Investigation into the feasibility and operation of a magnetized target fusion reactor : insights from mathematical modelling

Magnetized target fusion reactors are a modern idea to generate hydrogen fusion energy on earth. The design entails confining a plasma with a magnetic field and crushing it in an imploding shell of molten metal. Such a design has many unresolved questions in terms of its feasibility as a power source and ways to make it efficient. In this thesis, we will look into two of the approaches undertaken to explore these questions. Firstly, we use a coordinate transformation and implement a novel flux-limited, split-step, finite volume scheme for nonlinear coupled hyperbolic partial differential equations. With this numerical scheme, we do a parameter sensitivity analysis for the design performance. Secondly, by a careful series of asymptotic arguments, we establish a leading order asymptotic expression for the plasma compression. This expression is qualitatively consistent with the numerical work, but it also gives new insights into how the device operates. Together these approaches allow us to infer key design parameters for the success of magnetized target fusion. We will conclude with a look into the viability of magnetized target fusion and some problems for future work.Science, Faculty ofMathematics, Department ofGraduat