial confinement fusion. Advances in the numerical PIC algorithm used in the code VLPL are reviewed here.

A kinetic analysis of the electrostatic dust cyclotron instability in a weakly ionized collisional dusty plasma is presented. In a plasma with negatively charged dust and a current along the magnetic field B, it is found that the instability can be excited by ions drifting along B. The effect of dust–neutral collisions is stabilizing, while the effect of ion–neutral collisions can be destabilizing. Possible applications to laboratory environments are discussed.

The spectrum of incompressible waves and instabilities of two-dimensional plasma geometries with background flow is calculated. The equilibrium is solved numerically by the recently developed program FLow Equilibrium Solver (FLES). The spectra of the equilibria are computed by means of another new program, the INcompressible 2-dimensional FLow Eigenvalue Solver (IN2FLES). Magnetic instabilities and instabilities driven by the two-dimensionality and the flow are found. For linear equilibria, the eigenvalues for elliptical geometries remain close to the curves on which the eigenvalues for circular geometries lie. These curves may be found for unbounded domains by a calculation in Fourier space [see Lifschitz, A. In: Proceedings of 1995 International Workshop on Operator Theory and Applications (ed. R. Mennicken and C. Tretter), pp. 97–117, Birkhäuser, Boston, 1998]. Here the relation between a new continuous spectrum of unbounded domains and the discrete spectrum of bounded domains is investigated. Finally, it is found that the two-dimensionality and the background flow may lead to an overstable cluster-point.

The structure of magnetosonic perturbations around a pair of X lines of a toroidal magnetic configuration is analysed in the framework of ideal MHD, by means of a WKB technique. The conditions for wave trapping are investigated. It is shown that the wave equation for the displacement is separable in the vicinity of the X lines. The relevant eigenvalues and the different types of ray trajectories are discussed.

This work shows creation of phase-space holes when an initially perturbed plasma evolves in time, in the absence of external magnetic fields. When such a field is applied to the plasma ab initio, these structures are not created. If such hole structures are created with the magnetic field turned off, the holes are destroyed under the influence of a magnetic field when one is applied to the plasma.

This paper is concerned with one-dimensional and time-dependent multifluid plasma models derived from multifluid MHD equations. In order to reduce the number of equations to be solved, the impurities are described in the framework of the average ion approach without restricting the impurity densities to be small compared with the hydrogen plasma density. Equalizing the plasma temperatures and adopting the condition of quasineutrality, we arrive at a three-fluid description of a current-carrying plasma, and analyse the ability of the self-consistent system of model equations thus obtained to support stationary solutions in a moving frame. This system is reduced to a currentless plasma description assuming at first different flow velocities of the particles and then a currentless, streaming plasma where all particles move with the same velocity. Introducing Lagrangian coordinates and adopting an equation of state, a single reaction–diffusion equation (RDE) for the temperature is obtained. The impurity density, which affects the radiation loss term and the heat conduction coefficient of the RDE, has to be calculated as a function of the temperature by solving additionally a first-order differential equation. This is demonstrated for carbon and high-Z impurities.

We describe the parallel implementation of semi-Lagrangian Vlasov solvers, which are an alternative to particle-in-cell (PIC) simulations for the numerical investigation of the behaviour of charged particles in their self-consistent electromagnetic fields. The semi-Lagrangian method, which couples the Lagrangian and Eulerian points of view, is particularly interesting on parallel computers, since the solution is computed on grid points, the number of which remains constant in time on each processor, unlike the number of particles in PIC simulations, and thus greatly simplifies the parallelization process.

The nonlinear interaction between four electrostatic waves in a plasma media is investigated analytically in the presence of linear damping or growth and also frequency mismatch, using a nonlinear perturbation method. Depending on the various initial conditions of the wave amplitudes, solutions of different types are discussed.

The nonlinear plasma dielectric function due to relativistic electron motion is derived. From this, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing in comparison with ponderomotive non-relativistic self-focusing at very high laser intensities. When the laser intensity is very high, ponderomotive self-focusing will be dominant. However, at some point, when the oscillating velocity of the plasma electrons becomes very large, relativistic effects will also play a role in self-focusing.

F. Osman, R. Castillo and H. Hora, Relativistic and ponderomotive self-focusing at laser–plasma interaction [J. Plasma Phys.61 (2), 263–273 (1999)] There was a typesetting mistake in the title of this paper. The correct title is as above. We apologize for this error.

The transition phase between two nonlinear regimes of electron-beam–wave interaction depending on the amplitude and the nature of the effective dissipation is investigated with the help of numerical simulations. Effective dissipation due to wave escaping to infinity out of the beam–wave interaction region as well as to collisions in the background plasma is considered. If the dissipation is strong enough, the evolution of the electron beam proceeds in a general way, independently of the type of dissipation and of the nature of the considered waves: structures of strongly concentrated electron bunches are formed. These bunches are not trapped in the wave, and decelerate continuously owing to friction on waves: in the presence of dissipation, the usual quasiperiodic exchange of energy between the wave and the trapped particles, which prevents the wave from collapsing, does not occur. Considering beam interaction with a finite number of waves (modulated wave packet), it is shown that, if the dissipation is strong enough, the structure of electron bunches is dynamically stable in a range of times exceeding several characteristic times of their formation.

Laser-beam or soliton propagation is best modelled for fast computation using a split-step Fourier method based on an orthogonal transform technique known as the beam-propagation method. The beam-propagation split-step Fourier-transform technique in one and two dimensions for the propagation of a soliton or laser beam respectively in a nonlinear plasma and a split-step Hankel-transform-based algorithm for cylindrical-beam propagation close to circular cross-sectional symmetry and its computational implementation are discussed. Attention is particularly focused on the verification of the paraxial approximations of the soliton or the laser beam using these techniques, after a brief review of the beam-propagation method.

