Mode Coupling in a Non-Uniform Magnetised Plasma

[摘要] This thesis presents an analysis of radial waves in a helically structured cold plasma. The problem is solved by numerically integrating a set of coupled differential equations for the electric field. Results showing the conversion of energy between different modes of propagation are presented. Relevance to plasma heating is discussed, and the merits and demerits of different solution methods are compared. Chapter 1 surveys the ubiquity of the plasma state and focuses on two areas which motivate this work: coronal loops and tokamak heating. In Chapter 2, the mathematics necessary for the description of the plasma state is introduced and the cold, multi-fluid equations used later in the thesis are derived. An overview of linear waves in a cold plasma is presented. A general survey of the modelling of non-uniform plasma media is given in Chapter 3, where the WKB solutions and the notion of a local dispersion relation are introduced. The specifics of our chosen system are introduced in Chapter 4. A consistent equilibrium field, of constant magnitude, but varying in direction is obtained and described. Linear wave solutions to the cold plasma equations for electrons are sought, and a set of coupled odes for the electric fields are derived, in the regime of negligible equilibrium flow. It is shown that asymptotic solutions may be obtained for these equations, and their form and range of validity is discussed. Wave equations for the electric field which include the full effects of equilibrium flow are then discussed. Splicing the helical field onto a uniform one at a fixed radius gives a useful simple model of a number of relevant physical structures, whose solution is investigated in detail in Chapter 5. Expressions for amplitudes of converted and reflected waves are found in terms of the value of electric fields and their gradients at the boundary between the two regions. The values of these are found numerically for a variety of plasma. parameters. and the implications of the results discussed. The results are compared with the asymptotic approximations found earlier, and the agreement found to be very good. The possibility of deriving WKB solutions to the model equations and of applying one other commonly used technique is considered in Chapter 6. Chapter 7 summarises the conclusions of this work, and gives suggestions for future research. The original work of this thesis is contained in Chapters 4 to 6.

[发布机构] University:University of Glasgow

[关键词] Plasma physics