Title:

Numerical modelling of low temperature plasma

The intention of this thesis is to gain a better understanding of basic physical processes occurring in low temperature plasmas. This is achieved by applying both analytic and numerical models. Low temperature plasmas are found in both technological and astrophysical contexts. Three different situations are investigated: an instability in electronegative plasmas; electron avalanches during plasma initiation; and a phenomenon called the Critical Ionisation Velocity interaction. Industrial plasma discharges with electronegative gases are found to be unstable in certain conditions. Fluctuations in light emission, particle number densities and potential are observed. The instability has been reproduced in a variety of experiments. Reports from the experiments are discussed to characterise the key features of the instability. An, as yet unconsidered, physical process that could explain the instability is introduced. The instability relies on the plasma's transparency to the electric field. This mechanism is investigated using simple zerodimensional numerical and analytic models. The results from the models are compared to experimental results. The calculated frequencies are in good agreement with the experimental measurements. This shows that the instability mechanism described here is relevant. For the remaining two problems a threedimensional particle model is constructed. This model calculates the trajectories of each individual particle. The potential field is solved selfconsistently on a computational mesh. Poisson's equation is solved using a Multigrid technique. This iterative solution method uses many grids, of different resolutions, to smooth the error on all spatial scales. The mathematical foundation and details of the components of the Multigrid method are presented. Several test cases where analytic solutions of Poisson's equation exist are used to determine the accuracy of the solver. The implemented solver is found to be both efficient and accurate. Collisions are vitally important to the evolution of plasmas. The chemistry resulting from collisions is the reason why plasmas are so useful in technological applications. Electron collisions are included in the particle model using a MonteCarlo technique. A basic method is given and several improvements are described. The most efficient combination of improvements is determined through a series of test cases. The error resulting from the collision selection process is characterised. Technological plasmas are formed from the electrical breakdown of a neutral gas. At atmospheric pressure the breakdown occurs as an electron avalanche. The particle model is used to simulate the nanosecond evolution of the avalanche from a single electronion pair. Special attention is paid to the inelastic collisions and the creation of metastables. The inelastic losses are used to estimate the photon emission from the electron avalanche. The Critical Ionisation Velocity phenomena is investigated using the particle model. When a neutral gas streams across a magnetised plasma the ionisation rate increases rapidly if the speed of the neutrals exceeds a critical value. Collisions between neutrals and positive ions create pockets of unbalanced negative charge. Electrons in these pockets are accelerated by their potential field and can reach energies capable of ionisation. The evolution of such an electron overdensity is simulated and their energy gain under different density and magnetic field conditions is calculated. The results from the simulation may explain the discrepancy between laboratory and space experiments.
