The theory of ion heating in a Q-machine Barium plasma by the electrostatic ion cyclotron instability is considered in some detail. Linear and quasi-linear theories are considered. The effect on resistivity of the instability is also considered. The ion temperature was observed, optically, to increase to a value in excess of 25 000°K by a mechanism attributable to a collisionless process. Energy transfer from the drifting electron current to the ions is analyzed explicitly. Detailed comparisons with experiments are presented.

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak- coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one- and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Nonlinear theory of Rayleigh—Taylor instability in plasma supported by a vacuum magnetic field shows that the growth rate of the mode, unstable in the linear theory, increases if the wavelength of perturbation π lies between

and 2πcrit. This might have an important bearing on the proposed thermonuclear MHD power generation experiments.

The current-driven Alfvén instability is discussed analytically. The instability is driven by the resonant Landau and transit-time terms for propagation not parallel to B0. The critical current for instability is slightly less than the corresponding one for the ‘k-like’instability; thus, the instability discussed in this paper may be the more important for the parameter range in which our approximations are valid. The effect of current flow on the magnetosonic mode is also discussed, but no instability is found.

The formation of an electrostatic double sheath at a magnetic separatrix is described, with particular reference to the polytron. Results are discussed for a collisionless plasma, and for a simple MHD model where the sheath thickness is determined by collisional effects. Expressions are given for the sheath thickness in the polytron. Of more general interest is the result that the formation of a sheath makes the resistance of the plasma to current flow across the separatrix proportional to ωτ, not ω2τ2 as expected for a homogenous magnetic field.

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.

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.

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.

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.

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.