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PhD Candidate: Michael R Lindstrom
Mathematics, UBC
Thu 7 May 2015, 9:00am SPECIAL
One Time Event
Room 203, Graduate Student Centre, UBC
Exam: Investigation into the Feasibility and Operation of a Magnetized Target Fusion Reactor, and Qualitative Predictions of Magnetic Field Profile Perturbations Induced by Surface Roughness in Type II Superconductors: Insights from Mathematical Modelling
Room 203, Graduate Student Centre, UBC
Thu 7 May 2015, 9:00am-11:00am


In this thesis we study two problems, one concerning fusion energy and another superconductivity.

Magnetized target fusion reactors are a modern idea to generate hydrogen fusion energy on earth. The design entails magnetically confining a plasma and crushing it in an imploding shell of molten metal. The design has many unresolved questions in its feasibility as a power source and its efficiency. We study the problem with two approaches. Firstly, we use a coordinate transformation and implement a novel flux-limited, split-step, finite volume scheme for nonlinear coupled conservation laws and do a parameter sensitivity analysis for the performance. Secondly, by a careful series of asymptotic arguments, we establish a leading order expression for the plasma compression. This expression is qualitatively consistent with numerical simulations, but it also gives new insights into the device operation. We then infer key design parameters for the success of magnetized target fusion.

The second problem involves computational modelling of superconductors. In type II superconductors where the coherence length ξ is small compared to the London penetration depth λ, the London equation predicts that magnetic fields decay exponentially in magnitude with the depth into the superconductor with length scale λ, provided the surface is flat. Various measurements of λ using low energy muon spin rotation on superconductors such as Yttrium-Barium-Copper-Oxide measure field profiles that differ from this prediction. There seems to be a dead layer, a distance δ over which the magnetic field magnitude does not decay. Speculation has been made that this may be due to surface roughness. Surface roughness has been studied for a simple sinusoidal model of surface roughness. We extend this work firstly by using Atomic Force Microscopy data of Yttrium-Barium-Copper-Oxide (a type II superconductor) crystals and predicting the field profiles the crystals could produce with the London model given their actual surface geometry; and secondly, we consider how roughness could affect experimental values for λ and δ. We find that dead layers are unlikely due to roughness alone, that the measurement of λ may be influenced by surface roughness, and that the field orientation may be perturbed, negligibly, within the superconductor.