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.

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.

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.

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).

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 explore the long-term nonlinear evolution of a tearing-mode-unstable sheared-field plasma in a turbulent environment. Two different physical configurations are modeled, and a different computational system is used for each. Results of both sets of calculations show that magnetic tearing arises spontaneously provided that the initial turbulence energy level is below the natural saturation level of the tearing instability.

We discuss briefly the relationship between our results and those of previous calculations, concluding that there are no significant unexplainable disagreements.

In this paper we develop spectral laws for the small- and large-wavenumber regimes of the energy and enstrophy cascades in electrostatic turbulence and discuss how these spectra differ, owing to compressibility effects, from those for two-dimensional hydrodynamic turbulence. We also show that the compressibility effects on the scaling laws can be described as intermittency corrections formulated according to the log-normal model of Obukhov and Kolmogorov.

Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic.

A study has been carried out of free double layers formed within the plasma volume of a low-pressure mercury-arc discharge at high current densities. The free double layer is observed to form as a visible boundary, which drifts slowly from the central section of the discharge. Current-driven instabilities are observed as the discharge current is gradually increased to a critical value, at which current limitation is observed to occur. This process, which is accompanied by high-current spikes, ceases when the free double layer becomes visible as a sharp boundary dividing the discharge column into two regions of different luminosities. The layer is observed to form in the later stages of current limitation, the onset of which occurs for a ratio of drift to thermal speed of electrons of about unity. Electrical energy is converted by the layer into kinetic energy of the charged particles. Accordingly, high-energy ions were measured by means of an electrostatic energy analyser. The multiple-sheath character of the free ‘double layer’, which is inferred from probe measurements of potential profiles, is discussed and comparisons with other space-charge structures with the same topology are made.