Electrostatic instabilities excited by an energetic ion beam injected at an arbitrary angle with respect to the magnetic field in a collisionless plasma are discussed. Threshold conditions on the angle of injection and on the beam density are derived for the cross-field ion-ion mode, the modified two-stream mode and the ion-acoustic modes. The time evolution of the momentum and the thermal energy of each plasma component in the presence of the instabilities is calculated from moments of the quasi-linear equation. The background ions are significantly heated by most of the waves, exceptions being the modified two-stream mode and the resonant ion-acoustic mode. A wave with phase velocity close to the slow ion-acoustic wave has been found when the beam has a small density and a velocity greater than the acoustic speed by approximately a factor of five.

We have derived a set of coupled mode equations which govern the nonlinear interaction of three high-frequency electrostatic surface waves through a low-frequency density perturbation produced by them. The set is compared with that obtained when a similar problem is solved for bulk waves in an infinite plasma. Some differences are shown to exist caused by the specific features of surface waves such as the amplitude attenuation normal to the interface and their hybrid nature.

The coupled mode equations which govern the nonlinear interaction of three electrostatic high-frequency surface waves and a low-frequency density perturbation are analysed considering time-dependent solutions only. We show the existence of a filamentation instability in the static limit for the low-frequency density perturbation. In the opposite case (density perturbation close to the lowfrequency surface wave resonance) we arrive at a decay instability where only surface waves take part. The parametric approximation (growth rate and threshold) as well as the nonlinear evolution of both types of instabilities are studied.

The parametric decay of a magneto-acoustic pump wave into low-frequency waves modified by finite temperature effects is considered. The excited waves are the kinetic Alfvén wave and the ion-acoustic wave. The former wave plays an important role in linear heating schemes employing the mode conversion of magneto-acoustic waves at the Alfvén resonance. Here we calculate the parametric growth rates and pump thresholds for excitation of these waves. The main result is that finite temperature effects tend to reduce the growth rate of Alfvén waves.

A generalization of the stability analysis of rippled non-neutral electron beams is presented. The treatment covers regimes ranging between those known as ‘Brillouin flow’ (ωpe = ωc/2½) and ‘immersed flow’ (ωpe≪ωc). It considers electrostatic surface waves with azimuthal symmetry (l = 0) as well as harmonic modes (l≠0). Both long-wavelength and short-wavelength domains are analysed. A general discussion of instability is given in terms of the solution of the Mathieu-Hill equation. New unstable modes are found and their growth rates are derived and compared.

Analytic calculations of three important effects of toroidal field ripple on suprathermal ions in tokamak plasmas are presented. In the first process, collisional ripple-trapping, ions become trapped in local magnetic wells near their banana tips owing to pitch-angle scattering as they traverse the ripple on barely unripple-trapped orbits. In the second process, collisionless ripple-trapping, ions are captured (again near a banana tip) owing to their finite orbits, which carry them out into regions of higher ripple. In the third process, banana-drift diffusion, fast-ion banana orbits fail to close precisely, due to a ripple-induced ‘variable lingering period’ near the banana tips. These three mechanisms lead to substantial radial transport of banana-trapped, neutral-beam-injected ions when the quantity α*≡ε|τ|/Nqδ is of order unity or smaller.

The existence of finite-amplitude Langnwir solitary waves in a two-electron-temperature plastia is investigated. A now type of soliton, in which the density depression and the electric field amplitude scale in the same manner, and which travels at the effective sound speed, has been found.

Previous investigations of the stability, in particular the critical thickness for marginal stability, of an electron configuration of double-layer type are extended in order to include effects of (i) unequal plasma densities in the field-free regions, and (ii) finite values of the parameter eΔø/kTe. The results obtained are compared with the corresponding quantities in various experiments, and a striking coincidence is found.

The dyadic Green's function, relating currents and fields in transverse-k space, is determined for a homogeneous magnetoplasma, and then extended to a plane- stratified system by means of the reflexion and transmission matrices of the medium, taking into account multiple reflexions at the source and observation points. A conjugate problem is next considered, in which the propagation eigenvectors have a certain mirror symmetry with respect to those in the original problem and, by relating the scattering matrices in the two cases, a Lorentz-type reciprocity theorem is derived relating currents and fields in the original problem with the mirrored currents and their associated wave fields which characterize the conjugate problem.

It is found that convective cell diffusion leads to a kind of resistive instability for negative energy interchange modes.

Single axis tokamaks as well as doublets may be unstable toward axisymmetric MHD instabilities. Such instabilities may, for the case of a single-axis tokamak, be slow when the plasma is surrounded by a relatively close fitting conducting wall, such as a vacuum chamber; the growth rate may be proportional to the resistivity of the wall material. For the case of doublets, slowly growing instabilities with growth rates proportional to the plasma resistivity exist. Such slow instabilities can be stabilized by feedback control of the currents through coils surrounding the plasma; since it is only required that the amplifiers used in the circuits respond fast compared with the growth time of the slow instabilities, this feedback stabilization is not technologically demanding. This paper describes a formalism for the stability analysis of such a system consisting of the plasma, surrounded by a conducting wall or vacuum chamber and coils with their control system.

Nonlinear excitation of electrostatic and magnetostatic zero-frequency modes by finite-amplitude lower-hybrid waves is considered. It is found that modulational instabilities can give rise to enhanced plasma vortices. Dispersion relations, as well as analytical expressions for the growth rates, are obtained. The enhanced vortices may cause anomalous cross-field diffusion which can affect plasma confinement in tokamak devices when lower-hybrid waves are used for plasma heating or current drive. We found that magnetic fluctuations associated with the parametrically driven magnetostatic mode are of particular importance in tokamak plasmas.

Sufficient conditions for the stability of parallel flow of a warm N-component cylindrical plasma to electrostatic perturbations are obtained. In the unperturbed state the jth plasma component is assumed to have axial velocity Vj0(r), r being the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the zeroth-order equations. The L2-norms of certain system variables are shown to be bounded uniformly in time. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.