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.

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.

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.

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.

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.

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.

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.

The method of generating steady azimuthal currents in a cylindrical plasma column by means of a rotating magnetic field is investigated numerically and analytically for the case where an external steady azimuthal magnetic field is applied to the plasma. For a plasma of low resistivity, the effect of imposing a strong azimuthal field is a substantial reduction in the amount of current that can be driven. For a resistive plasma the effect is more complicated. In some cases the azimuthal field enhances current drive as has been observed in recent experiments.

Ordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. Weakly relativistic resonance broadening, frequency downshift and damping are found to alter dramatically the dispersion predicted by the corresponding strictly non-relativistic (‘classical’) theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. All classical resonances and cut-offs are removed except the cut-off at the plasma frequency ωp. At frequencies above ωp the infinite family of classically predicted modes is replaced by a single weakly damped mode whose dispersion differs only slightly from that predicted by cold plasma theory. No weakly damped modes exist in the range of harmonics s satisfying (ωp/Ωe)⅔/8 ≲ S < Ωp/Ωe, however, one such mode is located immediately below each harmonic for s ≲ (ωp/Ωe)⅔/8. A companion paper investigates extraordinary solutions of the dispersion relation.

Extraordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. As in a companion paper, which treated ordinary modes, weakly relativistic effects are found to modify dramatically the dispersion predicted by strictly non-relativistic ‘classical’ theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. The infinite families of classical Gross–Bernstein and Dnestrovskii–Kostomarov modes are truncated to include only harmonics s satisfying s ≲ (ω2p mc2/4kB TΩ2e)⅓ and s ≲(ωp/Ωe)⅔/8 respectively where ωp is the plasma frequency and T the temperature. All classical cut-offs and resonances are removed apart from the x– and z– mode cut-offs. The only coupling between large- and small-wave-vector modes is between the z mode and a Gross–Bernstein mode near the upper-hybrid frequency and between the x mode and the second Gross–Bernstein mode near 2Ωe. Dispersion of the weakly relativistic counterpart of the x mode departs only slightly from that predicted by cold plasma theory except near Ωe and 2Ωe.

The theory of the slow reaction of charged particles in the presence of a high-frequency electromagnetic field (oscillation-centre motion) is developed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The flexibility introduced by the latter features allows us to construct a theory which is manifestly gauge-invariant and involves only physical concepts (electromagnetic fields and particle velocities instead of potentials and canonical momenta). A complete description of the oscillation-centre dynamics is derived. The known expressions of the ponderomotive force are derived as special cases of our theory.

The effect of the ion temperature on ion acoustic solitary waves in a collisionless relativistic plasma is discussed using the Korteweg–de Vries equation. The phase velocity of the ion acoustic waves decreases as the relativistic effect increases, and increases as the ion temperature increases. Only a compressional soliton of the ion acoustic wave is formed in this system. Since its amplitude increases for the lower ion temperature as the relativistic effect increases, we deduce the formation of a precursor by the presence of the streaming ions. In contrast, for the higher ion temperature, the amplitude decreases slowly. Furthermore, it is shown that the oscillatory solution of the Korteweg–de Vries equation smoothly links with the nonlinear Schrödinger equation in a relativistic plasma.

The motion of a single particle under the influence of the ponderomotive force directed perpendicular to the external magnetostatic field is analysed. By solving the exact equation of motion for a specific applied electromagnetic field, the resultant ponderomotive drift is compared with the prediction of a single-particle theory using the oscillation-centre approximation. The regime of validity of this theory is discussed. It is shown that, for certain values of the amplitude and frequency of the electromagnetic field, the particle motion is unstable and therefore the concept of a single-particle ponderomotive force is meaningless.