Small-amplitude ion-acoustic double layers in a magnetized plasma have been studied, taking account of Poisson's equation. Both analytical and numerical solutions are obtained for compressive and rarefactive double layers. It is found that the results are significantly different from the case when quasi-neutrality is assumed.

The dependence of the efficiency of current drive by lower-hybrid waves on the shape and intensity of the wave spectrum is discussed in the case where no d.c. electric field is present. The discussion is based on a simple formula arising from a one-dimensional kinetic treatment of the problem.

An exact form of the dielectric tensor for a wide variety of relativistic magnetized plasmas is derived from the fully relativistic linearized Vlasov-Maxwell equations. The equilibrium function chosen incorporates a loss-cone in perpendicular momentum space, and a net drift along the external field-line. This choice of distribution function is fully relativistic, and the resulting form of the dielectric tensor is valid for arbitrary value of temperature, arbitrary degrees of loss-cone, and arbitrary drift velocity along the field-line. The exact result is simplified in several limiting cases relevant to various physical applications.

New self-similar solutions of the MHD equations for the dynamics of a high-density plasma in a linear Z-pinch are derived, taking into account the finite electric conductivity of the plasma. In a number of particular cases the self-similar solutions obtained are expressed in simple analytic form. Radial distributions of the MHD variables in the self-similar profiles show that during current heating and plasma expansion regimes with essential plasma heating on the pinch boundary are possible both with decrease and concentration of the current density on the outer pinch boundary.

In this paper the theoretical aspects of the stochastic acceleration of photoionized pick-up ions upstream of a comet's bow shock are examined. The acceleration is due to the resonant interaction of the ions with Alfvén waves. By making physically reasonable assumptions for the turbulent fields and by including an exponential spatial factor in the injection term, it is found that, with spatial diffusion ignored, exact solutions can be found.

Dispersion relations are obtained for Alfvén surface waves in a two-ion-species cylindrical plasma with finite edge density. A simple step density profile is used. The results are compared with those obtained in a plasma surrounded by a vacuum layer. For modes with positive poloidal mode number m the finite-density edge region introduces an ion-cyclotron resonance and a waveguide cutoff in the surface-wave dispersion relation at the cyclotron frequency of each ion species. For negative-m modes a new dispersion-relation branch is introduced at frequencies just below the ion-cyclotron frequency of each species. The origin of these effects is analysed in terms of the wave types that can propagate in the regions of constant density, and their interaction with the Alfvén and ion-ion hybrid resonances in these regions. This interaction is shown to be determined by the polarization of the wave fields. The relevance of the results to the Alfvén-wave and ion-cyclotron-resonance heating schemes is discussed. The possibility that the excitation of high-m surface waves contributes to the anomalously large fraction of power that is found to be deposited in the plasma edge during ion-cyclotron-resonance heating is considered.

Thomson scattering from a magnetized plasma is considered, taking into account the dielectric properties of the plasma. General results for the geometrical form factor are given in explicit form. The scattered power detectable by a heterodyne receiver is discussed and some numerical calculations are presented. The results are applied to the scattering of millimetre waves in tokamak plasmas near the electron-plasma and electron-cyclotron frequencies.

The stability of oblique modulation of ion-acoustic waves in a collisional plasma with one and two electron-temperature distributions is studied using the KBM method. For the case of one electron distribution it is found that collisions give rise to regions of physical instability that are otherwise stable in the absence of collisions. For the two-electron-distribution case in the presence of collisions the domains of physical instability of the wave are studied with respect to the values of the temperature ratio and relative concentration of the two electron species.

Resonant absorption of Alfvén waves in tokamak plasmas is studied numerically using the linearized equations of resistive magnetohydrodynamics. A numerical code based on a finite-element discretization is used for determining the stationary state of a cylindrical plasma column that is excited by an external periodic driver. The energy dissipation rate in the stationary state is calculated and the dependence of the plasma heating on electrical resistivity, the equilibrium profiles, and the wavenumbers and frequency of the external driver is investigated. Resonant absorption is extremely efficient when the plasma is excited with a frequency near that of a so-called ‘collective mode’. The heating of a plasma by driving it at the frequencies of discrete Alfvén waves is also investigated.

We present an analytical investigation of the stimulated scattering of an electromagnetic wave by an upper-hybrid wave in a two-electron-temperature plasma using a hydrodynamical model. The nonlinear dispersion equation of the upper-hybrid wave is derived and the growth rate is calculated. It is found that increasing the concentration ratio of hot to cold electrons decreases the growth rate of the upper-hybrid wave.

A study is made of ion-acoustic double layers in a plasma consisting of any number of cold positive and negative ion (and cold electron) species in addition to one isothermal electron population. The Sagdeev potential is obtained in general, together with limits on both compressive and rarefactive solutions for ion-acoustic double layers and/or solitons. Weak ion-acoustic double layers are described by a modified Korteweg-de Vries equation. Such double layers are not possible in plasmas with only positive ion species and one electron population. When one or more negative ion and/or cold electron species are included above a certain threshold density, rarefactive ion-acoustic double layers occur, but no compressive ones. The double-layer form of the potential is given, together with an application to a plasma with one positive and one negative ion component. It is shown that there is indeed such a threshold density for the negative ion density, depending on the charge-to-mass ratios of both types of ions. The threshold density is determined numerically for a range of such ratios and discussed in view of possible relevance to auroral and experimental plasmas. In the discussion, cold electrons can play the role of the negative ion species.

