The motion of electrons and ions in the self-consistent fields of a compact toroidal equilibrium maintained by means of a rotating magnetic field is studied. It is found that the particles are confined although the lines of the instantaneous magnetic field are open. The results are compared with those obtained in an earlier study of the motion of charged particles in the self-consistent fields appropriate to cylindrical plasma equilibrium maintained by means of rotating magnetic fields.

A two-dimensional model of a magnetic flux tube confined in a gravitational stratified atmosphere is discussed. The magnetic field in the flux tube is assumed to be force-free. By using the approximation of large scale height, the problem of a free boundary with nonlinear conditions may be reduced to one involving a fixed boundary. The two-dimensional features are obtained by applying the perturbation method and adopting the Lüst–Schlüter model as the basic state. The results show that the configuration of a flux tube confined in a gravitational stratified atmosphere is divergent, and the more twisted the magnetic field, the more divergent is the flux tube.

It is found that the inclusion of the electron inertia effect (parallel to an external magnetic field) can provide a linear coupling between the electrostatic drift and the convective modes in a non-uniform plasma. This coupling leads to new branches of rapidly growing modes, which are calculated in the kinetic as well as in the hydrodynamic regimes. To study the saturation of the linear unstable modes, we account for the mode coupling and derive a set of model nonlinear fluid equations. A perturbation technique is employed to obtain a nonlinear evolution equation. In the steady state, the latter yields the saturated electric potential. It is argued that the enhanced low-frequency fluctuations can cause anomalous particle transport in a magnetoplasma.

Plasma behaviour during magnetic field-line reconnection which is driven by a rapid toroidal current reversal in a tokamak is investigated by calculating plasma flow speed from the magnetohydromatic equations with variables measured in the experiment. A strong plasma acceleration appears in the outside region of the X-type separatrix formed in the poloidal magnetic field lines. The induced electric field inside the plasma is evaluated directly from Ohm's law by using the fact that the toroidal current density vanishes during the current reversal. Then, plasma resistivity is estimated in the cross-section and the resulting value of energy flow is compared with that given by Poynting's theorem. It is found that the input energy is dissipated effectively through anomalous resistivity in the reconnection region.

The influence of a realistic energy equation on the stability of a cylindrical magnetized plasma in a force-free magnetic field is discussed. Thermal conduction, heating and line radiation are included in the treatment. Explicit growth rates for the m = 0 and m = 1 modes are derived and compared with the standard adiabatic or incompressible time-scales. Finally, the relevance of these results for laboratory and solar plasmas is discussed.

The role of relativistic effects in the problem of drift instabilities in an inhomogeneous magnetized plasma is analysed. The kinetic approach is developed, taking into account a non-zero plasma pressure and the electromagnetic character of the perturbations. The general dispersion relation for the perturbations in an inhomogeneous relativistic plasma is obtained. As in the case of a non-relativistic plasma, the dispersion relation is written in terms of the modified dielectric permittivity tensor. This tensor is calculated by taking into account the non-Maxwellian character of the equilibrium momentum distributions of the particles. The relation between the modified dielectric permittivity tensor and the ordinary tensor of dielectric permittivity of a homogeneous plasma is elucidated.

The generalization of the kinetic theory of low-frequency long-wavelength drift instabilities (instabilities due to the number density and temperature gradients and an instability of the Kelvin–Helmholtz type) is given for the case of a relativistic plasma. The role of relativistic effects, taking into account the anisotropy of the particle momentum distribution function, is clarified. Particular attention is paid to the investigation of instabilities of these perturbations in a relativistic electron-positron plasma.

