Dispersion and accessibility conditions for electron cyclotron waves are investigated for arbitrary weakly relativistic plasmas and for specific isotropic and loss-cone distributions. The transition between the cold plasma and vacuum dispersion relations is investigated as a function of temperature and density. The behaviour of mode structure (including mode coupling), cut-offs and resonances are also examined. Generalizations are obtained of earlier results which indicate that access by extraordinary waves to regions nearthe cyclotron layer from the low-field side is easier in weakly relativistic plasmas than predicted by cold plasma theory because of a reduction in the cut-off frequency of the fast extraordinary mode. This effect is found to be more pronounced in loss-cone distributions than in isotropic distributions, permitting access at temperatures considerably lower than those predicted in the isotropic case. Extra loss-cone modes are found to appear near the cyclotron frequency in loss-cone plasmas which also exhibit instabilities near the cyclotron harmonics.

A theoretical study is made of the generation mechanism of quasi-electrostatic VLF emissions observed in the distant magnetosphere, with frequency greater than half the electron gyrofrequency and with wave normal around the cold plasma oblique resonance cone. The two-component plasma is treated, composed of cold electrons and hot electrons with bi-Maxwellian and loss-cone distribution functions. The effects of various plasma parameters on the instability characteristics are examined in order to estimate their relative importance in determining the properties of unstable waves. It is found that both types of hot plasma distribution function can account for quasi-electrostatic half-gyrofrequency emissions. The frequency where the maximum growth rate occurs is mainly determined by the temperature anisotropy of the hot plasma, and the wave normal angle where maximum growth is expected is determined by the temperature of the hot plasma and the ratio of the cold to hot plasma densities. These theoretical considerations form the basis of a suggested plasma model which is able to explain our experimental direction-finding results.

A pseudo-spectral three-dimensional Strauss-equations code is used to describe internal disruptions in a strongly magnetized, electrically-conducting fluid, with and without an externally applied, axial electric field. Rigid conducting walls form a square (x, y) boundary, and periodic boundary conditions are assumed in the axial (z) direction. Typical resolution is 64 × 64 × 32 and the maximum Lundquist number is approximately 400. The dynamics are dominated by a helical current filament which wraps itself around the axis of the cylinder; parts of this filament can sometimes become strongly negative. The ratio of turbulent kinetic energy to total poloidal magnetic energy rises from very small values to values of the order of a few hundredths, and executes ‘bounces’ as a function of time in the absence of the external electric field. In the presence of the external electric field, the first bounce is by far the largest, then the plasma settles into a non-uniform quasi-steady state characterized by a poloidal fluid velocity flow. At the large scales, this flow has the shape of a pair of counter-rotating bean-shaped vortices. The subsequent development of this fluid flow depends strongly upon whether or not a viscous term is added to the equation of motion. Inclusion of viscosity tends to damp the flow and leads to pronounced subsequent bounces suggestive of sawtooth oscillations, though the first bounce remains substantially the largest. By means of a three-mode (Lorenz-like) truncation of the Strauss equations, the evolution of the largest spatial scales alone may be examined. Some time-dependent solutions of the low-order truncation system suggest qualitative agreement with fully resolved solutions of the Strauss equations, while other solutions exhibit interesting dynamical-systems behaviour which is thus far unparalleled in the fully-resolved simulation results.

The linear stability of finite-thickness, compressible, ideal magnetohydrodynamic sheared flows along the z direction, with a magnetic field in the (y, z) plane is studied. This paper extends earlier work with the magnetic field parallel to the flow. The present formulation also includes the effects of density and pressure gradients in the equilibrium shear layer. Analytical solutions are obtained for strongly and weakly magnetized shear layers having a vortex sheet profile (where the velocity is a step function). For an equilibrium layer having a linear velocity profile, and uniform pressure and density, contour plots of the real and imaginary parts of the perturbation frequency (corresponding to unstable waves) are numerically generated in (wavenumber, Mach number) plane using a shooting technique. The structure of two distinct regimes of instability (unstable standing modes and unstable travelling modes) is mapped out for various values of the inverse plasma beta, and various angles of propagation of the mode to the flow and the magnetic field.

