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The increasing sophistication of the magneto-fluid equations permits their application to a wide variety of physical problems in thermonuclear fusion research, in astrophysics and in geophysics. The equations are in general non-linear, and of mixed hyperbolic, parabolic and ordinary differential type, and are frequently supplemented by elliptic equations, and for their full elucidation, they must clearly be studied numerically. While one-dimensional calculations have successfully been applied for a number of years, severe difficulties have limited the extension to multi-dimensional problems. In this thesis the fully ionised magnetohydrodynamic equations have been studied numerically in the R-Z plane, and the difficulties of such an approach are analysed. For many problems explicit methods may be adapted, and it is shown that a sophisticated fluid model can readily be solved on existing machines. The problems posed particularly, by the advection of fluid variables on a general Eulerian mesh without corrupting physical diffusion, by large variations in the Alfven velocity, and by the necessity of solving elliptic equations at each timestep are overcome. Two physical and contrasting problems are considered. The first problem and main application of the work has been to the study of the dense plasma focus - a non-cylindrical z-pinch phenomenon where the magnetic field is restricted to the azimuthal direction, so that the space remains iso-tropic. The plasma is described by six conservation equations for the density (p), momentum (pv), magnetic flux (Be), electron and ion pressure. Transport processes include electron and ion heat conduction, the resistive and Hall electric fields and ion viscosity. Cyclotron orbiting effects for both electrons and ions are included so that a mixed collision-less, collision-dominated regime is permitted. Good agreement with the limited experimental knowledge of the plasma focus has been obtained. The dynamics of the shock formation of the plasma focus and particularly the axisymmetric nature of the shock are well described. The extremely high kinetic energy densities obtained in the numerical fluid experiment as the result of adiabatic compression and viscous heating agree well with experiment. Three features in the plasma focus are isolated: an anode cold source; a hot pinch region; and an axial shock. The 'anomalously' long lifetime of the plasma focus is shown to be the result of axial flow, with stabilisation of magnetohydro-dynamic modes through the ion stress tensor in the intermediate collision-less, collision-dominated regime. Estimates of the neutron yield based on the numerical fluid experiment concur with experimental yields, and are the result of thermally reacting deuterons in the hot pinch region. The plasma parameters of interest determined from the hot pinch region suggest that the ion distribution function will not have a simple Maxwellian form and this in particular may account for the discrepancy with experiment on the anisotropy in space of the neutron yield.

In this thesis we attempt to predict the performance of a device, known as a flow coupler, which consists of an M.H.D. generator coupled to an M.H.D. pump so that one stream of fluid is induced to move by the motion of another. The change of magnetic field experienced by a moving conductor as it passes into an M.H.D. device can cause large eddy currents to circulate within the M.H.D. duct. We have used apparatus in which we represent the moving stream of liquid by an annular disc of aluminium, to investigate the perturbation of the applied magnetic field and of the electric potential distribution caused by these eddy currents. We then examine both experimentally and theoretically, devices in which large currents flow through a moving conductor and through an external circuit. These currents are injected into the moving conductor through electrodes which have a high resistance to currents in the direction of motion. We show that for compensated devices, that is, devices in which the external conductors are arranged so that they produce no transverse magnetic field, the perturbed magnetic field does not depend upon the current through the external circuit and is the same field that would exist if there were no contact between the moving metal and the external circuit. We observe experimentally that when two conductors move side by side through the gap of a magnet the magnetic field in one moving conductor is little affected by the motion of the other. We compare the measured performance of a simulated M.H.D. generator and of a real M.H.D. pump with their computed performances and we calculate the expected performance of a flow coupler. We suggest that the presence of a slowly moving liquid in the boundary layers adjacent to the duct walls may adversely affect the performance of a flow coupler and we conclude that an efficient flow coupler would require non-conducting duct walls and a high magnetic field.

Part A of this thesis is concerned with the study of the mechanism of discharges in shock heated Argon between cold electrodes, in a configuration similar to that of a MHD generator. A model which describes the total voltage between the electrodes as a function of the current density J is proposed. This model takes into consideration boundary layer conditions and electrode processes. Experiments were carried out with different electrode cross sections to check the theory and its range of application. The current was found to vary smoothly with the voltage and reached higher values than the saturation ionic current density through the cathode sheath, so that field emission in the cathode is a conduction mechanism present in the high current regime. A determination of the profile of ne(electronic density) behind the shock front was also carried out using interferometric techniques. These results have been used in Part B of the thesis which is concerned with MHD Power Generation using the same facility and very similar geometry to that in Part A . The performance of the generator was studied with the help of a model which takes account of the finite dimensions of the electrodes This model was extended to a case when voltage electrode losses appear, and variations of the flow parameters and B due to the strong interaction were considered. Faraday and Hall configurations were used with different electrode/insulator ratios and external loads. The Faraday generator performance showed good agreement with the theory if electrode voltage losses were taken into account, and the power output was high. When the ratio insulator/electrode was small, power output dropped sharply due to leakage currents; a explanation is given and a parallel to the ease with high Hall coefficient is drawn. The influence of electrode losses on the performance is also studied. The Hall generator performance does not agree with the theory and the power output is very low. This is tentatively explained in terms of electrode voltage losses and shorting between adjacent electrodes.