The dynamics and thermonuclear fusion parameters of a spinning gas-puff staged pinch are investigated by considering a DT-fibre plasma seeded with a Kr impurity. The effects of anomalous heating, line radiations from Kr, α-heating and radiative collapse are studied for different spin velocities Ω0, keeping the spin coupling parameter f0 (=0.1) fixed. Numerical results indicate that the choice of Ω0 is highly critical. Large values of the spin velocities although provide stabilization against the R–T instability in the final stage of compression, but causes an adverse reduction in the values of the plasma parameters that are essential to achieve controlled fusion. Our analysis suggests that a judicious choice of spin velocity can provide the desired temperature and density when we seed a DT-fibre plasma with a small fraction of Kr impurity to initiate radiative collapse.

The Langevin approach to the kinetics of a collisional plasma is developed. Some collision models are considered, and the corresponding stochastic differential equations are derived. These equations can be regarded as an alternative to the description of a plasma in terms of a distribution function. The method developed here allows one to simulate plasma processes, taking account of both collective kinetics effects and Coulomb collisions. Results of the numerical simulation of the intervention of laser pulses with an overdense plasma are presented. The dependence of the absorption coefficient on the plasma parameters is calculated. The features of the plasma dynamics under the action of intense laser radiation are observed and discussed. The results of numerical tests of the validity of this method are also presented.

Multiple-scales perturbation methods are used to study wave interactions in magnetohydrodynamics (MHD), in one Cartesian space dimension, with application to cosmic-ray-modified shocks. In particular, the problem of the propagation and interaction of short wavelength MHD waves, in a large-scale background flow, modified by cosmic rays is studied. The wave interaction equations consist of seven coupled evolution equations for the backward and forward Alfvén waves, the backward and forward fast and slow magnetoacoustic waves and the entropy wave. In the linear wave regime, the waves are coupled by wave mixing due to gradients in the background flow, cosmic-ray squeezing instability effects, and damping due to the diffusing cosmic rays. In the most general case, the evolution equations also contain nonlinear wave interaction terms due to Burgers self wave steepening for the magnetoacoustic modes, resonant three wave interactions, and mean wave field interaction terms. The form of the wave interaction equations in the ideal MHD case is also discussed. Numerical simulations of the fully nonlinear cosmic ray MHD model equations are compared with spectral code solutions of the linear wave interaction equations for the case of perpendicular, cosmic-ray-modified shocks. The solutions are used to illustrate how the different wave modes can be generated by wave mixing, and the modification of the cosmic ray squeezing instability due to wave interactions. It is shown that the Alfvén waves are coupled to the magnetoacoustic and entropy waves due to linear wave mixing, only in background flows with non-zero field aligned electric current and/or vorticity (i.e. if B·∇×B≠0 and/or B·∇×u≠0, where B and u are the magnetic field induction and fluid velocity respectively).

Calculations are presented on the phenomenon of plasma–sheath resonance in an inhomogeneous plasma. In certain cases, this resonance coincides with a local resonance occurring in the plasma, the local plasma frequency being equal to the resonant frequency of the entire system. The theory does not describe the mechanism of absorption, but does predict the magnitude of the power involved. Some limitations of the theory are discussed.

Fluid descriptions of plasmas, which are usually applied to a collisional plasma, can only be justified for very small Coulomb Knudsen numbers. However, the scrape-off layer (SOL) plasmas of experimental magnetic confinement fusion devices tend to have operational regimes characterized by a Coulomb Knudsen number around 0.1. In interesting detached regimes of an SOL plasma in a tokamak, when the plasma detaches from the limiters or divertors, this number may increase along with the local plasma gradients. Plasma gradients are also known to increase (and thus drive non-local effects) in inertial confinement fusion. Neutrals, which are being produced owing to plasma recombination at the plasma–divertor interface, may be in a mixed collisional regime as well. Thus simultaneous kinetic treatments of plasma and neutral particles with self-consistent evaluation of boundary conditions at the material walls are required. We present a physical model and a numerical scheme, and discuss results of purely kinetic simulations of plasmas and neutrals for actual conditions in the Alcator C-Mod and Tokamak-de-Varennes experimental tokamaks. Results for both steady-state and transient regimes of SOL plasma flow are presented. Our approach, unlike particle-in-cell and Monte Carlo methods, is free from statistical noise.

The relativistic expressions for the dielectric-tensor elements can be expressed as a double integral over both parallel and perpendicular momenta. The anti-Hermitian (damping) parts can be integrated over a delta function for either one of these two momenta, leaving a single integral over the other momentum variable. We review these expressions for either integration option, and compare them with statements in the literature. We give the limits on the remaining integral explicitly, for all positive or negative values of the parallel refractive index, whose magnitude can be less or greater than one. This single-integral form can be applied to electron cyclotron harmonic damping for any distorted electron momentum distribution function. As an example, we recover the results for a Maxwellian distribution. We also provide approximate results when the distribution function can be taken as a Maxwellian only in the perpendicular-momentum direction. A computer program will be written for a distribution function subjected to distortion by both electron cyclotron and lower-hybrid waves.

Externally amplitude-modulated ion acoustic waves with high frequencies of 200–320 kHz are experimentally shown to form plasma cavities and to be trapped in them at an early stage. Thereafter, the trapped waves are observed to suffer nonlinear modulation and create new lower-frequency waves with average frequencies as low as 20–40 kHz within the cavities. As a result, the externally excited high-frequency ion acoustic waves are found to be nonlinearly converted into lower-frequency ion waves in the cavities. Finally, the pressure gradients of the waves effective in cavity formation and nonlinear modulation of the trapped waves are discussed.