In this paper we discuss the stability of three genetically similar non-uniform flows to compressive disturbances whose wavelengths are much shorter than the length scales characterizing the background flow. The results are relevant to theoretical models of cosmic ray shocks and solar wind type flows involving heat conduction. A JWKB expansion solution yields an equation which determines how the amplitudes of the perturbations may grow (or decay) as they propagate within such structures. It is shown that, in all three of the models considered, the perturbations exhibit spatial growth if the background flow is sufficiently supersonic and decelerating. The associated equations describing the evolution of the wave action are also studied with a view to deciding whether or not the behaviour of this attractive variable can provide an unambiguous answer to the question of stability. In the case of a shock transition dominated by heat conduction, it is shown that the effects of dissipative heating within the transition more than offset those of wave growth, with the result that wave amplification is accompanied by wave action decay. Therefore in general it would appear that the wave action equation alone cannot unambiguously settle stability questions.

An experimental study of the interaction of a conducting object with a flowing plasma is described. Particular attention is given to the deflection of ions in the sheath of a negatively charged body. The experiments were conducted in a double plasma device in which a relatively weak longitudinal magnetic field may also be present. For the particular conditions used in these experiments, it was found that ion deflection occurs primarily near the edge of the body. A simple physical model is discussed which accounts for the observed dependences of the convergence of ion streams on the body potential and ion beam velocity. A density rarefaction wave is also observed in the wake region, which propagates into the ambient plasma at roughly the ion acoustic Mach angle. Finally, some preliminary observations of the spatial distribution of plasma noise in the wake region are presented.

This paper investigates the stability of a cosmic ray shock to long-wavelength perturbations. The problem is formulated in terms of finding the transmission coefficient for compressive waves across a cosmic ray shock by solving the generalized, two-fluid Rankine-Hugoniot relations. For strong shocks, the transmission coefficient confirms that compressive waves can undergo considerable amplification on passage through such shocks. The resonances of the transmission coefficient provides us with the dispersion equation governing the stability of the shock to long-wavelength ripple-like distortions. By using the principle of the argument method, it is established that cosmic ray shocks are stable.

This paper considers the linear theory of ion-acoustic-like instabilities in a homogeneous Vlasov plasma with two ion components, a less dense beam and a more dense core, with a relative drift velocity. Numerical solutions of the full electrostatic dispersion equation are presented, and the properties of the ion–ion acoustic instability are studied in detail. The following properties are demonstrated: (i) At relatively cold beam temperatures, the instability is fluid-like, but it becomes a beam resonant kinetic instability as the beam temperature becomes of the order of the core temperature; (ii) if the mode is unstable, its threshold lies well below the threshold of the electron–ion acoustic instability; (iii) an electron temperature anisotropy T⊥/T‖e > 1 enhances the instability and (iv) at sufficiently large beam-core relative drift speeds, electron magnetization can either detract from or enhance the instability. If field-aligned ion beams are to drive the ion-acoustic-like enhanced fluctuations observed upstream of the Earth's bow shock, the effective beam temperature must be much smaller than values quoted in the literature.

It is shown that double vortices are a special class of stationary solutions of the set of nonlinear equations that governs the dynamics of modified convective cells and shear Alfvén waves in a cold rotating magnetized plasma. Criteria for the existence of dipole vortices as well as several analytical expressions for the vortex profiles are presented. It is suggested that modified convective cell and Alfvén dipole vortices may cause anomalous cross-field particle transport in a low-β plasma, such as the ionosphere.

Electrostatic two-stream and electromagnetic filamentation instabilities for a light ion beam penetrating a plasma are investigated. The dispersion relations of these instabilities including the effect of plasma heating by the ion beam are solved analytically and numerically. Stability conditions are derived for propagation through a plasma. Attention is paid to the finite size effects of beams with small diameters of the order 0·1 cm typical for pinched gas discharges. The results are illustrated by plotting stability boundaries for a 100 keV proton beam propagating through a plasma.

