The structure of the boundary layer separating a collisionless plasma from a one-dimensional magnetic field has been studied for anisotropic particle velocity distribution functions of the form

,

where F± is a weighting function, H± is the Hamiltonian, a± is a parameter, pz is generalized momenta, m± is particle mass, and δ is the Dirac delta function. Charge neutrality was preserved throughout the boundary layer and self- consistent solutions were obtained for particles having two or three degrees of freedom and moving against either a plane or circular boundary. The results were compared with those for the structure of a boundary layer consistent with a cold streaming plasma having a particle velocity distribution of the form

.

Guiding centre approximations are used to derive the dielectric tensor of a collisionless plasma. This approximate dielectric tensor is used to obtain the dispersion relation of Alfvén waves in a warm plasma. In a ‘low/ β’ equilibrium plasma Alfvén waves are shown to suffer considerable Landau damping if the propagation vector is almost perpendicular to the magnetic field. In a non- equilibrium plasma Alfvén waves can be generated by ‘negative Landau damping’ even if β is low. For sufficiently high β the well-known ‘garden hose’ instability can occur and is then probably dominant. The importance of these two instabilities in the magnetosphere and in the solar wind is discussed.

The nature of the dynamic positive ion sheath formed in front of the negatively going anode of a gas discharge valve is considered. Approximations valid for thick sheaths at the high voltages appropriate to mercury valves are discussed, and a transient analysis of an idealized model performed. Expressions relating anode—cathode voltage and current to sheath thickness are derived. Approximate forms of these expressions are obtained, and numerical comparison is presented in one situation.

More accurate methods of measuring microwave attenuation and phase are constantly being sought, particularly for such applications as plasma diagnostics. The microwave bridge technique described here was developed for the study of a quiescent plasma having an electron density of 1015 to 1018 m−3 corresponding to a plasma frequency of 3 × 108 to 1010 Hz, and an electron collision frequency of 1010 to 1011 s−1. The plasma had a broad dimension of 0·3 m. For such a plasma a probing frequency of 10 GHz was considered to be the most suitable; at this frequency the attenuation α and phase shift δβ expected were 0·1 < α< 50 dB and 1° < δβ < 1000° respectively.

A stochastic method has been employed to investigate the distribution function of free electrons in gases in the field of a positive ion. Stochastic results have been obtained for several pressures and for both large (Langevin) and small ions, and the results have been compared with the solutions of the diffusion approximation and Pitaevskii's Fokker—Planck approximation to the Boltzmann equation.

The resonance oscifiations of low temperature, bounded, non-magnetized in-homogeneous plasmas are studied using different methods of solving the linearized Vlasov—Maxwell equations. A low-temperature expansion method of solving the orbit-integral solution of the Vlasov equation is compared to fluid descriptions of the plasma using the truncated moment equations. Numerical results for a one-dimensional plasma slab show qualitative agreement but some quantitative discrepancies.

Recently the question of existence and stability of laminar one-dimensional coffisionless shock waves has received some new attention (Montgomery & Joyce 1969). These electrostatic shock waves are usually thought of as being generated by ion acoustic waves (pulses) in a plasma with Te ≫ Ti Apart from the well- known class of shock solution with oscillatory structure (Moiseev & Sagdeev 1963) there exist, at least within the framework of Vlasov theory, monotonic transitions from one asymptotic state to another (Montgomery & Joyce 1969). For these shock-wave like solutions it is easy to see that the electrons cannot be in thermal equilibrium (have a Maxwellian distribution) in the downstream state, if they are so in the upstream state. Hence it appears to be natural to investigate first the stability of the homogeneous downstream state (which tells us if the transition is possible at all) by investigating the properties of the class of permitted distribution functions for the electrons, before attacking the much more involved problem of the possible instabilities arising from the inhomogeneitythe transition region of the shock.

The instabilities in a two stream plasma in which the density across the stream is variable are studied from the point of view of a scattering problem. Approximate dispersion relations are developed, one of which is identical with the infinite, homogeneous case. A second relation is obtained which depends upon the scale of density variation.

The effect of weak collisions on ion-acoustic wave instabifities in a plasma with large ratios of electron to ion temperatures is investigated. The critical current for instability is shown to be signfficantly reduced by collisions. At the critical current the instability first occurs at non-zero values of kλe. As kλe increases the collisional effects become less and less significant.

Ions reflected from the sharp potential rise in a magneto-plasma, perpendicular shock wave result hi a broad, small-amplitude ‘foot’ in the magnetic field proffle. A theory is given for the structure of this foot, which shows its shape to be a rather flat parabolic curve commencing at about half a Larmor radius in front of the shock front proper. The theory also predicts the amplitude of the foot just in front of the sharp rise as a function of Alfvén—Mach number. Close agreement with experiment is found.

This paper compares computed results with upstream and downstream thermal pressures, and the downstream ion density and vector flow velocity measured by the Ames plasma probe on the Pioneer 6 spacecraft as earth's bow shock was traversed. The upstream ion density and vector flow velocity measured on Pioneer 6 by this experiment are used as independent variables, together with Pioneer 6 magnetic field measurements. MRD Rankine—Hugoniot equations for an isotropic plasma are used for these computations. Reasonable agreement is obtained between the measured and computed downstream ion density, thermal pressure and convective velocity magnitude and orientation, only when a 1γ change is made to a downstream magnetic field value used in the calculation. There is disagreement between several determinations of shock orientation and that deduced from coplanarity of the reported magnetic fields, and the shock orientation provides the co-ordinate system for solving the Rankine—Hugoniot equations. If a shock orientation determined by velocity coplanarity is used in the calculations, all computed quantities agree well with the experimental results. Other results suggest that a disagreement between computed and measured upstream thermal pressures may not be negligible in comparison with experimental uncertainties in upstream velocity and density. If the computations included anisotropic pressure terms and/or other factors such as plasma turbulence, better agreement might be obtained between computed and measured upstream thermal pressures.

The dispersion relation for the. Bernstein modes is derived, in the presence of a Fokker—Planck type collision term. Numerical solutions are obtained, and the results give an approximate formula for the collisional damping. The possibility of observing this damping experimentally is discussed.

In the course of an experimental investigation of the Manley Rowe oscillations, we have been led to define some of the conditions required for an ideal coupling between three travelling waves. It is shown that, because of homogeneity conditions, the only possible pumping wave is the electron cyclotron wave. Experimental values are given to within an order of magnitude for finite geometry.

Resonances of a plasma driven into a weakly non-linear régime are investigated by two different models.

(1) A cold plasma driven by an extended wave source is considered. It is found that resonances can occur at fractions as well as multiples of the normal mode resonances. For the fractional resonances the response amplitude grows linearly with time, whereas for the harmonic resonances it grows exponentially with time.

(2) An unmagnetized Vlasov plasma is excited by a two-grid source below the plasma frequency. A resonance is shown to occur when the driving frequency approaches one half the plasma frequency. It is argued that such non-linear resonances may be responsible for the Alouette II observations of resonances at fractions of the plasma frequency.

The statistical mechanics of the weakly turbulent plasma is treated in an original manner by introducing the waves by means of the van Kampen modes. A system of coupled equations is derived which relates the correlations between waves and waves, waves and particles, particles and particles. The quasilinear theory is obtained at the first order, and the coupling wave equation at second order, under suitable assumptions.