Dimensional analysis is used to predict the functional relationships amongst the characteristic variables of the ablation of a cold dense fluid by an imposed external heat source. From these relations, self-similar limiting forms are identified and evaluated. Numerical simulation is used to investigate the interpolation between these limits. Self-similar forms generalizing well-known existing solutions of relevance to laser-plasma are demonstrated and include a general proof of Nemchinov's hypothesis for the heating of small targets of limited mass.

The Kelvin-Helmholtz (KH) instability of a tangential discontinuity between two compressible plasmas in relative motion is investigated, by solving the dispersion equation for two cases. In the first, neutrals are excluded; in the second, collisions between neutrals and ions are introduced in the form of a drag force in the momentum equation. The velocity of neutrals is assumed to be perpendicular to the interface. In both cases the growth rate of the KH instability is obtained as a function of the density jump between the plasmas. Although it has often been remarked that compressibility should, in general, stabilize a plasma, it is found that this ceases to be true when allowance is made for a significant density jump at the interface. Thus, for a large density jump and a large velocity shear, the instability growth rate in a compressible plasma may considerably exceed the growth rate obtained when incompressibility is assumed. Collisions, it is shown, may either stabilize or destabilize a tangential discontinuity, depending on the change in the product of density and collision frequency (pv), as one moves with the neutrals across the interface; when pv decreases, the instability is enhanced (and vice versa).

The combined effects of negative ions and higher-order nonlinearity on ionacoustic solitons are studied using the reductive perturbation method. The basic set of fluid equations for a plasma consisting of negative cold ions, positive cold ions and hot electrons (non-isothermal and isothermal) reduces to the modified Korteweg-de Vries equation and the Korteweg-de Vries equation for the first-order potential, and to the linear inhomogeneous equation for the second-order potential. Stationary solutions of the coupled equations are obtained in the case of negative ions, retaining terms up to the third order in the usual reductive perturbation method.

Kinetic theory, including ion Larmor radius effects, is used to analyse the Alfvén wave heating of cylindrical plasmas using axisymmetric waves excited by an antenna at frequencies up to the ion cyclotron frequency. At the Alfvén resonance position, the compressional wave is mode converted to a quasi-electrostatic wave (QEW) which propagates towards the plasma centre or edge depending on whether the plasma is hot or warm. The energy absorbed by the plasma agrees with the MHD theory predictions provided the QEW is heavily damped before reaching the plasma centre or edge; if it is not, then QEW resonances may occur with a consequent increase in antenna resistance. The relation between ion cyclotron wave resonances and QEW resonances in a hot plasma is shown. The behaviour described above is demonstrated by numerical solution of the wave equations for small and large tokamak-like plasmas. WKB theory has been used to derive useful expressions which quantify the QEW behaviour.

Numerical solutions of a dispersion relation for low-frequency electrostatic waves in a current-carrying, cold, weakly collisional, magnetized two-ion plasma are used to discuss the two-stream and resistive natures of the ion-ion hybrid instability. An instability with analogous behaviour is found to be associated with the light ion cyclotron frequency. Analytical results explain the behaviour. A numerically derived transition diagram summarizes the parameter values for which transitions between different modes take place.

The effect of toroidal geometry upon the distribution function of weakly RF-heated minority ions in a tokamak plasma is considered. An analytic scheme to solve the corresponding bounce-averaged Fokker-Planck equation is developed and explicit solutions are given in the limits of high and low velocities. It is found that trapped-particle effects may significantly reduce the RF-induced anisotropy in the distribution function.

Spherically symmetric plasmas with high expansion velocities have been produced by irradiating targets with eight beams from the Helios CO2 laser in the presence of gases at various pressures. Attention was given to the properties of the target-emitted ions in order to obtain information about the ion acceleration mechanisms in plasma expansions. Photo-ionization of the ambient gases by the soft X-ray emission from the laser-irradiated targets produced background plasmas, permitting plasma counterstreaming experiments to be performed in spherical geometry. Successful laser-target coupling in the presence of background gases is obtained, modification of the ion acceleration in accordance with isothermal-expansion models is observed, and an absence of collective coupling between collisionless counterstreaming plasmas is found.