The extraordinary-mode eigenvalue equation is used to investigate the local stability properties of relativistic, non-neutral electron flow in a planar diode. The local stability analysis assumes gentle equilibrium gradients and short perturbation wavelengths. The lowest-order local dispersion relation is derived assuming that localized solutions for the eigenfunction exist, and stability properties are investigated numerically over a wide range of System parameters for perturbations with frequency small in comparison with the electron cyclotron frequency. It is found that the local dispersion relation supports three solutions in this frequency regime. One of the solutions corresponds to a stable diocotron mode driven by the local density gradient. The other two branches are found to exhibit instability over a wide range of electron density. These modes are electromagnetic in nature and require relativistic electron flow with velocity shear in order for instability to exist. Moreover, the growth rate of the unstable electromagnetic mode can be substantial (a few per cent of the electron cyclotron frequency).

An approximate analysis of different types of electromagnetic wave propagation in a weakly relativistic electron plasma is presented. The particular case of wave propagation near the cold plasma cut-offs is considered, and possible applications of the results to diagnostics of magnetospheric parameters are discussed. It is pointed out that wave propagation near plasma resonances in some cases requires relativistic consideration, especially for extraordinary waves. Almost parallel right- and left-hand polarized waves as well as almost perpendicular ordinary and extraordinary wave propagation are considered in detail. It is shown that, in the vicinity of certain frequencies, relativistic effects on the refractive index of these waves cannot be disregarded even when the electron energy is quite small. The problem of wave energy focusing along and perpendicular to the magnetic field is considered with relativistic effects taken into account.

Transport in ‘transport-optimized’ stellarators at low collision frequencies has been studied using a numerical method of solution of the bounce-averaged Fokker–Planck equation which describes both ripple-trapped and non-ripple-trapped particles in a stellarator. Diffusion rates in ‘transport-optimized’ stellarators had not previously been calculated at collision frequencies which are low enough for the effects of a radial electric field to be important. It was found that the configurations which were optimized for transport at the highest collision frequencies at which ripple-trapped particles exist give improved transport at all lower collision frequencies of interest, and also at higher collision frequencies. Standard stellarators have also been studied since in these cases the results can be compared with existing analytic theories and the transport mechanisms have been clarified as a result. Comparisons with Monte Carlo calculations show excellent agreement, and, although existing analytic methods of solution can strictly only be applied in rather few cases, some extensions of analytic results are discussed which enable us to explain quantitatively the behaviour observed.

Two coupled equations describing the nonlinear evolution of modified convective cells with a finite but small wavenumber parallel to the external magnetic field B are derived. It is found that, for oblique propagation, the electrostatic and magnetostatic convective mode do not decouple as in the strictly perpen-dicular case. Various aspects of the governing equations are investigated. In the weakly nonlinear lirait, a three-wave interaction study shows the possibility of dual energy cascading, or of cascading to larger wavenumbers only, depending on the direction of the parallel wavenumber component of the pump wave. Furthermore, solitary wave solutions in the form of double vortices are considered.

It is shown that for certain values of the parameters of weakly relativistic plasma, the perpendicular ordinary and extraordinary refractive indices are equal. This permits a transformation between these waves when the wave normal angle θ is close but not equal to ½π Explicit formulae for the corresponding transformation coefficients are derived.

The Zakharov equations are derived using the weak turbulence expansion with approximate forms of the nonlinear response tensors from kinetic theory. The method is used to generalize the equations to the magnetized case. The range of validity of the Zakharov model is discussed briefly.

The systematic derivation of transport coefficients for the semi-classical two-component strongly coupled plasma is presented. Starting from a detailed kinetic memory function formulation, a hydrodynamic projection operator method is applied to find a transport model equivalent to the two-Sonine polynomial approximation. The electron thermal conductivity K, d.c. electrical conductivity σ, and the thermoelectric power coefficient are expressed in terms of exact static correlation functions, which are calculated in the hypernetted chain approximation. Numerical values of k and σ are given and comparisons are made with other theories and molecular dynamics simulations of strongly coupled hydrogen. Predictions of σ and k for strongly coupled carbon are also presented.