Experiments show that plasma may be temporarily confined in a potential well created by three symmetrically spaced inverse pinches. X-type neutral points form at each of the three points of first contact of the inverse pinches and these three neutral points act as flux switches impulsively transferring flux into a central confinement region. The confinement is terminated by a transition to anomalous resistivity at the centre of the device resulting in rapid annihilation of the confining flux by resistive dissipation. The subsequent magnetic field pattern is much more like the vacuum field having only one hyperbolic neutral point.

The plasma configuration can probably be made stable for longer periods of time and should also be of interest for studies of interactions between laser light and a plasma in a state of microturbulence.

We show how the Hamiltonian description of an ideal fluid can be used for a two fluid plasma. Translation to wave variables leads to a simple rule to obtain coupled-mode equations if the energy is known as a function of wave variables. In this context we discuss the intimate connexion between a particular dynamical model, specified by the interaction Hamiltonian, and the associated invariants of motion. By this method we derive an improved version of Zakharov's equations for Langmuir and ion sound waves with the correct invariants of motion. As a result of these corrections we find a stationary power law k−2 for the plasmon energy.

A like-particle collision operator is derived for an inhomogeneous plasma with a periodic equilibrium potential which traps part of the particle population. The derivation is made in the guiding centre approximation (one-dimensional orbits along a strong magnetic field), and only resonant interactions are considered. The effect of the particle bouncing replaces that of the three-dimensional orbits in this limit. For resonances between different harmonics of the bounce motion the operator does not vanish as happens in the classical one-dimensional case. A discussion of the general equations describing this effect is presented together with some estimates.

This paper studies the linear dispersion properties of ion temperature anisotropy instabilities in an infinite, homogeneous Vlasov plasma containing a second, cooler-ion component. The cooler component enhances the T‖>T⊥ firehose instability, as well as the T⊥>T‖, ion-cyclotron instability, by making the waves more resonant with the ions. The effect of various parameters on this enhancement is studied numerically.

By introducing field line potentials for the magnetic induction and current line potentials for the current density, it is shown that the equations which describe a static equilibrium system, in the ideally conducting magnetohydrodynamic approximation, may be derived from two equivalent variational principles. The problem of integration is essentially that of finding a transformation of the potentials which changes one of the associated Lagrangian functions into the other. The assumption that the current density has no component in one direction of a rectangular Cartesian coordinate system leads to a new class of fully three dimensional equilibria having a plane symmetry.

The turbulent diffusion of plasma across a magnetic field is studied theoretically using a three-dimensional model which includes the full dynamics of the diffusing particles and which is valid for arbitrary magnetic field strengths. The theory is confined to perpendicular turbulence, i.e. where the build-up of the fluctuations lies primarily in the plane perpendicular to the magnetic field (although it is more generally applicable). A single expression for the diffusion is derived in terms of the fluctuation spectrum, particle energy, the dispersion characteristics of the excited modes and the magnetic field. Earlier results for equilibrium plasmas are confirmed. We demonstrate the continuous transition from anomalous (1/B) diffusion in regimes of low fluctuation levels (or strong magnetic fields) to classical (1/B2) diffusion in regimes where the fluctuation level destroys the coherence sustained by the magnetic field. In this latter regime, the particles behave as if unmagnetized except for a turbulent drift which appears in the presence of anisotropic spectra.

The problem of harmonic and subharmonic generation of electrostatic waves in a general collisionless plasma, or in some other electromagnetic medium, is treated anew, using coupled-mode theory based on two time scales. A novel feature is that one of the two interacting waves may be a negative energy wave. Furthermore, the model describing the medium need not be specified, only a general linear and nonlinear conductivity or an equivalent description is required. Just by invoking wave energy conservation, the coupled-mode equations are obtained in such a way that unequivocal conclusions can be drawn.

When both waves have positive energy, they exchange part of it in a periodic fashion, provided they both have some energy initially. If initially all the energy is in the fundamental, then all of it will eventually end up (irreversibly) in thesecond harmonic. If, on the other hand, all the energy is in the harmonic initially, then no generation of the fundamental (or subharmonic) will take place. If one of the two waves is a negative-energy wave, however, an explosive instability develops, and this regardless of initial values. For comparable conditions, the instability time depends on whether the negative energy wave is in the fundamental or in the upper harmonic.

We report on an experiment designed to study collisionless shock waves in an inverse pinch discharge using argon. A magnetic disturbance was generated which propagated ahead of the driving field at twice the piston speed. Measurements of the magnetic and electric field structures, electron density and temperature, as well as ion velocities revealed that the disturbance was produced by a beam of plasma moving through the ionized ambient plasma rather than by a true shock wave. Calculations of ion trajectories using measured electric fields demonstrated that the beam originated at small radii and early times, and was not the result of a steady specular reflexion from the piston field. It is concluded that the ions comprising this stream, which were collisionless relative to the ambient ions, did not couple to the background plasma even though a strong magnetic field was applied.

