The guided propagation of Alfvén waves in a cold plasma is discussed from several points of view. First the field of a line source is calculated at infinity. This calculation leads to a divergence in the radiated power in two directions forming very small angles with the magnetic field.

The divergence is removed if the line source is replaced by a strip source of finite width. It is shown that propagation from a strip source only a few kilo-metres wide is strongly guided by the magnetic field, with almost no spreading, along a field line extending up to, say, 4 earth radii for wave periods of about 100 sec.

A systematic continuum theory based on the method of matched asymptotic expansions is developed to deal with electrostatic probes in a slightly ionized gas. To the first approximation of thin space charge sheath, the sheath solution is shown to become common to the geometries considered, i.e. plane, cylindrically and spherically symmetric probe surfaces: the main interest lies in the last geometry. The second-order approximation strongly affects the last two geometries. Detailed numerical calculations are presented to illustrate the effects of a finite ratio of the Debye length to the characteristic body dimension; including a contraction of the sheath region and enhancement of the electric field from the asymptotic (first-order approximation) values.

Previously reported numerical investigations of the non-linear Vlasov equation are extended to an intensive study of the two-stream instability. Strongly unstable initial conditions for the one-dimensional electron plasma are followed in time until the state of the plasma has become essentially time independent. Both the electric field and the distribution function appear to be characteristic of an inhomogeneous equilibrium, as previously conjectured (Armstrong 1966).

The propagation, along the magnetic field, of a point disturbance in a cold two fluid linear plasma is solved asymptotically in various space-time régimes. The main disturbance is a pulse front travelling at approximately the Alfvén speed divided by the electron to ion mass ratio. Its proffle envelope is an Airy function. It oscillates at the mean of the gyro-frequencies and is effiptically polarized. The disturbances remaining behind this front are of two kinds: an oscillation at the sum of the gyro-frequencies which is circularly polarized and represents the ‘extraordinary’ wave, and an oscillation at the ion gyro-frequency which is elliptically polarized with changing eccentricity and orientation of axis.

The rectified electron current to a non-magnetic and to a magnetic spherical plasma probe has been investigated as a function of the frequency of the applied alternating potential, the discharge current in the plasma source and the magnitude of the magnetic field produced by a Helmholtz coil pair. The frequency at the main peak in the rectified current was found to be always greater than the gyro- frequency and to lie within a range of frequency predicted by Crawford from an analysis of a simplified model. The results of this laboratory work have been applied to a rocket-borne experiment on resonance rectification previously carried out by R.S.R.S.

The stability of oblique magnetohycirodynamic shock waves is studied with respect to a disturbance that excites magneto-acoustic waves. The problem is solved numerically by the normal mode analysis and it is shown that slow shocks are unstable in the sense that the disturbance grows exponentially with time. Growth rates are calculated for a particular Mach number and for different values of the magnetic field and obliqueness. The fast shock appears to be stable.

The problem concerning the interaction of electromagnetic fields with a warm, slightly ionized magneto-plasma is analysed by means of the multiple time scales asymptotic technique. Only initial value problems in an infinite plasma are here considered in detail. It is shown how the full set of Vlasov–Maxwell equations, modified through a standard Boltzmann collision integral to take account of the elastic electron-neutral encounters, can be reduced, in the basic limit assumed, to a set of two coupled non-linear integro-difl�erential equations for the dominant terms of the longitudinal fields and of the electron distribution function. Once the initial conditions are specified, the behaviour of the transverse initial field is also described. A particular example has been given for the so-called progressing-wave initial conditions.

The non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma is considered for the case in which a single wave of small, but finite amplitude is excited initially. The Vlasov–Poisson equations are solved using the method of strained co-ordinates in which the independent variable t, the electric field and the distribution function are expanded in the form of asymptotic series, the terms of which are founded by an iterative procedure. An ordering parameter e is introduced, which is proportional to the initial amplitude of the electric field given by linear theory. Differential equations are derived which can be solved sequentially to obtain uniformly valid solutions to all orders in ε. Solutions are given to second order and applied to the case in which the background distribution function is Maxwellian. It is found that the changes in the real and imaginary part of the frequency are small in comparison to the values obtained in the linear theory; that the free-streaming terms decay exponentially in time with a damping rate proportional to ε2, in contrast with the linear theory where they are Un- damped; and that the analysis allows us to calculate the changes in the background distribution function for large time, resulting from particle-wave interactions.