The possibility of a collisionless shock in a plasma not subject to electrostatic instabilities nor immersed in a permanent magnetic field is investigated. The equations governing a steady shock in an electron-ion plasma are deduced and their limitations are discussed. Attention is given to the fact that the velocity distribution in a collisionless plasma may not be Maxwellian. This yields a parameter which is a measure of high-energy particle density. It is found that almost always no steady shock exists. The inverse of the electron plasma wave-number k0=ωp/c provides a scale length for the shock, though the dampening effect of the ions indicates a shock thickness much in excess of . It is concluded that the mechanism for such shocks may be important in a gas such as the solar wind.

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

.

The influence of the presence of a low density, cold plasma on the stability against electrostatic perturbations of a cylindrical layer of charged particles moving in a uniform magnetic field is considered. It is shown that the influence of the plasma is important when the thickness of the layer is small, and the effect is stabilizing or destabilizing whether the dielectric constant of the plasma is smaller or larger than 1. In particular it is shown that the plasma can cause an unstable precession of the layer.

It is shown how to construct shock-like time independent solutions of the electrostatic Vlasov and Poisson Equations in one dimension. The positive ions are assumed to be at zero temperature. The electrostatic potential is assumed to increase monotonically through the shock from zero to a constant value. The most important feature of the solution is a population of trapped electrons in the shocked plasma. In contrast to time-independent solutions based upon fluid equations, there is no upper limit on the amplitude of the shock.

Ion acoustic waves propagating in a collision-free gravity-supported one-dimeiisional plasma are studied, including conditions where the wavelength is of the order of the scale height of the equilibrium plasma. It turns out that the fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is overcome by Landau damping up to wavelengths of the order of the scale height or even larger, depending on the ratio of the electron and the ion temperatures.

The effect of curvature of magnetic field lines on plasma instabilities due to a large gradient of the ion temperature has been studied. It is shown that none of the discussed effects can be obtained so long as the curvature of magnetic field lines is simulated by a fictional gravitation field. In configurations with large enough minimum-B, the usual temperature-gradient instability is stabilized in collisionless plasma. However, a new dissipative instability arises due to ion–ion collisions with the maximum growth rate γmax ˜ Vii/40.

The influence of the lack of neutrality on the drift instabilities (collisionless and collisional) of a non-uniform, isothermal plasma is considered. It is shown that the local dispersion relation depends on the derivatives of the electric field present in the equilibrium of the nonneutral plasma. In particular the influence of the first two derivatives is discussed.

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.

A magnetically confiuied, slightly non-uniform and non-neutral plasma column is considered. The existence is shown, in plane, infinite geometry, of a mode whose characteristic properties agree with those of an unstable wave detected in a recent experiment.

Variational methods are used to determine the structure of dynamically stable plasmoids. The total energy of the plasmoid is varied subject to a set of constraint integrals on the flow. It is demonstrated that the resulting flow structure results in a plasmoid of the type observed experimentally when the angular momentum of the plasmoid is not conserved. This is the collinear vortex structure. New experimental results are presented which demonstrate that the structures observed in mirror trapping experiments may be of the type predicted by the variational calculation.

It is demonstrated that the collinear plasmoid structures can propagate in a surrounding conducting gas as members of a class of non-linear transverse waves that trap and transport fluid mass. They may also exist as standing waves in a surrounding medium which supports currents and acts as a force-bearing shell. The interaction of the non-linear transverse waves (plasmoids) with each other and with the magnetic mirror field produces a reversed-field closed configuration. Experimental results are presented which illustrate these effects and show details of the structures.

It is also demonstrated that a modification of these solutions that assumes conservation of angular momentum of the plasmoid describes another type of plasma structure which is centred on the magnetic field lines and moves at right angles to the field. This is the field-aligned plasma structure.

The primary quantities characterizing the electricaJ carriers of a flowing plasma in a low density wind tunnel have been determined from measurements using electrostatic probes immersed in the plasma. With the exception of the ion temperature, the plasma parameters have been obtained from the current—voltage characteristics of two types of single electrode probe. The probes consist of a cylinder, the major axis of which is aligned parallel to the flow of the plasma, and a disk, the exposed surface of which is normal to the direction of flow. Experiments with a double electrode probe consisting of a disk-shaped collector electrode which is screened from direct exposure to the plasma by a fine wire mesh, grid electrode, made it possible to obtain current—voltage characteristics with the ion and electron components separated from one another. From the current—voltage characteristic corresponding to collection of ions, using the screen grid probe, values of the ion temperature and drift velocity have been obtained. The measurements have been made at various points along the centre line of flow, for one particular value of the flow rate using argon as the test gas. For a given position of the probes, one value of the ion temperature has been evaluated, together with two independent values of each of the other primary quantities characterizing the electrical carriers of a flowing plasma. Each pair of values agree satisfactorily amongst themselves, good agreement being generally obtained between probe theory and experiment.

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.

The stability of a stationary non-linear wave set up by two counter-streaming cold beams of electrons immersed in a background of stationary ions is examined without recourse to an expansion in terms of the amplitude of this wave. It is found that this wave is unstable to small perturbations and hence one would not expect such waves to exist in practice.

In this paper, the electrostatic oscillations of a plasma having a Fermi distribution of energies are discussed. The electrons, assumed to be tightly bound to the magnetic lines of force, are acted upon by a linear restoring force which causes the electrons to oscillate with a fixed angular frequency ω0. The dependence of the frequencies of oscillation of the plasma on electron density is calculated in the two limiting cases ωp0/ω0 ≪ and ωp0/ω0 ≫ 1.

The propagation and the linear transformation of high-frequency electrostatic waves in a hot magnetoactive plasma with a radially decreasing density is investigated. It is shown that in the region of the hybrid resonance cold plasma waves with a long wavelength are transformed into the Bernstein modes with a short wavelength. By this shortening of the wavelength the absorption of the waves increases, particularly for the frequencies near the electron cyclotron harmonics. It might be the cause of the electron heating in plasma—beam experiments.

We present a brief survey of the phase velocities and polarizations of linear waves in an infinite, uniform, high β plasma using the two-fluid approximation. Questions of wave-particle damping are deferred. Several features of high β plasma waves differ from the familiar low β case.

Electron and ion density distributions and the problem of electron/ion current partitioning are studied in a large radius Z-pinch in argon. Radial scans of the electron density and temperature proffles in the propagating sheet are obtained with a multi-purpose microwave interferometer which measures the complex refiexion coefficient from the plasma. At 70 GHz the probe resolves densities up to 1017 cm−3 over dimensions of ˜ 4 mm. Proffles of the electric and magnetic field components are obtained using standard probe techniques, and these data are used to calculate ion and electron current components in the sheet.

Within the approximations of MHD theory, calculations show that the overall axial current pattern is built up of four interior zones alternately dominated by electron or ion current. This structure is observed to be closely correlated with variations of the Hall parameter, Wb/vc, about the value of unity through the sheet, which suggests that this parameter might be used as a guide to the relative importance of ion conduction in pinch discharge current sheets.

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0 are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.

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.