The paper investigates the stability of electrostatic waves in non-uniform magnetoplasmas, governed by anti-loss-cone distributions. A new high- frequency anti-loss-cone instability occurs if ρ > ρc. (ρ is the parameter charactensing the strength of the anti-loss-cone.) An increase in ρ increases the growth rates for this instability, but stabilizes the low-frequency instability that exists even in the absence of the anti-loss cone. The growth rates can be of order 0.1Ωe.

Ion cyclotron waves cannot be quasilinearly stabilized in Q-machine experiments because the electron distribution function does not have time to flatten while electrons pass through the plasma volume. We invoke a turbulently dissipative (or ‘resonance broadening’) model to explain the observed steady-state mode saturation. We give a qualitative picture of the important nonlinear features and their implications for plasma heating experiments. We extend the turbulently dissipative model to give nonlinear frequency shifts and a description of the mode linewidths in steady-state experiments. Turbulent resistivity is calculated and found to be unobservably small compared to the classical value. Implications for further experiments are discussed.

This paper is a theoretical and experimental study of the propagation of longitudinal electron waves in a collisionless, homogeneous, isotropic plasma, whose velocity distribution function is a truncated Maxwellian. Using the method of residues and numerical calculation, the behaviour of the electric field is found to be in good agreement with experimental results. The plasma parameters can be deduced from the theoretical dispersion curves matching the experimental points; they are found to agree well with those measured by electrostatic probes. In conclusion, a pragmatic approach to the resolution of the plasma inverse problem is discussed.

Computer simulation experiments of linear and nonlinear collisionless interactions between electron beams and background plasmas, for conditions relevant to active magnetospheric experiments, were carried out. Both electrostatic and electromagnetic interactions were simultaneously considered. The beam-plasma systems were infinite and homogeneous.

The relative beam concentrations considered were ε ≡ nb/np, = 1, 0·1 and 0·01. In all cases, the background plasma (1 eV thermal energy) was penetrated by an electron beam of 1 keV streaming energy and 5 % thermal spread in the streaming direction.

The paper presents a full description of the results and a brief discussion of their relevance to magnetospheric active experiments.

The off-angle propagation case in unmagnetized plasmas is also briefly discussed.

In propagation perpendicular to the magnetic field, the lower hybrid frequency is the transition between long electromagnetic and short electrostatic waves. Cold, warm and hot plasma theories are applied to the case of a plasma composed of different ion species. For cold and warm (adiabatic) theories, the dispersion curves are not qualitatively different from the single-ion case. In the hot microscopic theory, the dispersion curves, the so-called ‘Bernstein modes’, have a structure mainly related to the lightest ion gyroharmonics, even in concentration as low as 1 %. The theoretical results can explain the ray structure observed in the ISIS II and Electron Echo 1 experiments.

The Green's function (or matrix) for a source of sinusoidal time dependence in an infinite homogeneous absorbing magneto-ionic plasma is written as a Fourier integral over wavenumber space. It is shown that this Fourier integral solution exists, and is unique as a generalized function. By extending the Fourier integral to complex wavenumbers, it is shown that the far-field expression for the Green's function may be written as an integral over sections of the dispersion surface, which in this case is a complex sub-manifold of the space of three complex variables. Use of the saddle-point method in two dimensions allows a further simplification of the far-field result. The matrix coefficients in the resulting expression are shown to represent a decomposition into modes. Corresponding results are also obtained for sources with spatial dependence, described by either functions of compact support or rapidly decreasing functions.

A ray or quasi-optical approximation is developed, using complex rays. The ‘amplitude’ terms are matrices, rather than vectors that represent the wave polarization. Thus, the way the propagation resolves a source into various modes is described. The second term in the amplitude series is shown to include a type of inter-mode coupling. It is shown that initial values needed to integrate along the rays can be chosen so that the leading term of the approximation agrees with the far-field solution for localized sources in a homogeneous medium. By invoking the ‘canonical problem’ method, the result is extended to give an approximation for the Green's matrix in a slowly-varying medium.

For the purpose of deriving appropriate Lagrangians for equations in plasma physics that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first and second order quasi- linear partial differential equations. This results in convenient forms of the sufficient conditions, under which the given differential equations are Euler Lagrange equations of a Lagrangian. These conditions are then applied, to determine the necessary transformation that converts equations, apparently not already in it, into Euler—Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained. As an additional example, the Lagrangian is derived for a resistive transmission line.