The propagation and stability of ion and electron drift waves in a non-homogeneous plasma containing impurity ions is considered. It is shown that the presence of impurities in the plasma may significantly affect the stability criteria of these low frequency waves. Furthermore, perturbations at frequencies which are multiples of the impurity ion cyclotron frequency may also be unstable when ½K2u R21 > 1.

The forced radial magneto-acoustic oscillations in a plasma column with nonuniform mass density and temperature are investigated. It turns out that the oscillations have a resonant character similar to that of the magneto-acoustic oscillations in a uniform plasma column. The properties of the axial and azimuthal components of the oscillating magnetic field are discussed in detail.

Several features of the equilibrium and non-equilibrium statistical mechanics of a two-dimensional plasma in a uniform d.c. magnetic field are investigated. The calculations have been motivated by the recent derivation of Bohm's diffusion coefficient given by Taylor & McNamara for this system. The charges interact only through electrostatic (logarithmic) potentials. The problem is considered both with and without the guidiiig-centre approximation. With the guiding centre approximation, an appropriate Liouville equation and BBGKV hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially non-uniform situation, a guiding-centre ‘Vlasov’ equation is discussed, and is solved in special cases. The most interesting features of thermal equilibrium theory (with and without the guiding-centre approximation) are (i) a collapse of the system above a critical value of the plasma parameter, and (ii) a divergence in the electric field fluctuation spectrum (minus the selfenergy terms) for small plasma parameter and very large systems. For the nonequilibrium, non-guiding-centre case, a Boltzmann equation and a Fokker—Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral, which must be cut off on physical grounds. Several unsolved problems are posed.

Stability of MGD shock waves can be investigated either by disturbing the shock discontinuity by incident waves and then considering whether the response of the shock is unique and determinate or not, or by studying the behaviour of the dissipative shock structure with variations in the magnitudes of the dissipations. Both approaches yield the same results, which appears at first sight to be a coincidence. In this paper we show, from a single treatment that includes each as special cases, why the two methods yield the same conclusions.

Also, by including the Hall term on Ohm's law, we are able to resolve the uncertainty about the stability of switch-on and switch-off shocks that occurs in the usual MHD treatment of the problem. Finally, it is shown that the Hall term also introduces the possibility of electric field layers in the unsteady shock and thereby reduces the number of shock boundary conditions. This throws some doubt on the value of the wave-interaction theory for shocks in real plasmas.

The Thomson scattering spectrum, for laser light scattered by a low density plasma, is determined by the Doppler shifts from the moving electrons. It is shown how the full three-dimensional distribution function may be constructed if spectra are observed in several directions. Calculations using a model loss-cone distribution show that four spectra are sufficient for a faithful reconstruction of f(v). Most of the complications that arise at relativistic electron velocities can be avoided by placing a diffraction grating in the scattered laser beam.

The field of a test charge at rest in a plasma is known to be shielded via the collective interaction between the test charge and the particles of the plasma. In a thermal equilibrium plasma, the shielded potential has a spatial variation of the Debye form exp (— r)/r. In this note we will show that, in a collisionless current-carrying plasma, the potential profile along the radial direction parallel to the current changes from the Debye form to a potential well form, and causes a reversal of the ele ctric field of the test charge. The formation of the Debye potential well is attributed to the resonant interaction between the particles and the waves stationary in the test charge frame when the net flux of charged particles is different from zero. This is the same type of resonant interaction which leads to the well-known Landau damping (Landau 1946).

The electrostatic shielding of a test electron embedded in a magnetically confined pure electron gas column is investigated. For rigid-rotor equilibria with nearly uniform density in the column interior, it is shown that the shielding length is the local electron Debye length for the case that the test electron is at rest relative to the mean motion of the column.