A class of exact stationary statistical states for the inviscid magnetohydrodynamic equations in two dimensions and in various geometries is found and the corresponding fluctuation spectra are calculated. Some solutions agree with previous computations in the canonical ensemble while other solutions are found. In particular, the Navier—Stokes limit is recovered and maximum cross helicity solutions exist in two dimensions. The difficulty of proving existence and uniqueness of statistical solutions for non-dissipative two-dimensional turbulence is quoted in terms of rugged constants and associated Gibbs measure.

Numerical solutions of the momentum and energy equilibria in a two-temperature diffuse pinch show that it is possible for the electron temperature to have a radially oscillating component with a wavelength of the order of ae(mi/me)1/2, where ae is the electron Larmor radius. This is also the order of magnitude of the optimum wavelength for growth of an electro-thermal instability in a homogeneous plasma (studied in part 3 of this series) and suggests this kind of instability as a possible primary source of a current filamentation in the plasma. It has also been revealed both analytically and computationally in this strictly steady state model that the pressure of one species (ions or electrons) is finite at the wall boundary; the same study carried out on a neo-classical model shows, however, that strict confinement is possible provided some restrictions are imposed upon its free parameters. This is also found with a model employing classical tensor conductivity (studied in part 2).

A tensor conductivity model for a fully ionized, two-temperature, cylindrical and diffuse pinch is constructed and its properties analyzed under energy and momentum equilibria conditions. The set of Braginskii's classical two-temperature tensor transport equations are solved for the strict steady state and the radial equilibria profiles of the relevant parameters produced. Unlike the scalar conductivity model (part 1 of this series) tensor coefficients yield profiles with the appropriate ideal boundary conditions, namely zero pressure and temperatures at the plasma radius. Furthermore, spatial oscillations of the electron temperature only occur for extreme values of the free parameters.

Using a test particle approach, the potential of a trapped electron is calculated outside the Debye sphere in the electrostatic limit. The potential strongly depends on some characteristic parameters, such as bounce frequencies of the test and background trapped particles, the total number of trapped particles, etc. In some cases, the potential falls off as the inverse of the distance r. The model is limited to the single-wave case; possible generalizations to the many-wave situation in a turbulent plasma are discussed.

A fully relativistic stream superposition model is employed to conduct a linear numerical simulation of a self-consistently confined sheet of collisionless, neutral plasma. This multi-stream model employs a novel variable termed the ‘canonical momentum potential’ (or ‘action function’) to follow the ion and electron dynamics. For the classic, unsheared sheet pinch, growth rates obtained for the tearing instability are in reasonable agreement with previous estimates using an approximate Vlasov approach. Current shear is then introduced into the sheet and growth rates are again measured. Stabilization of the shorter wavelength modes is observed.

The two-dimensional stability of Langmuir solitons in investigated taking into account the dynamic ion response and electron nonlinearities. A variational principle for the growth rate is derived which allows one to determine growth rates and regions of instability by standard numerical procedures. The validity of previous methods using trial functions and the variation of action method, as well as the limitations of the corresponding results for the growth rates, neglecting the dynamic ion response, are critically examined.

The beam-whistler and ion cyclotron instabilities are proposed as principal mechanisms for the generation of precursor turbulence in shock waves propagating along the constant magnetic field. The beam is formed from ions which are reflected from a potential barrier whose existence inside the shock layer is assumed. We find that these reflected beam particles drive unstable a spatial continuum of zero group velocity (with respect to the shock front) precursor whistler waves.

Magnetoacoustic waves were generated in an argon plasma by passing an RF current through a solenoid antenna surrounding the plasma column. The complex impedance of the antenna was measured as a funcion of wave frequency in order to investigate the column geometric resonances and to obtain estimates of ion density and electron temperature. Although this technique yielded reliable estimates of the ion number density, the wave &litudes near resonance were found to be anomalously low and reliable temperature measurements could not be obtained.

Structures of the current layer between two magnetized anisothermal plasmas are studied on the basis of a kinetic formulation. It is shown that the structure of the current layer is dominantly controlled by the hotter species of the plasmas. The thickness is characterized by the ion gyroradius if the ion temperature is much greater than the electron temperature. The structure is, in general, insensitive to the asymptotic potential difference and the relative flow velocity between plasmas on the two sides.

The problem of a monochromatic plane electromagnetic wave incident from a vacuum onto a plasma slab is considered. The method of solution is based on the representation of the disturbance in the plasma layer as that generated by an appropriate current source in the complementary regions into which, for the purpose of the representation, the plasma is conceived to extend. The normal incidence case is treated first for both the specular reflexion and the absorption boundary conditions, with the extension to oblique incidence following in a later section of the paper.

Parametric decay of magneto-acoustic oscillations in a cylindrical plasma column is considered, including the Hall effect and the effects of finite resistivity. Growth rates for axisymmetric modes in decay instabilities are derived and applied to the problems of parametric excitation of Alfvén waves and supplementary heating of plasmas. It is shown that both the slow (ion cyclotron) and fast (compressional) modes may be parametrically excited. The threshold &litudes for nonlinear dissipation of pump field energy are calculated and briefly discussed.

The propagation of a linear wave packet in a generally dispersive, but non- absorbing, medium is considered. By an extension of the principle of stationary phase to higher inverse order in time, an approximation is derived that encompasses both the main signal propagating at the group speed, and the precursors that precede and follow it.

In this note we investigate the stability of large-amplitude longitudinal relativistic plasma waves. We find that they are secularly stable, that is, small perturbations grow in time proportional to time but not exponentially with time. Similar results have recently been obtained for transverse waves by Romeiras (1978)