The structure of modes for which k┴B0 and ω≪Ω_ (ion waves) has been studied qualitatively in the two limits κR+ ≪ 1 and κR+ ≫ 1, where R+ = (κT+/MΩ+)½ is the mean thermal Larmor radius, without the usual electrostatic approximation. Asymptotic forms of the dielectric tensor elements εij are developed in these two limits. The modes having appreciable k × E can be called ‘generalized’ Bernstein modes. The approximation which yields the familar electrostatic Bernstein modes is εxx = 0. This approximation is shown to be valid only for large κR+ and low β. However, for small and moderate values of κR+ the generalized Bernstein modes partake of a ‘mixed’ electromagnetic- electrostatic character. In particular, for κR+ ≲ 0(1) (but ω/κ < c) the electrostatic Bernstein modes are incorrect approximations. The warm plasma electromagnetic theory is discussed with reference to cold plasma theory for a low β plasma, and it is shown that: (1) the lower hybrid frequency is only an approximate resonance in the warm plasma; (2) electromagnetic cut-offs occur at all harmonics of the gyrofrequency as k → 0; (3) electrostatic resonances occur at all harmonics of the gyrofrequency as k→∞; (4) propagation can occur in warm plasmas at frequencies above the lower hybrid.

A numerical iteration procedure has been used to obtain the solution of an integrodifferential (linear) equation which gives the energy distribution of the electrons of a low-temperature, diffusion-dominated discharge. The equation takes explicitly into account the effects of inelastic electron-neutral collisions. The results presented here have been obtained, as an instance, for helium and neon discharges, in presence of a static and uniform magnetic field.

The motion of a charged particle in the field of a plane circularly polarized wave propagating along a uniform magnetic field B0 is investigated. For the wave magnetic field small compared with B0, the equations of motion simplify to those of the pendulum, and a simple picture of what happens for particles near gyro- resonance results. Expressions are found for the amplitude and period of the pitch angle oscillations. Departures from uniformity and possible applications to the magnetosphere are briefly discussed.

The problem of transition from ambipolar to free diffusion due to charged particle density gradients in a decaying plasma of spherical symmetry is investigated in this paper. This investigation is carried out within the framework of the approximate procedure set forth by Allis & Rose (1954). A further simplification is introduced by using only the time-dependent ‘imperfect’ ambipolar diffusion coefficients for the electrons and ions evaluated at the centre of the plasma for carrying out calculations. The results for the time dependence of these ‘imperfect’ ambipolar diffusion coefficients and spatial distributions for the charge density, electric field, and potential which are obtained by this procedure are valid for all values of time in the neighbourhood of the centre of the plasma and for all other positions of space only during the time while the plasma is diffusing in an almost ‘perfect’ ambipolar manner.

A uniform, unbounded, cold plasma stream, with relativistic velocity (0, U, 0), traverses a vacuum half-space y > 0 and a dielectric half-space y < 0. A plane electromagnetic wave in the plasma stream in y > 0 is incident obliquely on the face of the dielectric. The criterion for determining which characteristic waves are present in each half space is discussed, and it is shown that, for the polarization in which B is parallel to y = 0, there is one reflected wave and three transmitted waves. One of the latter can be an amplifying wave. A first approximation to the transmission and reflexion coefficients is found in the case when the density of the stream is low.

The microwave reflexion from and transmission around the shock-produced argon plasma whose electron density is greater than 102 times the critical electron density for the 9 Gc/s wave have been found to be similar to those of a metal rod. But the skin depth of the wave in the plasma plus the thickness of the shock boundary layer is found to affect significantly the amount of microwave power transmitted round the cylindrical surface of the plasma.

Starting with the Chew, Goldberger & Low equations, an analysis is made of instability arising due to a tangential velocity discontinuity in a dilute plasma. The velocities on either side are parallel but oppositely directed. Two cases are considered: (i) the magnetic field is uniform and everywhere transverse to the motion, and (ii) the magnetic field vectors on either side are orthogonal, being parallel to the motion on one side and perpendicular on the other. The conditions for instability are obtained and it is found that the effect of magnetic field is destabilizing in both cases. The effect of orthogonality of magnetic fields on the conventional fire-hose instability for a uniform, static plasma is also discussed as special case.

Closed forms are found for the dispersion relations describing the propagation through a uniform anisotropic plasma of the three modes of electromagnetic waves whose wave vectors are perpendicular to a steady and uniform magnetic field. Such relations are found to be conveniently expressed in terms of hypergeometric functions of the second order.

A numerical experiment is described in which a one-dimensional plasma model is used to simulate the resonance probe. The trajectories of a large number of plane electron sheets are followed in a self-consistent calculation which takes account of a spatially dependent but smeared-out ion background, and externally applied static and r.f. potentials. No differentiation between sheath and plasma regions is introduced, nor is there any linearization.

The typical resonant rectification curves, with resonance below ωp, are obtained. A comparison is made between the plasma behaviour at resonance and in frequency ranges above and below the resonance. For example, the phase of current collection w.r.t. probe potential is studied. Fourier analysis of potential and density variations is used to obtain further information on phase relationships. Orbit diagrams of electrons forming the current under resonant conditions are presented, and a model for the mechanism of resonant rectification in terms of electrons at the sheath edge put forward.

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.

The investigation deals with a collapsing, cylindrical, ionizing shock in an applied axial magnetic field. The magnetic field in the nonconducting gas ahead of the shock increases as the shock converges and the consequent increase in the Lorentz force behind the shock produces a retardation. It is shown that no accelerating self-similar solution exists and the governing equations are then solved numerically.

