Analytic modelling of laser-produced plasmas has generally been restricted to one-dimensional flow. Multi-dimensional hydrodynamic approximations are available, and are explored in this paper. Two configurations are examined. The explosive mode in which the entire body of material is uniformly heated is treated by the self-similar form, and the aspect ratio of the resulting expansion is determined. Ablative flows can be approximated by the hybrid model, and the self-regulating flow from a solid target can be calculated in this way.

The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

The renormalization-group method is applied to the problem of forced turbulence in the simplified Alfvén model of Chen and Mahajan. The effects of small unresolvable subgrid modes on the large-scale turbulence leads to a renormalized response function ε. In certain limits, the resulting recursion relation for the response function can be converted into a differential equation that can be solved analytically. For Gaussian forcing terms satisfying a power-law wavenumber correlation k–y but white-noise frequency spectrum, it is found that the response function exhibits second-harmonic generation of waves at frequency ω = 2ΛvA for all exponents y ≥ 0, where Λ is the wavenumber separating the subgrid and supergrid modes.

Ion-acoustic waves in sheet plasmas, which are of thickness of order of the ion Larmor radius ρi, have been investigated numerically. The frequency range considered is less than the ion cyclotron frequency ωci. An integral equation in wavenumber space is derived from the linearized Vlasov-Poisson equations and analysed numerically. Eigenfrequencies and eigenfunctions of the wave have been studied systematically by varying the plasma thickness, plasma density, electron-to-ion temperature ratio and parallel wavenumber. Electron-acoustic waves are found when the parallel wavenumber is very small (e.g. k∥ρi = 0·005) and the electron and ion temperatures are comparable.

If the rotamak is regarded as a spherical field-reversed mirror then, according to conventional ideal MHD analysis, it should be unstable to co-interchange modes localized near the vortex point of the magnetic field. It is shown that to study these instabilities in a typical rotamak plasma, the Hall term in Ohm's law cannot be ignored. The effect of the Hall term on the ideal MHD analysis of co-interchange modes is investigated and a stability criterion is derived.

The modulational instability of a whistler wave propagating along an external magnetic field is investigated, taking into account the dispersion of the low-frequency modulations. The dispersive effects are significant if the modulation frequencies Ω are comparable to or greater than the ion cyclotron frequency ωci. It is shown that in this case there are four unstable branches: the long-wave modulational instability and three others with much larger growth rates. At Ω≪ωci the latter correspond to fast magnetic sound, Alfvén and slow magnetic sound branches.

We consider here the nonlinear development of ion-acoustic waves in a magnetized plasma, and give a further discussion of the analytical properties of the Zakharov-Kuznestov equation that governs the latter problem. First we discuss the solitary-wave solutions and show that they give a good description of recent experimental results about the manner in which the magnetic field influences the solitary waves. We then exhibit recurrence and Lagrange stability of solutions of the Zakharov-Kuznestov equation.

The stability of the MHD equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves used in cosmic-ray-shock acceleration theory (e.g. McKenzie & Völk 1982) is analysed for linear compressive instabilities. It is found that the inclusion of wave effects implies that the forward propagating sub-Alfvénic mode is unstable on wavelength scales greater than 1 parsec. The role of the instability in astrophysical models is considered.

The mode conversion of an electrostatic whistler wave into a Bohm–Gross mode at plasma resonance is analysed for a magnetized plasma with a longitudinal density gradient (i.e. ∇n0 X B = 0). It is found that a whistler incident upon plasma resonance from inside the plasma converts, without producing a reflected wave, into a short-wavelength Bohm-Gross mode that carries energy down the density gradient away from resonance. The detailed structure of the electric field near the resonance is found analytically. It is shown that the production of the Bohm-Gross wave by mode conversion can be described by a model of plasma resonance driven by a k = 0 electric field (i.e. the capacitor plate model). The relation between the driver amplitude and the amplitude of the incident whistler is derived.

A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.

