A kinetic analysis is made of a reacting plasma dominated by three-body recombination and ionization, together with collisional and radiative excitation and de-excitation of atomic states. The plasma includes excited atoms, ions, electrons and photons. The kinetic theory yields rate equations for these species, together with explicit expressions for relevant rate coefficients. In the limit of spatial homogeneity and assuming atom and electron densities are close to equilibrium, an explicit form is obtained for the radiation absorption coefficient per unit length. A criterion is then constructed for population inversion. Application to a helium-like active medium (e.g. Al+11) and hydrogen-like passive medium (e.g. A1+12), at electron temperature of 300 eV, reveals that population inversion ensues at electron densities in excess of 1020 cm−3. Algebraic solution of atomic state rate equations demonstrates that the absorption coefficient grows insensitive to photon-atom interactions with increasing electron density.

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ = 0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

Using ideal, one-dimensional MHD equations, numerical and analytic solutions are presented which describe the nonlinear behaviour of an imploding current sheet in a low-fl plasma. Initially the current density is uniformly distributed in asheet of finite thickness, and the Lorentz force tending to pinch the plasma together is unopposed by any fluid pressure force. As the implosion develops the current density in the sheet is concentrated into a thin layer at the centre of the sheet, and both the current density and the current in this layer become infinite in a finite time if β = 0. At the moment this occurs, fast-mode shocks are produced which propagate outward from the centre of the current sheet, and as the shocks move away an infinitely thin current sheet is left behind. Although the solutions are related to electric discharges, they are also closely related to a problem posed by Dungey concerning the evolution of a uniformly distributed current in the vicinity of an X-type magnetic neutral line. The implications of these solutions for Dungey's problemare discussed.

With respect to the propagation through a cold, unmagnetized, electron plasma of nonlinear, highly superluminous, plane waves of fixed profile, with electric vector in a fixed plane parallel to the direction of propagation, it is known that, in addition to the familiar longitudinal and quasi-transverse waves, there can also be a third periodic wave. The perturbation method by which this third wave has previously been analysed is of restricted validity, and fails to describe how the wave disappears in the approach to the small-amplitude limit, where the longitudinal and transverse waves alone survive.

The influence of a metallic wall on the velocity distribution of the neutral particles in a plasma has been experimentally determined by spectroscopic measurements of a Doppler broadened line. Typical characteristic facts of the plasma –wall interaction can be explained quantitatively by means of a one-dimensional kinetic equation, which is solved in the plasma –wall interaction region, assuming reasonable boundary conditions on the wall surface.

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

The hydrodynamic approach to a relativistic gas is studied on the basis of methods used by Chew, Goldberger & Low and by Scargle. As the result of this study, the explicit form of the energy–momentum tensor is obtained by straight-forward application of Lorentz transformation. The term corresponding to non-zero momentum density in the plasma frame of reference is included in the energy–momentum tensor. For the limiting case of small bulk velocities compared with the speed of light in vacua, the energy flux as described by non- relativistic theory is immediately recovered. For the special case of scalar pressure, the energy–momentum tensor considered by Taub and by Harris follows directly from our expression. In a small-perturbation approximation, it is possible to close the system of MHD equations. As a result the solution describing all possible wave modes is derived. This solution coincides with the solution obtained by means of the kinetic theory.

The relativistic dielectric tensor of a magnetized Maxwellian plasma is obtained in a general way, for electron cyclotron waves at arbitrary incident angle. A new expression is provided for the computation of the relativistic (Shkarofsky) dispersion functions.

Kaira & Kathuria used the method of multiple scales to develop nonlinear analysis of Rayleigh–Taylor instability of a plasma in a magnetic field. Their calculations remain valid only for wavenumbers k away from the linear cut-off value kc, and break down for wavenumbers near kc. The purpose of this paper is to treat the latter case. The solution uses the method of strained parameters. The results show the instability persists even at k = kc, despite the cut-off predicted by the linear theory.

In this paper, we have discussed the possibility of excitation of zero-frequency modes by a finite-amplitude electron-sound wave in a highly non-isothermal (Ti ≫ Te) magnetoplasma. According to our investigation, the modulational instabilities of the electron-acoustic waves may produce enhanced twodimensional vortices (convection cells) and magnetic field fluctuation. Both of them can, in turn, modify transport properties of a hot magnetoplasma.

Our results could be applicable to plasmas in the earth's magnetotail (Frank, Ackerson & Lepping 1976) or thetapinches, both of which have Ti≫Te. However, for thetapinch application, one should actually modify our results to include plasma non-uniformities. In such a situation, instead of electron-acoustic waves, one encounters ion drift waves (e.g. Shukla, Yu & Varma 1981) whose modulational instabilities can readily be studied following the procedure discussed here.

Owing to the lack of experimental data, we cannot at present verify predictions of our theory for plasmas either in space or in a laboratory. However, a typical example shows that the growth rates of both the convection cells and the magnetostatic modes are quite substantial. Hence, the phenomena discussed here may indeed appear in nature.

We are grateful to Ming Yu for many useful discussions. The work of one of us(P. K. S.) was performed under the auspices of the Sonderforschungsbereich Plasmaphysik Bochum/J ülich. One of us (H.U.R.) thanks the Deutsche Akademische Austauschdienst for the award of a fellowship.