It is proved in the surface potential waves approximation that not oniy a bounded plasma with flows along the magnetostatic field, but also a plasma with a finite ‘longitudinal temperature’ of the electrons can be unstable against axially asymmetric perturbations of magnetohydrodynamic type. The branches of surface oscillations of a cold plasma, and the conditions for their excitation by an admixture of electrons with a sufficiently high ‘longitudinal temperature’ in various geometrical configurations, are also derived in the aper.

In this paper the electric fields of an infinitesimal dipole oscillating in a hot plasma are derived in the absence of an external magnetic field; explicit expressions are obtained by making an approximation on the background electron velocity distribution function. These results are applied to investigate the resonance observed at the plasma frequency, and to estimate the radiation resistance of the dipole.

Recent calculations for hydromagnetic analogues of the classical Rayleigh– Taylor problem with Hall effect are compared. It is shown that an early calculation is the limiting situation of the work of Taiwar & Kaira, which confirms that the Hall effect introduces new instabilities.

Conditions for the instability of longitudinal waves in a single-component two-stream plasma, in which the streams have the same velocity spread, are given in the form of simple relations between the density ratio and the mean velocity difference of the streams.

The electrostatic modes for which k is perpendicular to the impressed field B0 (the ‘Bernstein modes’) have been examined, and dispersion curves (w vs. k) have been calculated numerically for hybrid frequencies in the vicinity of the thirtieth to fortieth harmonic of the gyrofrequency. Although the calculations were performed for the lower hybrid case (ion branch), they also apply to the upper hybrid cases in which the plasma parameter The structure of the dispersion curves for these large values of plasma parameter differs from that for smaller values investigated by others, in that broad bands in wave-number space have very small group speeds in narrow frequency bands close to many of the gyrofrequency harmonics. All of the Bernstein modes examined have group speeds less than 37 % of the ion thermal speed, and can be classified as very slow waves. Furthermore, the spectrum of propagating Bernstein modes is broadened as becomes large, with an effective total transmission region from the gyrofrequency up to several harmonics of gyrofrequency above the hybrid frequency.

Transport coefficients have been computed for partially ionized hydrogen at pressures of 0·01, 0·1, 1 and 10 atm and temperatures up to 50,000 °K. Theoretical expressions containing accurate collision integrals for charged particles were employed for the calculations. The electrical and thermal conductivities are compared with recent measurements in the wall-stabilized electric arc. Generally satisfactory agreement is noted for the electrical conductivity to 19,000 °K, but the computed thermal conductivity is considerably lower than that measured.

The structures of some laminar boundary layers in high-density, shock heated, 1 eV argon plasma flows have been investigated theoretically. The analysis is based upon a three-fluid continuum formulation. Boundary-layer equations have been solved numerically on a digital computer by a finite difference technique for the case of thermochemical equilibrium and no radiation and applied electromagnetic fields. The induced electric field has been considered and shown to be important. It strongly couples the diffusive motions of the electron and ion fluids, thus forming ambipolar motion except in a sheath region adjacent to the wall. Argon transport properties, calculated from simple kinetic theory, have been used in the analysis. Important parameters, such as the Prandtl number and the density-viscosity product have been found to vary one or two orders of magnitude in the argon plasma boundary layer, a finding in sharp contrast with results for classical, non-ionized boundary layers. Solutions have been developed for the simple Rayleigh's boundary layer (forming over an infinite flat plate with an impulsively started motion in its own plane) and for the shock-tube side-wall boundary layer (forming behind a plane, ionizing shock wave moving over an infinite, plane wall). Even in terms of appropriate similarity parameters, solutions (for e.g. velocity and temperature profiles) exhibit strong dependence upon free- stream conditions. Assumptions of chemical and temperature equilibria have been checked from the equilibrium solution. Results indicate equilibrium ionization would not be present in typical argon boundary layers, e.g. at temperatures below 9000 °K, at a pressure of 1 atm. Similarly, due to ineffective energy transfer rates between the electron and the heavy-particle fluids and the difference in electron and ion–atom thermal conductivities, the electron temperature would deviate from the heavy-particle temperature in the same temperature region. The electron temperature has been calculated in a linearized model and found to be larger than the ion–atom temperature.

A pair of electrodes was placed in an electromagnetic shock tube to measure the electric field induced by the flow of an argon plasma through a transverse magnetic field. This investigation suggested that the plasma consisted of two regions, the first of which was non-luminous. Flow velocities, deduced from the variation of induced voltage with electrode separation, were compared with luminous front velocities measured photoelectrically. The first plasma region moved more slowly than the second, and its velocity and duration were consistent with shock-heating. The second region, which was dominant in most, experiments, flowed at the luminous front velocity, and had probably been ejected from the driver discharge. It is proposed that the flow velocity in the second region exceeded that in the first owing to an extensive leakage of gas through the boundary layer at the contact surface.

The evolutionary condition for transverse and normal shock waves, and the fire- hose and mirror instability conditions for the associated flow, in a collisionless, anisotropic plasma having a strong magnetic field are determined using the theoretical representation of Chew, Goldberger & Low (1956) for such a medium. The results are expressed in terms of the Mach number, Alfvén Mach number, and the ratio of the temperatures parallel and perpendicular to the magnetic field in the flow approaching the shock wave, and applied to ascertain in what range of these parameters various types of instabilities may occur. The effect of the heat flux, which does not vanish generally in a collisionless plasma, on the shock stability is discussed.