The transport of plasma under the influence of a significant flow velocity in a toroidal stellarator has been modelled using an efficient numerical scheme based on ‘propagators’. The particle density has been calculated in a poloidal cross-section from the fluid particle conservation equation, using a flow velocity and a diffusion coefficient derived from experimentally obtained values. The formation of hollow density profiles during ECH has been examined, by varying the flow velocity v(r,θ) of the bulk of the plasma while ensuring that (its component in the minor-radial direction, averaged over poloidal angle θ) is consistent with experiment. A radial flow does not seem to account for the very hollow profiles observed in experiment. Hollownesses of between 1·5 and 5 were obtained for other plausible forms of v(r, θ).

The active and reactive power resonantly absorbed by a linear passive system is calculated in terms of its continuum eigenfunctions and the spatial–temporal spectral density of the external force. An application to the resonance absorption of electromagnetic radiation by a cold inhomogeneous plasma is given.

A gyrokinetic formalism using magnetic co-ordinates is used to derive self-consistent, nonlinear Maxwell–Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic co-ordinates is an important feature of this work since it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the action-variational Lie perturbation method of Cary & Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfvén perturbations in slab geometry or electrostatic perturbations in toroidal geometry. In this present work fully electromagnetic perturbations in toroidal geometry are considered.

In this paper we determine the asymptotic behaviour of the spectral function for two types of waves generated in a turbulent plasma: plasma waves generated by a kinetic electron beam instability, and lower-hybrid waves. It is shown that the wave spectrum behaves in the lowest-order approximation as K–6 and K║–3 in the respective cases (where k and k║ are the wavenumber and the wavenumber parallel to the magnetic field) and is bounded below by an appropriate value. The distribution function is evaluated self-consistently in each case.

It is shown that, in addition to magnetic helicity and cross-helicity, a modified form of kinetic helicity is also conserved in MHD fluids if the Hall effect is taken into account. The consequence of including this modified kinetic helicity as a conservation integral in a variation of the system energy is the emergence of an unconditionally MHD-stable solution that is realized in migma plasmas and may be expected to emerge as a self-organized configuration from an initially turbulent magnetofluid.

The dispersion relation obtained from a linear analysis of the hydrodynamic system of equations of Duhau is used to study the behaviour of the fast and slow magnetosonic and entropy modes in an electron-heat-flux-conducting plasma. The evolution of the hydrodynamic modes different from the Alfvén mode are studied as the electron heat flux is increased from zero as well as around the borders of overstable regions, for any anisotropy condition of the ions. The development of the domains of mirror and electron-heat-flux overstabilities are established and the regions of absolute stability are shown

A recently described numerical theory for obtaining the Sagdeev and real potential profiles of stationary wave forms in a plasma consisting of double-Maxwellian electrons and two or more species of warm ions is used for the study of solitons in such a plasma. The effects of ion temperature and light-ion concentration on rarefactive ion-acoustic soliton profiles in a double-ion plasma obtained with this large-amplitude theory are compared with those predicted from a Korteweg–de Vries equation. Application of the theory to the work of Nakamura and co-workers is discussed, and we draw attention to ion thermal effects.

The generation of lower-hybrid waves in an inhomogeneous electron beam is examined. Wave amplitudes are invariably limited by the convective nature of the instability. The self-consistent shear of the magnetic-field geometry due to the beam current is limited to the role of dividing the general problem into separate cases according to the relative orientation of the wave vector and direction of inhomogeneity. Moreover, the limiting case of small shear is smoothly connected to the case where shear is altogether negligible. Estimates of the amplification of lower-hybrid waves propagating across the electron beam are made for the various cases.

The flow fields induced by spherical blast waves propagating into dusty gases are investigated numerically. In the case of a moderate blast wave the gaseous phase is assumed to be perfect, while for strong blast waves real-gas effects are accounted for. The effects of the dust loading ratio and the initial energy used to generate the blast on the suspension properties are investigated and discussed in detail. Owing to the fact that the physics involved inside the exploding charge is very complicated, the present solution is appropriate for simulating the flow induced by the blast wave outside the exploding sphere only.