The spectral density of electrostatic fluctuations is investigated in a plasma containing an excess of suprathermal particles. As a model for the statistical distribution of the suprathermal particles, the kappa velocity distribution is used. It is found that the Debye length λD for such a plasma depends strongly on the spectral index κ of the velocity distribution, and can be much smaller than is commonly found for Maxwellian plasmas. Consequently the plasma parameter g=1/nλ3D can be larger, and plasma effects that depend on particle discreteness more important, than for a Maxwellian plasma. Consequently, levels of fluctuation are higher, and their extent in wavenumber and frequency greater, in plasmas containing suprathermals. Results for a number of different ‘concentrations’ of suprathermal particles are discussed and interpreted in terms of the normal- as well as transient-mode behaviour of the plasma. Both the cases Te[Gt ]Ti and Te=Ti, as well as κe[Lt ]κi and κe[Gt ]κi, are investigated.

A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function   (r, t). The wave phase   (r, t) is implicitly determined by an equation of the form f( )=r·n( )−λ( )t, where n( ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f( ) determines whether the wave is a centred (f( )=0) or a non-centred (f( )≠0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase   plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

We investigate theoretically the aspect-ratio dependence of Alfvén-wave current drive (AWCD) in ‘simulated’ tokamaks, in the range 1.1[les ]R/a[les ]10 (where R and a are the major and minor radii, respectively). The study is carried out within the framework of resistive MHD, and is based on the consistent solution of the full-wave equation (E∥≠0); both shear and simulated toroidicity effects are taken into account. The AWCD includes components due to (wave) momentum transfer, helicity injection and plasma flow. The aspect-ratio-dependent features investigated include the radial profiles as well as the integrated power absorption, current drive and efficiency; the effects of antenna parameters (wavenumbers and frequency) are also explored. The numerical code developed and used for these computations has been benchmarked with the aid of analytical solutions obtained for the antenna–metallic-wall system in vacuum, as well as by the smooth transition from the vacuum case to the actual plasma case. Results of extensive calculations for the so-called Alfvén-continuum frequency range are presented and discussed.

Ordered structures as well as chaotic motion of the magnetic electron drift vortex (MEDV) mode in a unmagnetized nonuniform plasma are discussed. In the collisionless limit, the nonlinear MEDV waves can self-organize into dipolar vortices or vortex chains. The latter exist in the regime where dipolar vortices are forbidden. When dissipation is included, the governing equations for the MEDV mode can be cast into the form of the Lorenz equations, so that chaotic solutions can exist.

Asymptotically matched solutions for electron and ion density, electron and ion velocity, and electric potential are obtained in the boundary region of a dense low-temperature plasma adjacent to perfectly absorbing walls – walls that absorb, without reflection, incident electrons and ions. Leading-order composite solutions, valid throughout the boundary region, are constructed from solutions in three subdomains distinguished by different physical length scales: the geometric length, the ion mean free path and the Debye length. The composite solutions are used to assess the impact of electron–ion recombination in the ionization nonequilibrium region on sheath and presheath profiles, and on quantities evaluated at the wall. While, at leading order, the velocity profiles throughout the boundary region are not influenced by recombination, the density and potential profiles are significantly altered when recombination is included. These results show that the region of rapid change in these profiles lies closer to the wall when recombination is explicitly included in the model. The influence of recombination on the presheath potential, and consequently the wall potential, is found to scale as the natural logarithm of the recombination length. The broadening of the density profile results in a larger flux of ions accelerating through the sheath and impacting on the wall. The influence of recombination on the ion power flux to the wall is found to scale with the inverse recombination length. This scaling influences the prediction of surface erosion rates in technological applications that utilize these plasmas.

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

We present stability results for plane soliton solutions of two versions of the two-dimensional KdV equation, namely the Zakharov–Kuznetsov (ZK) equation and the Kadomtsev–Petviashvili equation for positive dispersion (KP+ equation). To do this we use a linear variation-of-action method (VAM). Others have used this method, but with little success when applied to these two equations. The best results have given the correct instability range, but the predicted growth rates have significant errors. For the ZK equation we show, by paying more attention to the spatially asymptotic form of the trial function, how better estimates of the dispersion relation can be obtained. We go on to obtain the exact dispersion relation for perturbations of the plane soliton solution of the KP+ equation.

The nonrelativistic motion of a charged particle in the electromagnetic field of a plane wave is studied. New analytic solutions of the equation of motion are found that manifest the dependence of the period of the particle motion on the wave amplitude.

Linear and nonlinear dust-acoustic wave propagation in a non-ideal classical dusty plasma consisting of electrons, ions and dust grains is investigated by incorporating the van der Waals equation of state for the dust component. For linear waves, it is found from the normal mode dispersion relation that the volume reduction coefficient enhances the phase speed of the dust-acoustic waves, while the molecular cohesive forces lead to a decrease in the phase speed. The relative magnitudes of the two contributions depend on the specific parameter regimes characterizing the non-ideal nature of the dust component. In the high-temperature limit, there is a net increase in the dust-acoustic phase speed, while near the critical point the phase speed is reduced when compared with that for the ideal-gas case. For large amplitudes, we discuss the existence of dust-acoustic solitons by deriving the exact Sagdeev potential. While supersonic solitons are found to be admissible in both the sub- and supercritical parameter regimes, subsonic propagation near the dust-acoustic speed is possible only for the supercritical case. For small but finite amplitudes, explicit analytical solutions have been obtained. A limiting case of these solutions is also discussed.

A theoretical investigation has been made of the nonlinear propagation of dust-acoustic waves in a magnetized three-component dusty plasma consisting of a negatively charged dust fluid, free electrons and vortex-like distributed ions. It is found that, owing to the departure from the Boltzmann ion distribution to a vortex-like one, the dynamics of small- but finite-amplitude dust-acoustic waves in a magnetized dusty plasma is governed by the modified Korteweg–de Vries equation. The latter admits a stationary dust-acoustic solitary-wave solution that has larger amplitude, smaller width and higher propagation velocity than that involving adiabatic ions. The effects of external magnetic field, trapped ions and free electrons on the properties of these dust-acoustic solitary waves are briefly discussed.

The propagation and dispersion relation of a TM mode in a plasma duct in a slab geometry has recently been studied by Parashar and Lalita [J. Plasma Phys.55, 387 (1996)]. It is the purpose of the present note to show that their dispersion relation is incorrect.