A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.

The electron distribution fonction in a particle-beam generated plasma is derived in its low- and medium-energy portion (under the first excitation threshold) from a Boltzmann equation, which contains elastic and inelastic collisional processes and a continuous source term. This equation is analytically solved and we discuss the importance of the non-Maxwellian deviations and their consequences for the determination of macroscopic values such as electron density or ‘temperature’. A numerical discussion is included for the case of an argon plasma created by a high-energy electron beam between 103 and 106 eV.

The equilibrium electron distribution in a general high-energy particle-beam generated plasma is analysed in detail by a Laplace transformation method in the neighbourhood of the first excitation threshold of the target gas, where all collisional processes, elastic and inelastic, must be taken into account concurrently with a continuous source term. Two continuity conditions for the distribution (and.its derivative) calculated below and above the first threshold, enable us to obtain an analytic representation of the macroscopic quantities such as electron temperature and density. A numerical application is made for the case of a high-energy electron beam ionizing atomic argon and the results are compared with those of the Plasma Group of Orsay.

Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves.

We derive the coupled-mode equations for the non-resonant interaction of three high-frequency surface waves propagating along a cold plasma column with sharp movable boundary. The plasma is then supposed to be surrounded by vacuum. Our boundary conditions take into account the effects of the presence of surface charges, as well as the movements of the boundary. The coupling coefficients are expressed in explicit forms and compared with previous results.

The linear dispersion relation for electrostatic electron waves is analysed in some detail. A method is described which allows the dispersion equation to be solved and the attenuation rate/growth rate to be derived for waves generated by electrons flowing through a stationary plasma along the field lines of a static magnetic field. The solution is derived from three simple curves (one for each of the real and imaginary parts of the dispersion equation and one for the growth rate) and is applicable for any propagation angle relative to the magnetic field lines (below a limiting value), for any wavelength, any magnetic field intensity, any electron density and temperature and any flow speed of a beam plasma component. The effects of cyclotron resonance start to be significant at an angle from the direction of the magnetostatic field lines that depends on most of the variables mentioned, but only in one specific combination, which is the measure of the ratio between thermal velocity of the electrons and the phase velocity of the wave at the cyclotron frequency. In contrast to numerical methods, the method described here provides a parameterization of the solutions to the dispersion equation and of the growth rate. It gives an overview of the dependencies on the variables in the equation over a large part of parameter space without any other computations than those involved in adjusting scale factors.

The lower-hybrid instabilities in high-beta (ratio of plasma to magnetic pressure) plasmas driven by ring-ion distributions in velocity space are investigated. A dispersion equation including electromagnetic effects is derived. In the low-beta limit, analytic expressions are obtained which illuminate the physical nature of the instabilities. The complete dispersion equation is solved numerically as a function of ring speed and plasma beta for several types of ring distribution. Electromagnetic effects are important for relatively energetic rings even in the low-beta regime, suppressing growth rates and shifting the angle of propagation to more oblique angles. Stabilization by thermal effects is also discussed. Application of these results to the Earth's bow shock, AMPTE, comets and solar flares is suggested.

A ring distribution of ions in velocity space can generate electrostatic waves which propagate predominantly along an ambient magnetic field at frequencies comparable with the ion plasma frequency. A dispersion equation which accounts for these waves is presented, and solved analytically and numerically. It was found that ion-acoustic-like waves are excited in a plasma even if the electron temperature is comparable with the ion temperature under the assumption of an anisotropic ion distribution.

Numerical solutions were obtained by Forbes, Priest & Hood (1982) for the resistive decay of a current sheet in an MHD fluid. To check the accuracy of the numerical solutions, a linear, analytical solution was also deived for the regime where diffusion is dominant. In a subsequent reinvestigation of this problem an error in the linear, analytical solution has been discovered. For the parameter values used in the numerical solution this error is too small (≲ 2%) to produce any significant change in the previous test comparison between the numerical and analytical solutions. However, for parameter values much different from those used in the numerical solution, the error in the linear solution can be significant.