The scattering of an ordinary electromagnetic wave into a circularly polarized wave by electron-acoustic oscillations is considered.

In this paper, we consider a parametric instability involving electron-acoustic waves which does not have a counterpart in a hot electron plasma, namely the scattering of an ordinary electromagnetic wave into a circularly polarized wave by electron-acoustic waves.

This paper is concerned with the Boltzmann collision integral for the one-particle distribution function of a test species of particle undergoing elastic collisions with particles of a second species which is in thermal equilibrium. This expression is studied as a function of the ratio of the masses of the test and host particles for the case when the test particle distribution function is isotropic in velocity space. The analysis can also be considered as referring to the zeroth-order spherical harmonic in velocity space of a general velocity distribution function. The resulting collision term, due originally to Davydov, is of Fokker–Planck form and effectively describes a diffusion in energy. The method of derivation employed here is more systematic than hitherto, and is used to calculate the first correction to the Davydov term. Differences between classical and quantum cross-sections are considered; the correction to the Davydov term is checked by means of a comparison with the exact solution of the associated eigenvalue problem for the special case of Maxwell interactions treated classically.

In the interaction of high-intensity lasers with target plasmas the transport of thermal enelgy from the region in which the radiation is absorbed, to the cold dense plasma in the interior of the target, is an issue of central importance. It is also one of great complexity and as such is still largely unresolved. Ion-acoustic turbulence, self-generated magnetic fields and the inadequacy of classical transport theory have all been widely canvassed by way of explaining the observations which show thermal transport much reduced below what would be expected from conventional arguments.

In this paper the role of ion turbulence as a flux limiter is addressed with particular regard to recent experiments in which target plasmas were irradiated by 1·06 µm neodymium laser light at irradiances of 1015W cm−2 and greater. Saturation levels of the ion-acoustic turbulence driven by a combination of a suprathermal electron current and a heat flux have been calculated on the basis of perturbed orbit theory.

The levels of turbulence are found to be markedly lower than those commonly estimated from simple trapping arguments and too low to explain the thermal flux inhibition observed in the experiments used as a basis for the model.

Using similarity methods, an investigation is made of a generalized nonlinear diffusion equation arising in plasma physics in connexion with several recently proposed models for turbulent plasma energy transport and particle diffusion.

In almost every field of physics, diffusion or transport equations of the form Ψt = Δ. (DΔΨ) play an important role. The theory of linear diffusion equations, where the diffusion constant D is independent of Ψ, has been developed to a high degree of sophistication (e.g. Carsiaw & Jaeger 1959).

The interaction of two weakly nonlinear sinusoidal ion-acoustic waves produces mainly a fundamental and a second harmonic diffraction pattern. The former is similar to the double slit pattern well known from physical optics, while it is found that the latter resembles a linear pattern generated by the superposition of three waves. The third wave is formed by mutual nonlinear interaction of the two fundamental waves. The intensity of the second harmonic pattern is modulated by the recurrence effect and it depends also on the angle between the local wave vectors.

The stability of steady flow of an N-component, warm or cold, cylindrical electrostatic plasma is considered. The plasma is immersed in a magnetic field B0(r), where r is the radial co-ordinate, which is allowed to have both axial and azimuthal components. The unperturbed quantities are allowed to be arbitrary functions of r consistent with the zero-order equations. A sufficient condition for the stability of a rotating flow to axisymmetric perturbations is obtained.

An important aspect of pre-flare current sheets in the solar atmosphere is the sudden enhancement of the effective electrical resistivity in the sheet due to the onset of a plasma micro-instability. Numerical and analytical solutions to the isothermal MHD equations are here presented that describe the evolution of a current sheet subsequent to such an enhancement in the resistivity. The solutions show that, if the initial width of the current sheet is less than the acoustic-diffusion length obtained by dividing the resistivity by the sound speed, then isomagnetic shocks are formed. These shocks propagate outward from the the centre of the current sheet and are transformed into fast-mode magneto-acoustic waves when they reach the edges of the current sheet. The fast-mode waves thus formed continue to propagate outward beyond the confines of the current sheet. In contrast to a previous study by Cheng, the present solutions demonstrate that flow speeds several times greater than the local fast-mode wave speed can be produced if the plasma beta parameter and the initial sheet width are sufficiently small. The results may be relevant to the triggering of a solar flare, as in the emerging flux model of flares.

It is shown that, under the influence of a monochromatic HF electric field (laser beam), both the electrons and the ions in a high-Z plasma reach a homogeneous and isotropic self-similar state (SSS) in which the distribution functions are of the factorized form: where W±(t) is a scaling velocity, the square of which is proportional to the effective temperature. Whereas the SSS for the electrons was known from previous work, with

it is shown here that the corresponding ion SSS exists and is characterized by a simple Maxwellian, øi ø exp (−v2). The discussion of the thermal velocities W±(t), which are obtained in analytical form, provides a transparent physical insight into the heating mechanism of the plasma by inverse bremsstrahlung absorption.

A uniformly-streaming, semi-infinite, incompressible, infinitely-conducting plasma subjected to a gravitational field is confined by a vacuum magnetic field aligned with the stream. The system is disturbed by introducing a source of external steady pressure acting on the interface between the plasma and the magnetic field. The resulting wave motion at the interface is studied by using the Fourier-transform method to determine the solution for the displacement of the interface.

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.