The global stability of closed plasma configurations is related to the dynamical principle of least constraint and the spacetime and gauge symmetries of the flow fields. This leads to an entirely new concept of MHD stability which is more basic than stability predictions which rely on a linearized perturbation analysis. The predictions of the theory are compared to recent experimental results obtained in studies of the stability of plasma confinement geometries. The theory predicts the violent ‘instabilities’ of these systems which are currently attributed to other mechanisms. Several pertinent details of the theory which are widely misinterpreted are discussed and clarified.

The reconnexion of magnetic field lines is described for a special case of steady, incompressible hydromagnetic flow in two dimensions. A similarity solution is obtained which corresponds to the flow of a perfectly conducting, inviscid fluid such that magnetic field lines are carried from two sides toward, then on the other two sides away from, the centre of an X-configuration. The effects of viscosity are important in shocks which form in the vicinity of the X-lines of the configuration. The effects of finite electrical conductivity must be taken into account near the centre of the configuration which, in the symmetrical case discussed, is an X-type neutral point. From an approximate solution valid in this region it is found that the fluid must flow from the larger to the smaller wedges of the X-configuration. Hence, the reconnexion process is such that oppositely directed magnetic field lines move towards the neutral point in the larger wedges, become reconnected at the neutral point, and move away in the smaller wedges. Since the solution in the vicinity of the neutral point appears to be no more than a response to the external flow, which is in turn controlled by conditions far from the neutral point and is essentially unaffected by viscosity and finite electrical conductivity, it is tentatively concluded that the rate of re-connexion of magnetic field lines does not depend on these quantities, and that, in general, re-connexion can be expected to take place rapidly if circumstances are favourable.

The effect of rarefaction, optical depth and ratio of conduction to radiation on the heat transfer through stagnant diatomic gas between parallel plates is investigated. A three-fluid formulation (translator–rotator–photon) at low temperature and [translator–(rotator and vibrator)–photon] at high temperature, based on continuous distribution functions, molecule–molecule elastic collisions, molecule–photon inelastic collisions, grey gas, and local equilibrium is solved by the linearized moment procedure for fully accommodating surfaces. Results include the error involved in decoupled total heat flux.

A method of plasma containment by means of spherical multipole (SM) magnetic fields has been developed. The analysis of the confining field geometry has proved that the high-order SM-configurations constitute minimum-B traps with a given number of point cusps instead of linear loss gaps which occur in a standard minimum-B geometry. Injection and trapping of a gun-produced plasma in the SM magnetic trap have been investigated and compared with those in a spindle-cusp trap.

The instability of electromagnetic waves propagating across a static magnetic field in the presence of a thermal anisotropy (T∥ > T⊥) is investigated. The marginal stabifity criterion as well as the rate of growth of the instability are derived. When compared with the fire hose instability (of electromagnetic waves propagating along the static magnetic field) it is found that higher electron pressures are required for this new instability to be set up; however, the maximal rate of growth is much larger than in the fire hose case.

The interplanetary plasma is stable to this thermal anisotropy instability; high β plasma devices may be unstable.

The T⊥ = 0 case treated by Hamasaki is recovered.

A method for obtaining a class of generalized solutions of the system of quasilinear equations has been developed for the case where the wave vector k and the velocity v of the particles are oriented in a general direction with respect to the magnetostatic field. The method is demonstrated on the case of the quasilinear relaxation of an ion beam penetrating a cold magnetoplasma.

Parts I and II of this paper present a comprehensive picture of longitudinal wave propagation in a warm homogeneous magnetoplasma. Part I discusses computed dispersion characteristics for propagation perpendicular to the static magnetic field. For a ring electron velocity distribution it is found that mode coupling and absolute instability can occur. Similar effects are predicted for a spherical shell distribution. The Maxwellian distribution gives rise to stable propagation of undamped waves, and attenuating standing waves. A mixture of ring and Maxwellian distributions can give absolute instability with stronger growth and lower instability thresholds than for the ring distribution alone. Propagation oblique to the static magnetic field will be dealt with in Part II.

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.

We study the quasifinear relaxation of an aperiodic instability, namely the instability caused by the temperature anisotropy of a collisionless electron plasma in the absence of an external magnetic field. We give a detailed description of the relaxation process and we examine the validity of the quasilinear theory (existence of separate time scales, quasilinearity of the particles' orbits).

The stability of a non-conducting, compressible fluid (gas) flowing across the surface of incompressible conducting fluid (liquid) is discussed. Finite resistivity and Hall current are included in the hydromagnetic equations, together with surface tension. Both subsonic and supersonic flows are treated and some new instabilities are found, together with modifications to real and oscillatory modes obtained in earlier treatments.

