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.

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.

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 BBGKY hierarchy for a two-dimensional magnetized plasma is considered in the weak-coupling and small plasma parameter limits for very large magnetic fields. The Fokker-Planck and Balescu-Lenard equations satisfy an H-theorem and conservation laws, and exhibit two cut-offs related to the periodicity of the particle orbits and to the distance of closest approach of a thermal particle.

We analyze energy and momentum exchange associated with Landau damping of hydromagnetic waves, from a macroscopic viewpoint, and compare the conclusions with those of the resonant quasiinear theory. It is found that the heating of protons and electrons is correctly given by the resonant theory, but that the momentum exchange is not correctly described by the resonant theory.

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.

The effect of thermal anisotropies on the Drummond-Rosenbiuth two-stream ion cyclotron instability is studied. The properties of the instability are found to be dependent on the ratio of parallel electron temperature to perpendicular ion temperature, T∥e /T⊥ ι which can alternatively be viewed as the product ofT∥e /T⊥ ι and the ion anisotropyT∥e /T⊥ ιThe critical drift velocity decreases and the growth rate increases with T∥e /T⊥ ι. However, the dependence on T∥e /T⊥ ι becomes less sensitive as this temperature ratio increases, and, in the limit of T∥e /T⊥ ι>1, the instability becomes independent of the perpendicular temperatures.

The stability of hydrodynamic longitudinal oscillations of an inhomogeneous magnetoactive plasma is analysed. If the non-uniformity of density is taken into account, it is shown to result in parametric-like instability at sub- and ultra- harmonics of natural plasma oscillation frequencies. The conditions for the development of unstable oscillations and their growth rates are determined.

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

The dispersion relation for gravitational instability has been given within the framework of a two-fluid theory. It has been shown that the Jeans criterion is changed by finite Larmor radius and by collisions for waves propagating perpendicular to the magnetic field. The critical wavenumber for instability decreases with increasing Alfvén velocity and with increasing gyroviscosity. Instability does not set in with overstabiity.

The frequency response of the h.f. quadrupole probe is calculated to be used as a diagnostic tool for measurements of electron density and temperature. In §2 the magnetic field is assumed to be zero, and ion motions are neglected. For a Maxwellian plasma, the so-called ‘Landau wave approximation’ is compared with various more sophisticated treatments, such as numerical integration or super-Cauchy and multiple water-bag models. The range of validity of this approximation is shown to be large, and the results can be applied to the most interesting parts of the experimental observations. All results previously established are recovered with greater speed. Having studied various disturbances (collisions, inhomogeneity and relative motion of the probe with respect to the plasma), it is deduced that the best way to determine the electron temperature is to use the anti-resonances due to beating between the Landau wave and the cold plasma field. In § 3 we describe the quadrupole probe, launched in December 1971 as part of the CISASPE rocket experiment. To deduce the electron density and temperature from these measurements, it is necessary to consider the influence of a static magnetic field, such as the earth's magnetic field. The general case could be treated by numerical integration, though with great difficulty, but it is shown that in most ionospheric conditions, in the vicinity of the upper hybrid frequency ωT the above treatment is again possible, the plasma frequency simply being replaced by ωT, and the thermal velocity slightly modified. These assumptions are used to deduce the electron density and temperature profiles.

The motion of a charged particle in a transverse wave of varying amplitude, wavelength and phase speed βp, propagating along a uniform magnetic field, together with a longitudinal electric field, is investigated. The equations of motion, in Hamiltonian form, are reduced to a system with two degrees of freedom in which integrable cases appear naturally. It is shown that particles may be locked in resonance with the wave, and expressions are found for the energy and momentum of such particles in terms of βp.