A new formulation of quasi-linear theory is presented, which allows for only resonant diffusion, caused by both growing and damped waves. Nonresonant terms do not appear in the diffusion equation, but contribute to wave momentum and energy, and ensure conservation of total momentum and energy.

The intensity of X-ray sources in a focused deuterium plasma produced by a coaxial accelerator has been analysed as a function of position, X-ray energy and time of emission. The X-ray source in the axial region can be resolved (by micro- densitometer readings on X-ray pinhole camera films) as a sequence of small sources (linear dimension ∼ 0.1–0.3 mm) of hard radiation ≳ 2 ke V inside a more diffused source (cylindrical region of 1–4mm diameter) of softer X-rays. In each discharge the point sources are distributed for the most part in the general axial region of the discharge and two or more sources with different radial positions can be frequently observed for one specific value of the axial co-ordinate. Images of localized X-ray sources are also observed in the off-axis halo region. Multiple repinching of the axial plasma column or emission from metal-vapour clouds (by anode bombardment) can be ruled out in this experiment (hollow central electrode, or anode, radius 3·4 cm). The source multiplicity can be related to a complex (filamentary) structure of the plasma.

A co-axial plasma focus device is operated in deuterium gas at ambient pressures from 0·2 to 0·7 mm Hg and condenser bank voltages from 10 to 22 kV. Magnetic probing reveals an axisymmetric parabolic current sheath which propagates down the co-axial tube (steady propagation region) and collapses off the end of the co-axial gun forming a dense plasma focus. The state of the plasma just before the focusing action is very much dependent on the velocity in the steady propagation region. This velocity is experimentally studied and compared with a snow- plough theory. The collapsing phase of the current sheath is studied using high speed framing photography and current and voltage measurements. The results indicate a focus of length 1·5 cm and radius less than 1·7 mm.

The field of a pulsed beam (a ‘wave packet’), travelling through a medium with moderate absorption, is calculated by the saddle-point method. The packet velocity (i.e. the velocity of the spatial amplitude maximum) has the same direction as the velocity Re (∂ω/∂k), a generalization of the group velocity ∂ω/∂k in non-absorbing media. It differs from the absolute value of this velocity by a correction factor depending on the absorption, beam width and pulse duration. This factor is unity for vanishing absorption and infinite beam width. The velocity Im (∂ω/∂k) has no apparent physical meaning.

With the generalized group velocity vg = Re (∂ω/∂k) for media with moderate absorption, derived in a previous paper, the Hamilton equations for group propagation in non-absorbing media are generalized to include moderate absorption. They contain directional derivatives not only in the direction of v but also in the direction of Im (∂ω/∂k). Two iterative computational methods are presented for ray tracing with the generalized Hamilton equations.

The boundary-value problem for diffusion-controlled breakdown of gases in microwave cavities is converted to a variational principle for the square of the reciprocal of the ‘effective’ diffusion length. For a rectangular cavity excited in the TEαγ0 mode, the resultant variational principle was minimized by an iterativevariational procedure. This was done using the high-frequency ionization coefficient of Herlin & Brown. However, any other functional dependence on the r.m.s. value of the electric field could have been used for this purpose. The resultant hierarchy of approximations to the variational principle obtained by this iterative-variational procedure for a cavity of square transverse crosssection is applied to the TE110 and TE220 modes of excitation. Adequate convergence is obtained with the first six approximations. Resultant plots of the ratio of the ‘effective’ to the characteristic diffusion length as a function of the Herlin & Brown parameter β, for various ratios of longitudinal to effective transverse cavity dimensions, imply that diffusion loss is greater for the TE220 mode of excitation. Also, from this theoretical investigation it is felt that the first ten approximations to the variational principle should provide adequate convergence for most situations encountered in practice with regard to β, as well as cavity dimensions.

The present paper examines the magnetic boundary layer along a curved interface between two opposing fluid streams carrying oppositely directed magnetic fields. This problem is known classically as the neutral sheet or X neutral-point problem. A formal two-dimensional theory is constructed that depends solely on the mechanism of magnetic diffusion and thus eliminates the need for any added MHD waves. This theory shows clearly the detailed structure of the neutral sheet boundary layer and, more importantly, the parametric dependence of the solution on free-stream parameters such as the magnetic Reynolds number and the Alfvén number. It is shown that a thin, powerful jet of high thermal and kinetic energy exists within the boundary layer. Sample numerical solutions are presented, and the various mathematical difficulties associated with this class of problems are discussed.

Nonlinear hydromagnetic waves propagating along a magnetic field in a cold collisionless plasma are investigated. A criterion for ergodicity of the waves is obtained using the usual method of analytical dynamics. According to this criterion, it is found that, if a parameter b00 is a rational number, the wave is periodic, and that, if b00 is an irrational number, the wave is ergodic. Therefore, the waves are almost always ergodic, i.e. the trajectory of the wave fills up a region in the phase plane of the magnetic field. On the other hand, periodic solutions can exist only with measure zero.

The exact form of a nonlinear, stationary wave, travelling against a background of cold plasma, is investigated for stability. The result is that it is marginally stable, and therefore can exist in practice. This is found without expanding in the wave amplitude. Another problem, that of a nonlinear wave at rest against a background of two counter-streaming cold electron beams, is also commented on.