The instability of a field-aligned electron beam of finite width streaming through a uniform magnetized plasma is investigated. An earlier paper presented an analysis of the normal modes for electromagnetic waves in a ‘top hat’ beam– plasma system. The present paper extends the analysis to higher frequencies and different system parameters. Besides discussing the nature of the normal modes, the wave field variation within the beam region is studied. In doing this it is found that an electrostatic approximation is useful in describing the general form of the dispersion relation, specifically showing how the beam width controls the range of allowed solutions. The electrostatic approximation is shown to be good for most of the range of frequencies considered. When the electron gyrofrequency is greater than the electron plasma frequency, the theory predicts that the cold plasma upper-hybrid resonance band (Z mode) is stable to negative Landau damping. A criterion for applying this result to beam-plasma systems other than the ones investigated here is developed, and it is found that the effect should be more readily observable in laboratory experiments than in space plasmas.

The Kelvin–Helmholtz problem in a Hall plasma, including the effects of rotation, is studied. In contrast to previous results, it is shown that if the angular velocity is normal to the wave vector that describes perturbations of the interface, the rotation does not affect the stability of a shear plane. The special case of very small angular velocity is studied and it is shown that the rotation has either a stabilizing or a destabilizing effect, according as the gravitational speed is greater or less than the Alfvén speed.

The energetic anti-loss-cone electrons can drive a low-frequency electrostatic instability, propagating transverse to the ambient magnetic field, in the presence of a cold plasma. The typical real frequency and growth rates associated with this instabifity are respectively, of the order of (ωp being the proton cyclotron frequency). The instability has a transverse wavelength ⋍10ρe (ρe being the Larmor radius of energetic electrons). For the parameters pertinent to auroral plasma at 1RE, the quasi-linear analysis shows that the instability can give rise to an oscillating electric field Esat ⋍0.5−25 mV/ m and an increase of 100–103 K in the temperature of cold electrons. The instability may be relevant to recent observations of low-frequency turbulence on the auroral field lines.

Current driven, ‘helical’ (non-axisymmetric) modes of a tokamak with arbitrary cross-section are considered in the straight (cylindrical) geometry approximation. The plasma is considered surrounded by a resistive wall. The plasma may be unstable on a fast time-scale, namely the MHD or tearing mode time-scale, on a slow time-scale given by the wall properties or it may be stable. The formalism given in this paper allows determination of stability by relatively simple numerical means. In the case of instability on the slow time-scale, the formalism allows determination of growth rates and mode structures. Since the formalism is an eigenvalue formalism with orthogonal eigenfunctions, it is well suited for calculation of the effects on a stable plasma of slow error fields caused by externally driven error currents flowing predominantly in the direction of the ignorable co-ordinate.

Propagation of longitudinal electron modes in Maxwellian plasma is discussed using both the Vlasov equation and the 13-moment equations. Both methods are shown to be consistent and in addition both methods are shown to predict a second (heavily damped) mode which propagates below as well as above the plasma frequency. The results are in excellent agreement with earlier experiments for near-equilibrium plasmas.

A Liapunov functional is constructed for the plane parallel flow of a multicomponent plasma in an external gravitational field. Sufficient conditions for stability to electrostatic perturbations are obtained. The L2-norms of certain system variables are shown to be bounded uniformly in time.

Plasmadynamical equations for a two-component plasma are obtained starting from the linearized Vlasov–Landau kinetic equation. Explicit formulae are given for the frequency dependent transport coefficients. Eigenvalues of ten plasmadynamical modes are also discussed.

This paper is the first part of a work concerning a statistical theory of Langmuir turbulence in which the destabilization of an ensemble of plasmons by self- modulation is considered as a critical phenomenon. The first part is devoted to a discussion of the existence of a statistical equilibrium for the ensemble of modes. A transition curve, which separates equilibrium from non-equilibrium, is found. Several properties of the plasma, when the self-modulation instability is saturated, are derived in the neighbourhood of the critical Langmuir energy density Wc. In particular, the Langmuir energy spectrum is found to be proportional to kd-3, the correlation length is found to diverge as üW–Wcü–half, and the anomalous conductivity at the plasma frequency is found to diverge as üW – Wcü-1.

Under the assumption of a general symmetry (dependency on two space variables only), a generalized Grad–Shafranov equilibrium equation is derived and discussed. An elementary formulation of the boundary conditions is given and the existence of solutions is investigated. It emerges that from the equilibrium requirements almost no restrictions follow for the two arbitrary functions appearing in the equilibrium equation.

Using a simpler formalism than in the original paper on this subject, we verify the earlier result that, for a pump frequency separation Δ approximately equal to twice the ion acoustic frequency Ω, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/Ω, the optimum value of t being ▵ 2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ ≪ Ω. The analysis presented in a recent paper is shown to be valid only for γ ≪ Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Te/Ti≫ 1).

The cold-plasma model of the radio wave scattering from spatially random fluctuations of electron density in an anisotropic plasma is extended to the warmplasma model, in which the effect of electron pressure is taken into account. Since the medium is compressible as well as anisotropic, there is the additional possibility of mode conversion from an incident electromagnetic wave to a scattered electron plasma wave. Some numerical results are also included.

Langmuir probe measurements have been carried out which confirm the occurrence of double-layers in an argon positive column. Pulsing the discharge current permitted probe measurements to be performed in the presence of the double- layer. Supplementary evidence, obtained from d.c. and pulsed discharges, indicated that the double-layers formed in the two modes of operation were similar. The double-layers observed were weak and stable; their relation to other classes of double-layers is discussed, and directions for future work are suggested.