The nonlinear wave structures of small-amplitude ion acoustic waves in a warm plasma with adiabatic negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures) in the vicinity of the critical negative-ion density are investigated using reductive perturbation method. The basic set of equations is reduced to an evolution equation that includes quadratic and cubic nonlinearities. The effective potential of this equation agrees exactly, for small wave amplitudes, with the Sagdeev potential obtained from the original fluid equations using a pseudopotential method. This implies that the evolution equation holds not only in the vicinity of the critical negative-ion density but also in the whole range of negative-ion density under the condition of small wave amplitude.

The existence and time evolution of charge separation at a plasma edge is studied using a code in which both ions and electrons are described by gyrokinetic equations that include the finite-Larmor-radius correction and the polarization drift. The ion finite-Larmor-radius effect allows the existence of charge separation between ions and electrons, and the polarization drift, which has opposite signs for ions and electrons, has a tendency to accentuate the charge separation in a time-varying electric field. We compare our results with those previously obtained using a code in which the ions were described by using a fluid guiding-centre model, and only the electrons were treated kinetically. In particular, we present results showing excellent agreement between the two codes on the transition of the spectrum of the nonlinear solution from a turbulent spectrum to one dominated by the fundamental mode, where the energy is condensing in the lowest-k modes (inverse cascade).

The three-dimensional currentless equilibrium code, HINT is revised so that it can handle equilibria with a net toroidal current, for example the bootstrap current. The revised HINT code is applied to Large Helical Device-like equilibria with good nested flux surfaces.

The ideal magnetohydrodynamic spectrum of gravitating plane plasmas with equilibrium flow is investigated. Flow makes the spectral problem non-self-adjoint, so that the spectrum can become overstable. The criteria for cluster spectra to appear are derived analytically and both stable and unstable sides of the spectrum are examined numerically. Above certain critical values of the shear flow at the resonant surface, the gravitating interchange modes disappear. However, the local extrema of the continua can then take over the cluster spectrum.

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 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.

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.

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).

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.