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.

We investigate strictly non-relativistic thermal effects on the dispersion of lefthanded (LH) ion cyclotron waves (ICW's) with real frequency and complex wave vector, propagating parallel to a uniform ambient magnetic field. Changes to the topology of the cold-plasma dispersion relations in the vicinity of the ion gyrofrequencies are studied in plasmas consisting predominantly of protons with a small admixture of a heavy ion. The two branches of the LH mode reconnect near the heavy-ion gyrofrequency as the heavy-ion temperature is increased or its relative density is reduced. The reconnection results in one mode in which waves can propagate at all frequencies below the proton gyrofrequency and another which allows propagation only in a narrow frequency range extending upwards from the cut-off frequency to a regime where strong damping occurs. The topology of the reconnected dispersion curves is quite different from that seen in the real wave vector – complex frequency case. This work is relevant to theories of ion heating and acceleration in multi-ion plasmas as are found in the solar wind, in solar and stellar flares, and in the Earth's magnetosphere. In particular, strongly species-dependent heating and acceleration can arise from wave–particle interactions between the various ionic species, and ICW's at frequencies near the respective ion gyrofrequencies. These interactions depend critically on the wave dispersion.

The application of Hamilton's principle to the problem of the determination of the structure of low free energy state plasmoids is discussed. It is shown that Clebsch representations of the vector fields and representations involving side conditions on the functional result in the same sets of Euler–Lagrange equations. The relationship of these representations to the problem of containment forces in vortex structures (plasmoids) is considered. It is demonstrated that the lowest free energy state of an incompressible plasma is always Lorentz force and Magnus force free. For a compressible plasma obeying the adiabatic gas laws, the Magnus force is finite. Introduction of conservation of angular momentum as an additional side condition also results in finite containment forces.

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.

It is shown that, in the hydrodynamic approximation, the spontaneous generated magnetic field does not act directly on the development of Langmuir plasma turbulence. It is shown that besides the magneto-modulational effects, it is necessary to take into account the purely relativistic effect, i.e. the dependence of the electron mass on velocity. In most cases the contribution of this relativistic effect prevails over the spontaneous magnetic field contribution to the development of the modulational instability of HF waves.

An asymptotic expression for the dielectric tensor e of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of ε into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as O·l% for a typical case.

The development of the modulational instability of a whistler wave is investigated in the linear and subsequent nonlinear stages. It is shown that some predictions of the linear theory remain valid up to the tirne when the wave amplitude modulation rate is of the order of unity.

A general solution condition for collisionless sheaths is developed. Previous work has assumed that the Bohm criterion or the generalized Bohm criterion ensures a self-consistent sheath solution. This paper shows that for nonmonotonic collisionless sheath structures, such as double sheaths containing trapped ions, the generalized Bohm criterion is a necessary but not a sufficient condition. The general solution condition developed is always sufficient and the generalized Bohm criterion is shown to be special case of it. The general solution condition is applied to a double emitter sheath containing trapped ions. First, it is shown that the low-energy part of the plasma ion distribution coming into the sheath cannot be neglected as claimed in some analyses, because the shift in mean ion velocity through the pre-sheath (generalized Bohm speed) depends strongly on low-energy ions. Second, it is shown that the presence of trapped ions moves the point of critical self-consistency away from the collisionless sheath-neutral plasma asymptotic match and into the collisionless sheath. Consequently, both the sheath structure and the generalized Bohm speed depend on the amount of trapped ions. Thus collisional effects may dominate the structure of a presumably collisionless sheath through the trapping mechanism and the collisional pre-sheath which determines the low-energy ion component entering the collisionless sheath.

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.

The process of parallel whistler-mode propagation in a weakly relativistic plasma is interpreted in terms of the periodic energy exchange between wave field and perturbed electron currents. The physical meaning of the thermal and relativistic corrections to the value of the refractive index of these waves in a cold plasma is considered in detail.

Accounting for an external electron current gradient, a set of nonlinear fluid equations governing the dynamics of kink instability in an inhomogeneous magnetized plasma has been derived. In the linear regime, the dispersion relation is analysed and the variation of the growth rate is graphically shown. In the nonlinear regime, it is shown that a quasi-stationary solution of the mode coupling equations can be represented as a dipolar vortex. Conditions under which the latter arises are given.

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⊥

This paper deals with the application of a Fokker–Planck code to the problem of heat conduction down steep thermal gradients. The results are compared with those obtained with other codes based on the Fokker–Planck equation in which various simplifying assumptions are made in the calculation of the Rosenbluth potentials. The particular problem considered is that of heat flow between spherical shells at different temperatures. The difference between the heat flows resulting from isotropic and anisotropic distributions is specially emphasized. The results show that, for calculating temperature, the usual Legendre polynomial expansion for the angular dependence of the distribution function gives reasonable results even when it is limited to two terms. However, the heat fluxes can differ by a factor of two when the Rosenbluth potentials are calculated from angular averages of the distribution function even when in the rest of the calculation the Legendre expansion is retained to all orders.