The stability of an anisotropic plasma jet has been investigated using equations of Chew, Goldberger & Low (1965) in both plane and cylindrical geometries. The main conclusions are as follows:

(i) For waves of small wavelength, when λ (the ratio of plasma density to the density of surrounding non-conducting medium) is much greater than unity, the plasma jet is stable only if 1/6(1 + σ) <p∥/p⊥ < 1 + 2σ, where p∥ and p⊥ denote the components of pressure parallel and perpendicular to the direction of magnetic field in the steady state, and σ denotes the ratio of magnetic pressure to the perpendicular component of plasma pressure.

(ii) When λ ≫ 1, the plasma jet is unstable if the parallel component of pressure exceeds the sum of the perpendicular component of pressure and twice the magnetic pressure of the plasma.

(iii) For long waves, we find that there exists an infinite number of growing and decaying waves. Expressions for the growth rates have been obtained.

This paper is an investigation of the effect of a magnetic field on transverse waves in a perfectly conducting gas which is rotating like a Rankine vortex about the axis of a cylinder. The magnetic field is assumed to be in the axial direction. There are three waves: two waves are rotating in the same direction as the gas, one faster and the other slower than the core speed of the gas, and one wave rotates in the opposite direction.

A wide-ranging investigation is rendered possible by a judicious combination of products of electric field components and electric polarization components for two distinct modes of propagation of electromagnetic waves in an anisotropic, ionized, stratified medium. The differential equations, governing oblique propagation in these two distinct modes in such a medium, are combined to yield various integral identities when integrated throughout the medium. These lead to a large number of relations between the reflexion and transmission coefficients (for incidence from below and from above) and the fields throughout the medium, each containing as a factor just one of the components of the external magnetic field pervading the medium.

Owing to the complexity of the Vlasov–Maxwell equations for inhomogeneous plasmas, it is of general interest to investigate simpler approximate models. We compare three specific models, proposed in the literature in connexion with the high frequency oscillations of such plasmas, by means of a singular perturbation expansion in powers of E = (λD/L)⅔, where λD and L are appropriate electron Debye and equilibrium scale lengths, respectively. Explicit formulas are obtained for the eigenfrequencies (to second order) and for the electric field eigenfunctions (to leading order), and the computation of these quantities for various equilibrium parameters becomes very simple indeed. We find that, whereas the electric field eigenfunctions differ in zero order for the three models, the eigenfrequencies are identical through first order.

An equation for magnetogasdynamic shock polar, given in terms of magnetic induction polar variables (i.e. the magnetic induction polar), is obtained. Evolutionary and entropy non-decrease conditions, given in terms of these polar variables, assume a very simple form, and admit immediate geometrical interpretation. It is found that this magnetic induction polar is far more natural and convenient to use than the shock polar given in terms of conventional velocity polar variables.

The system studied is that of a narrow-band electrostatic wave packet in a collision-free plasma. Inhomogeneous effects are represented by a wave-number, which varies linearly with distance. The system is excited by a weak resonant beam, and, to first order in a smallness parameter associated with the weakness of the beam, the resonant-particle distribution function and charge densities are calculated. It is found that second-order resonant particles become stably trapped in the wave, and, after a few trapping periods, make a dominant contribution to the resonant particle charge density. The growth rate due to the resonant beam was found to increase linearly with trapping time, and typically a pulse which traps particles for n trapping periods exhibits a growth rate ˜ n times the linear Landau value. Furthermore, a reactive component of charge density was found that was able to cause a steady change in wave frequency and wave-number. These features of large growth rates and changing frequency should appear in parallel problems involving other wave types. An obvious application is that of VLF emissions in the whistler mode.

The propagation of low-frequency, large-scale (compared to the ion Larmor frequency Ωi and radius Ri), oblique Alfvén waves in a turbulent plasma is investigated in the framework of kinetic theory. The turbulent field is the statistical average of one-dimensional ion-sound waves of very high frequency and short wavelength (ω ≫ ΩiRe≫ λ). In the absence of resonant particle effects, and to first order in a finite Larmor radius expansion, it is shown that the turbulence can lead either to spatial diffusion (damping) or anti-diffusion (growth), with Bohm scaling, of the low frequency wave. Finite Larmor radius and frequency effects in the propagation of oblique Alfvén waves are simultaneously obtained for arbitrary β plasma; the results can easily be generalized, merely by deforming certain integration contours, to obtain the corresponding Landau decrement.

The resonant interaction of three monochromatic waves propagating in a uniform magnetoplasma is considered in the electrostatic approximation. It is shown that, for arbitrary directions of propagation, the coupling coefficients are in general complex, and are symmetric with respect to interchanges of the wave vectors.

In this paper we employ similarity considerations to investigate the flow field produced by an electric discharge (mathematically a current source) and a jet of momentum emerging from the same hole of a plane wall bounding a viscous, incompressible conducting fluid, which extends to infinity. We also use similarity solutions in considering the axisymmetric configuration of a problem that has recently received some attention in connexion with field line reconnexion in conducting fluids. We derive the similarity equations for an incompressible, viscous conducting fluid, and discuss the solutions for the case when the fluid is perfectly conducting. When the electrical conductivity of the fluid is finite, we could not construct solutions, satisfying the appropriate boundary conditions.

A moment approach is used to find the thermal and collisional corrections to the ordinary wave in a plasma. Results are given that include like- and unlike- particle collisions.

In periodic, inhomogeneous plasma, the dispertion relation w(k) can begeneralized to a relation w(k, K), where K is the wave-number of the periodic steady state. Two models are studied: the ‘water-bag’ model and the ‘two-stream’ model. The solution for these models is obtained easily by the introduction of a Lagrangian formulation. Results are presented. It is shown that, in the water-bag case, the appearance of narrow bands of allowed frequencies practically discretizes the lower part of the spectrum. In the two-stream case, while the long wavelengths have a smaller growth rate, an increased instability is found for k/K = ½

The effects of thermal motions on the cyclotron radiation from test particles gyrating in a homogeneous magnetoplasma are studied. These effects take care of all singularities that exist in the theory of cyclotron radiation in cold magneto- plasma, e.g. the divergence in energy loss for small particle energies. Around the hybrid frequencies thermal corrections become of dominant importance. At these frequencies cold-plasma theory breaks down. Thermal effects arise in two ways: by modifying the wave modes known from cold plasma theory, and by the introduction of a new longitudinal wave mode, known as the Bernstein mode. All wave modes are damped (in stable plasmas), the damping increasing rapidly with the product (V/v|) (ω - s), where the wave frequency ω is measured in units of the gyro frequency; V is the thermal velocity; v| the parallel component of the particle velocity, and s is an integer.

A non-linear integro-differential equation is derived, governing the space time evolution of non-linear hydromagnetic waves in a finite β collisionless plasma. The theory is done for quasi-perpendicular propagation, for wave frequencies above ion cyclotron frequency, and wavelengths smaller than ion Larmor radius. In the low β limit, the derived equation reduces to a Korteweg de Vries equation.

A weak E layer in a non-uniform magnetic field will tend to precess as a rigid body in response to the radial focusing of external magnetic fields and fields due to wall currents. We study the interaction of this precessional mode with a background plasma, and we explicitly include dissipation mechanisms in the plasma, walls and external resistors. When the plasma background is treated in the MHD approximation, we find that the mode changes character from a precessional mode at low density to a compressional Alfvén wave at high density. For a very weak E layer, instability is found, even without dissipation, when a sufficiently high background plasma density is present. However, for moderate E-layer strengths, the modes are found to be stable, even with dissipation.

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.