Quasi-linear diffusion of charged particles due to a stationary and homogeneous spectrum of electrostatic field fluctuations is investigated via a Fokker-Planck approach. The energy of a given distribution of test particles is found to be conserved whenever the wave spectrum is isotropic and none of the spectral components of the field has a phase speed that equals the speed of any test particle. Quite generally, the energy is monotonically increasing for isotropic spectra. An interesting quantum mechanical interpretation of these results is given, and the special case of beam evolution in an isotropic spectrum of non-dispersive waves is studied in some detail. Conditions for isotropization of directed electron and ion beams from Coulomb collisions and collective oscillations are discussed in the context of the quasi-linear description. Some promising results from a beam-plasma experiment are quoted.

Recent laboratory measurements of plasma expansion in a plasma wake experiment are compared with analytical expressions which approximate the plasma expansion model of Crow, Auer & Allen. Good quantitative agreement was found between the data and theory for the velocity and position of the ion expansion front. These results provide an important insight into the behaviour of the expansion early in its development.

This paper considers the linear theory of waves near and below the ion cyclotron frequency in an isothermal electron-ion Vlasov plasma which is isotropic, homogeneous and magnetized. Numerical solutions of the full dispersion equation for the magnetosonic/whistler and Alfvén/ion cyclotron modes at βi = 1·0 are presented, and the polarizations, compressibilities, helicities, ion Alfvén ratios and ion cross-helicities are exhibited and compared. At sufficiently large βi and θ, the angle of propagation with respect to the magnetic field, the real part of the polarization of the Alfvén/ion cyclotron wave changes sign, so that, for such parameters, this mode is no longer left-hand polarized. The Alfvén/ion cyclotron mode becomes more compressive as the wavenumber ulereases, whereas the magnetosonic/whistler becomes more compressive with increasing θ, At oblique propagation, the helicity of both modes approaches zero in the long-wavelength limit; in contrast, the ion cross-helicity is of order unity for the Alfvén/ion cyclotron wave and decreases as θ increases for the magnetosonic/whistler mode.

A covariant formulation for the ponderomotive Hamiltonian is developed using Lie-transform perturbation theory. The case of unmagnetized as well as magnetized particles is discussed.

An exact nonlinear Alfvén wave in a low-β plasma is investigated. Both super-and sub-Alfvénic rarefactive solitons are found to exist depending upon the angle of inclination of the propagation vector to the magnetic field.

The classical problem of the motion of a charged particle in a slowly varying electromagnetic field is reconsidered in the framework of ‘pseudo-canonical transformations’ in a Hamiltonian formalism. As compared with Littlejohn's important recent work, we develop a method which we believe to be more transparent. It consists, in essence, of exploiting directly the requirement that the Lie brackets of the guiding centre variables be independent of the (new) gyrophase. By using this method, we construct explicitly the complete set of functional relationships between the guiding centre variables and the particle variables, up to second order in the drift parameter є These expressions are valid for magnetic and electric fields of arbitrary geometry (within the drift approximation), which may be slowly varying in time.

Second-harmonic generation of an extraordinary wave is investigated in the domain of phase synchronism with the pump wave. The conversion efficiency parameter is calculated for various values of the magnetic field, electron plasma density, angle of propagation and slab thickness.

The collisional transfer tensor for energy and transfer vector for momentum exchange between drifting tri-Maxwellians for an arbitrary central interaction force between neutral and/or ionized particles are evaluated. We introduce the new concept of a generalized Rosenbluth potential whereby the heat and momentum exchange rates can be written in a concise form. We also discuss the associated time-scales which depend on the masses, densities, temperatures, and drift velocities of the two colliding species.

This paper provides a new formulation of the resistive force-free evolution of cylindrically symmetric magnetic fields subject to purely radial motions. It is shown analytically that the evolution bounded by a perfect conductor ceases to exist after a finite time if the initial field has total axial flux of opposite sign to the field on the axis of symmetry. A numerical solution indicates that the evolution ceases to exist owing to the unlimited contraction of the field profile producing a line of infinite current density. The asymptotic form of this ‘blow-up’ is identified as the particular self-similar contraction for which the field direction is exactly reversed in the limit of large radius. Possible applications to solar flares and the reversed-field pinch are discussed.