The two-chamber model (TCM) of Singer and Langer is employed to study the plasma transport in the scrape-off and divertor regions of a tokamak. Collisiondominated transport along the field lines is considered, with a. geometric-mean flux-limited expression for parallel electron heat conduction. An analytic method for the catastrophe-theory study of the TCM is developed. Maxwell convention for the catastrophes is adopted. Catastrophes occur when the energy flux entering the divertor chamber from the main plasma scrape-off, the recycling coefficient and the ratio of electron temperatures in the scape-off to that in the divertor exceed some threshold values. It is seen that the behaviour of the plasma during these catastrophes is in qualitative agreement with the experimentally observed features of the plasma during the H-mode transition.

The (usually neglected) effect of shear on the equilibrium of rippled, magnetically focused beams of relativistic charged particles is investigated analytically in the cold-fluid approximation. Closed expressions for the beam-related parameters and magnetic and electric fields are derived. The results obtained in this work represent the basis for the stability analysis of sheared rippled beams that is required, for example, for beam stabilization and generation of free-electron laser devices.

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).

Since the first paper by Barston (1964) on electrostatic oscillations in inhomogeneous cold plasmas, it has been commonly accepted that all finite layers with a continuous profile in pressure, density and magnetic field cannot support normal surface waves but instead the waves always decay through phase mixing (also called resonant absorption). Here we reanalyse the problem by studying a compressible current sheet of a general structure with rotation of the magnetic field included. We find that all inhomogeneous layers considered in the high-β plasma limit do not support normal modes. However, in the limit of a low-β plasma there are some cases when normal-mode solutions are recovered. The latter means that the process of resonant absorption is not common for all inhomogeneous layers.

Simple higher-order approximations for the linear growth rate γ(k) of the electron Weibel instability are obtained by using fractional approximations for the plasma dispersion function. Approximate expressions for γ(k) are found that are valid in the regions T⊥/T‖ < 5 and T⊥/T‖ > 120 (where T⊥ and T‖ are perpendicular and parallel electron temperatures respectively).

A hydrodynamic theory is presented for plasma particles whose distribution function is close to a plateau in some phase-space region for a finite one-dimensional phase-spase interval. In the framework of the methods of moments, a series expansion of the particle distribution function in an appropriate system of orthogonal (Legendre) polynomials near the state with a plateau is carried out. Deviations from the plateau are due to the presence of a heat flux. The expansion obtained for the distribution function is used to truncate the chain of hydrodynamic equations and to calculate the additional terms arising from the finiteness of the phase interval. The case of one-dimensional Langmuir turbulence is considered as an example. Expressions are presented for the moments of the quasilinear integral of collisions, which describe the variations of the macroscopic characteristics of resonant particles in the respective hydrodynamic equations. Criteria for applicability of the equations obtained are presented. Approximate invariants of motion are obtained in the extreme cases of narrow and broad plateaux.

We study plasma-beam injection into transverse magnetic fields using both electrostatic and electromagnetic particle-in-cell (PIC) codes. In the case of small beam momentum or energy (low drift kinetic β) we study both large- and small-ion-gyroradius beams. Large-ion-gyroradius beams with a large dielectric constant ε ≫ (M/m)½ are found to propagate across the magnetic field via E × B drifts at nearly the initial injection velocity, where and M/m is the ion-to-electron mass ratio. Beam degradation and undulations are observed, in agreement with previous experimental and analytical results. When ε is of order (M/m)½ the plasma beam propagates across field lines at only half its initial velocity and loses its coherent structure. When ε is much less than (M/m)½ the beam particles decouple at the magnetic field boundary, scattering the electrons and slightly deflecting the ions. For small-ion-gyroradius beam injection a flute-type instability is observed at the beam-magnetic-field interface. In the case of large beam momentum or energy (high drift kinetic β) we observe good penetration of a plasma beam by shielding the magnetic field from the interior of the beam (diamagnetism). However, we observe anomalously fast penetration of the magnetic field into the beam and find that the diffusion rate depends on the electron gyroradius of the beam.

We investigate the effects of compressibility on magnetic reconnection, using as a basis the incompressible models of Priest & Forbes and Jardine & Priest. Our results show that compressibility modifies the reconnection process, without changing its essential character. In the region of inflowing plasma, compressibility tends to increase the convergence or divergence of the flow. Also, for regimes with a compression in the inflow the maximum rate of reconnection is increased, while for regimes with an expansion in the inflow the magnetic Mach number at the entrance to the diffusion region is increased. In the region of outflowing plasma the main effects of compressibility are to produce faster and narrower outflow jets, with a lower magnetic field strength.

We consider the transition scattering of waves on charged dust particles in a plasma. The scattered power is first derived from perturbation theory, for the case of weakly charged grains, where linear screening by the plasma particles can be assumed. In the case of a highly charged grain we first determine the nonlinear screening by the plasma particles, in a model where the grain can be treated as a small spherical probe at floating potential, and then solve the nonlinear transition scattering due to the electron shielding cloud. One of the results of our calculation is that the radiation pressure on the grains can be greatly enhanced with respect to the case of usual Thomson scattering on free particles, and some possible astrophysical consequences are discussed.