Part I of this paper has discussed longitudinal wave propagation, perpendicular to the static magnetic field, in a warm homogeneous magnetoplasma. Part II extends the work to oblique propagation. The ring and Maxwellian transverse velocity distributions, which are absolutely unstable and stable, respectively, for perpendicular propagation, are shown here to be both absolutely unstable for oblique propagation. Their instabilities are radically affected by the introduction of axial velocity spread. A detailed study is made for the cases of a Maxwellian transverse distribution with resonance and resonance-squared axial velocity distributions. It is shown that abolute instabilities occur at high energy anisotropies. These become convectively unstable as teh anistropy is reduced, and are quenched as isotropy is approached. The isotropic Maxwellian is treated in detail, and shows both cyclotron and Landau collisionless damping.

The consequences of the quasilinear equations are explored. Particular attention is paid to the differences between the one-dimensional and the two- and three-dimensional cases, and to the differences between the cases of discrete and continuous wave-number spectra. The possibilities of and problems associated with including damped waves are treated. The relation between conservation laws and the ‘resonance approximation’, in which the limit of zero growth rate for the unstable waves is taken at finite times, is clarified. Numerical solutions for the one-dimensional case with finite growth rate are presented.

We investigate the dispersion relation for travelling helicon waves in a uniform non-resistive plasma. We show that the effect of electron inertia for a cylindrical plasma bounded by conducting walls is qualitatively different from the plane wave case, leading to significant differences in the dispersion relation at all frequencies in the range 0 < ω < Ωe.

A self-consistent Vlasov equation treatment will be given for a type of echo which arises due to the relativistic velocity dependence of the gyrofrequency. We consider a relativistic plasma in a homogeneous magnetic field. If at t = 0 and t = T a spatially homogeneous external r.f. electric field is applied perpendicular to B0, then an echo response is produced at t = 2T. The amplitude of the echo is proportional to the amplitude of the first pulse multiplied by the square of the amplitude of the second pulse.

A unified treatment is given of low-frequency wave propagation in a weakly ionized magnetoplasma from the fluid equations in which ion inertia is retained. An analysis is made of the instabilities which arise due to the influence of drift of the electrons relative to the ions for three cases: (a) Parallel drift, E∥B, (b) Hall drift, E∥B, and (c) Diamagnetic drift, ∇n⊥B. In all cases an ion acoustic instability is found while additionally, for (c), there is a drift instability for strong magnetic fields. The instability boundaries in parameter space are delineated. Furthermore, for a transversely bounded plasma, the roots ω(kz real) and kz(ω real) of the dispersion relations are discussed and related to experimental observables. The results are applied to an interpretation of wave propagation and instability on a cylindrical positive column for which all three types of drift are simultaneously present. The relation of this work to the inertialess theories of the current-convective and crossed-field instabilities is also discussed.

Within the hydromagnetic approximation, the effects of resistive, viscous, and thermal conduction dissipation on the structure of shock waves is studied. A Perturbation analysis about the upstream and downstream stationary points is developed, which, when coupled with the shock evolutionary conditions, determines the conditions for the formation of discontinuities in the shock structure. The Viscous subshock for fast shock waves and the hydromagnetic analogue of the gas dynamic isothermal discontinuity for fast and slow shocks are analyzed. Very oblique fast shocks require both resistive and viscous dissipation for a steady shock structure. Strong slow shocks propagationg nearly along the magnetic field fail to steepen if only resistive dissipation is included. The rotational discontinuity does not possess a stable shock structure for any of the dissipation processes considered.

The first-order temperature terms for the anisotropic-temperature plasma susceptibility are calculated for each species, using the velocity moment equations and circular polarized co-ordinates. The results agree with the expanded terms for the Vlasov equation solution, for which a usefully simple derivation is given. An electrostatic wave result is given. Drift can be included by a transformation of the results for zero drift.

The influence of shock-induced precursor ionization on the steady-state structure of switch-on shock waves with non-equilibrium ionization and radiation is examined theoretically. A single-temperature monatomic gas is assumed, together with a Clarke–Ferrari model for photoionization of the upstream gas. It is found that the effect of the precursor depends in general on the ratio of a characteristic precursor length to a characteristic magnetic interaction length. For the slightly ionized case treated in some detail, this ratio is much greater than unity, indicating a precursor-independence for the magnetohydrodynamic shock structure.

The influence of collisions on the universal instability in a fully ionized in- homogeneous plasma is investigated by means of a simplified Fokker-Planck kinetic equation. For the Fokker-Planck model yields results qualitatively similar to the Bhatnagar-Gross-Krook model, but the two models give different collisional effects in the case where b ≥ 1. Further it is shown that collisions in general enhance the temperature gradient instability in a plasma when b ≪ 1 and reduce it when b ≥ 1.

Kinetic equations are obtained which describe the variation in one spatial direction of a plasma whose average properties are independent of time and do not vary in the perpendicular direction.

These equations consist of a coupled set giving the variation of the electric field fluctuation spectrum and the particle distribution functions. They take into account particle discreteness effects and describe the plasma both when it is stable and weakly unstable. It is suggested that they may be used to describe an infinite plane shock wave in a plasma.