Lie group point transformations applied to the one-dimensional Vlasov– Maxwell equations yield general similarity forms for the dependent and independent variables. One class of such solutions is seemingly like Bern-stein-Greene-Kruskal solutions in allowing a relatively free choice of electric field, but with a more complex time dependence. The phase trajectories of the particles are found here for both temporally damped and (possibly unphysical) growing electric fields in this class by numerical integration in the original and in transformed co-ordinates. The analysis, which includes an analytic consideration of phase-plane fixed (critical) points, shows the advantages of the new co-ordinates, and reveals qualitative features of the distribution function.

From the BBGKY equations for a pure electron plasma a derivation is made of a collision integral that includes the combined effects of particle gyration in a strong magnetic field and non-uniformities of both the distribution function and the self-consistent electric field on the collisional scale. A series expansion of the collision integral through the distribution function and the electric field on the collisional scale is carried out to third order in derivatives of the distribution function and to second order in derivatives of the electric field. For the strong-magnetic-field case when collision-term contributions to only first order in 1/B are included, a particle flux transverse to the magnetic field proportional to l/B2 is derived. The importance of long-range collective collisions in this process is shown. The result is in contrast with the classical l/B4 proportionality, and is in accordance with earlier studies.

Nonlinear regular structures in a magnetized plasma connected with drift magneto-acoustic waves (DMA) are investigated theoretically. Three-dimensional nonlinear equations of weakly dispersive DMA waves are obtained. These equations contain both the scalar nonlinearity and the vector one, and generalize the two-dimensional Kadomtsev–Petviashvili (KP) equation. The existence is shown of regular stationary structures due to the scalar nonlinearity: one-dimensional solitons, two-dimensional rational solitons, chains of solitons and so-called ‘crosses’. The stability of one-dimensional DMA solitons is investigated. It is shown that soliton stability depends on the sign of the wave dispersion as in the case of systems described by the KP-type equation.

The set of hydrodynamic equations for the ion component of a magnetized low-pressure plasma, including the nonlinear ion drift and waves related to it, taking into account dispersion effects of order k2⊥ρ2i (k⊥is the characteristic transverse wavenumber and ρi is the ion Larmor radius), is obtained. The reduction of these equations using the standard assumptions of vortex theory is given. The problem of the integrals of motion of the simplified equations is discussed. Account is taken of the gravitational force (which models curvature of the magnetic field lines), the three-dimensionality of the perturbations (drift-Alfvén effects) and plasma rotation. It is suggested that the ion-drift hydrodynamics discussed here should be the basis for the analysis of the ion drift and the vortices related to it, as well as for the theory of decay processes with participation of the ion-drift waves.

The problem of vortices of ion-drift and related flute-drift, balloon-drift and drift-Alfvén waves is analysed, taking into account the finiteness of the Larmor radius of the ions. It is shown that the structure of the stationary ion-drift vortices is similar to that of the Alfvén waves. It is found that the stationary ion-drift vortices in a plasma confined in a curvilinear magnetic field are characterized, generally speaking, by two different spatial scales. The role of plasma rotation in the vortex problem is investigated.

The problem of envelope solitons of surface waves is considered on the basis of results for the nonlinear dispersion relation of the waves in a plasma column. The soliton solutions are derived as particular cases of the general solutions obtained by a universal procedure and expressed in terms of Jacobi elliptic functions. Since the two types of interactions, namely the (ω + ω) – ω and the (ω – ω) + ω interactions (where ω is the frequency of the carrier wave) included in the nonlinear dispersion relation act in opposite ways, existence both of bright and dark solitons is shown to be possible. The effect of the ponderomotive force that in our case is expressed through the contribution of the (ω – ω) + ω interaction leads to the formation of dark solitons. The effect of the losses is also considered.

The two-dimensional Korteweg-de Vries equation is first derived for a weakly relativistic ion acoustic wave propagating in a collisionless plasma. We show that the relativistic effect greatly influences the phase velocity, the amplitude and the width of a solitary wave solution, and that the presence of streaming ions gives rise to the formation of a precursor. We also discuss three limiting cases of the present results.

Time-integrated measurements have been made of three-half harmonic light energy emitted from 0·26 μm laser-produced plasmas. The main results are the experimental dependence of 3/2ω0 conversion efficiency and threshold on electron density-profile shape. Various density profiles are achieved by irradiating different kinds of target; their shapes are estimated with the help of two-dimensional hydrodynamic simulations.

Nonlinear decay of large-amplitude ordinary and extraordinary electromagnetic waves into an electrostatic upper-hybrid wave and a slow shear Alfvén wave in a low-β plasma is considered. Expressions for the growth rates and thresholds are obtained. Applications of this investigation to both space and laboratory plasmas are pointed out.

Propagation of nonlinear ion acoustic waves in a multi-component plasma with negative ions is investigated in a double-plasma device. When the density of negative ions is larger than a critical value, a broad negative pulse evolves to rarefactive solitons, and a positive pulse whose amplitude is less than a certain threshold value becomes a subsonic wave train. In the same plasma, a positive pulse whose amplitude is larger than the threshold develops into a solitary wave. The critical amplitude is measured as a function of the density of negative ions and compared with predictions of the pseudo-potential method. The energy distribution of electrons in the solitary wave is also measured.

A kinetic theory for nonlinear processes involving Langmuir waves, developed in an earlier paper, is extended through consideration of three aspects of the temporal evolution, (i) Following Falk & Tsytovich (1975). the dynamic equation for the rate of change of one amplitude at t is expressed as an integral over T of the product of two amplitudes at t – T and a kernel functionf(T); two generalizations of Falk & Tsytovich's form (f(T) ∝ T) that satisfy the requirement f(∞) = 0 are identified, (ii) It is shown that the low-frequency or beat disturbance may be described in terms of fluctuations in the electron number density, and that its time evolution involves an operator that is essentially the inverse of f(t). (iii) The transition from oscillatory evolution in the reactive or ‘coherent-wave’ version of the three-wave instability to the secular evolution of the resistive or ‘random-phase’ version is discussed qualitatively.

A new approach to the theoretical study of turbulent behaviour of a collisionless plasma is developed. This approach is based upon the concept or probability maximization originally applied to collisional gases by Boltzmann. The probability-maximization theory deals with stochastic processes in a steady turbulent plasma by solving for the most-probable distribution. Our theory as applied to counter-streaming electron beams can quantitatively predict beam retardation, i.e. a decrease in the mean velocity of electrons injected from the system boundary. This is also in agreement with the results of a one-dimensional numerical experiment performed for such a beam-plasma system.

The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for P⊥ > P∥ and large β⊥