Starting from hydrodynamic equations, a dispersion relation is obtained for wave propagation through a hot electron plasma perpendicular to a spatially uniform external periodic magnetic field, B0 cos ω0t, and several excitation conditions are deduced.

The non-linear scattering of circularly polarized electromagnetic waves is studied. Expressions for matrix elements of interaction are derived and for interacting right-handed circularly polarized waves (whistler waves) the matrix is explicitly calculated for particular velocity distribution functions of electrons. Non-linear damping rates are computed.It is shown that non-linear scattering is not in general a dominant process for whistlers in the magnetosphere.

We discuss the structure of hydomagnetic shock waves of various types. The plasma is treated in the two fluid approximation and coffisional transport coefficients are used. This treatment should be valid in a collisional plasma subject to the usual caveat about the use of transport coefficients in situations where the density, temperature, etc., may change significantly over a mean free path. The approach may also have some validity for collisionless shocks if the dissipation mechanisms involve instabilities of sufficiently fine scale and high frequency that they can be described by effective transport coefficients.

The system studied is that of an electrostatic Gaussian wave packet in a cold uniform plasma being excited by a weak resonant beam. To first order in a parameter associated with the weakness of the beam the resonant particle distribution function and resonant particle charge densities are computed.

The theory of the development of thick sheaths given in an earlier paper (Sander 1969) is applied to planar sheath growth in practical situations. The results are compared with those resulting from a purely numerical method and from certain approximate equations suggested by other workers in the field.

Scattering of optical and radio frequency radiation from electron density fluctuations in a plasma has been extensively studied and bids fair to become a useful diagnostic tool (see, for example, Davies & Ramsden, 1964, 1966). The scattered spectrum, although difficult to observe, contains a great deal of information. The electron density, ion and electron temperatures, the shape of the tail of the electron distribution function, spectral fluctuations in unstable systems, the magnitude and direction of the magnetic field and the charge to mass ratio of the ions present all seem to be contained in it.

Local imperfections in the magnetic field can alter the topology of the magnetic surfaces, thereby allowing plasma to escape. A modest longitudinal magnetic field will maintain the nested surfaces near the plasma boundary, so that the residual topological changes near the separatrix become unimportant.

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964) but instead of his normal-mode analysis we employ the Laplace transform approach to solve the corresponding initial-value problem. We construct the Green function of the differential equation of the problem to show that there are branch-point singularities on the real axis of the complex frequency-plane, which correspond to the singularities of the Barston eigenmodes and which, asymptotically, give rise to non-collective oscillations with position-dependent frequency and damping proportional to negative powers of time. In addition we find an infinity of new singularities (simple poles) of the analytic continuation of the Green function into the lower half of the complex frequency-plane whose position is independent of the spatial co-ordinate so that they represent collective, exponentially damped modes of plasma oscillations. Thus, although there may be no discrete spectrum, in a more general sense a dispersion relation does exist but must be interpreted in the same way as in the case of Landau damping of hot plasma oscillations.

The interaction of homogeneous wave turbulence and a magnetohydrodynamic tangential discontinuity is studied. Attention is focused on the turbulent shear stress produced as a result of such an interaction. A magnetohydrodynamic description is used which is believed to be adequate for plasma problems in interplanetary space. As a model for wave turbulence, it is assumed that the turbulent wave field is made up of the seven modes of magnetohydrodynamic waves. They are the entropy waves, the Alfvn waves (two independent modes), the fast and slow waves (each with two independent modes). It is found that to a first approximation the turbulent shear stress acting on the surface of discontinuity is linearly proportional to the energy density of the fluctuating magnetic field and to the kinetic energy density of the plasma fluctuations. On applying the present theory to the problem of interaction between the turbulent waves in the magnetosheath and the magnetopause, it is found that the turbulent shear stress produced is too weak to produce any large-scale internal magnetospheric convection as was previously contemplated.

The hydromagnetic analogue of the Kelvin–Helmholtz problem is extended to include the effects of the Hall term. In contrast to other results in the literature it is shown that, in the case of incompressible fluids, the stability of a shear plane is unaffected by the introduction of the Hall term. The special case of a hot, uninagnetized fluid on one side of the interface and a cold, magnetized fluid on the other is studied in some detail. In this case it is shown that the presence of the Hall term can have either a stabilizing or a destabilizing effect, depending upon whether the sound speed in the hot fluid is very much greater than the Alfvén speed in the cold fluid or vice versa.