Quasisymmetry

Abstract

This thesis is a work in three parts on the concept of quasisymmetry. Quasisymmetry (QS) is a property of magnetic field-plasma systems (in particular stellarators) that enables at a basic level the containment of the plasma to undergo thermonuclear fusion. The concept of QS originated in the 80s, but the present work revisits the whole construction from a renewed perspective and explores unexplored questions. Part I of the thesis, Defining quasisymmetry, defines QS from the fundamental level of charged particle dynamics. This fundamental perspective, unlike the traditional consideration, allows the study of QS without making any assumption about the nature of underlying equilibria. This enables a deeper understanding of the property, as well as its interaction, both kinetically and at the fluid level, with equilibria including anisotropic pressure and large flows. Traditionally QS has been tied inextricably to the assumption of magnetohydrostatic equilibrium with isotropic pressure. Part II of the thesis, Constructing quasisymmetry, employs this renewed perspective on QS to attempt the construction of solutions. We commence with a detailed exploration of the often-used optimisation framework. We then present a novel energy principle to find energy minima solutions that are quasisymmetric. Obtaining explicit, non-numerical solutions is however not straightforward from either procedure. Solving the governing partial differential equations directly is also too complex, and thus, we consider an asymptotic description of solutions around their core. This framework allows for systematic construction of quasisymmetric fields, including when they are in equilibrium with anisotropic pressure, which elucidates and resolves a serious, historically encountered conundrum. We also use this asymptotic description as an approximate model to unveil a structured topological phase space of quasisymmetric solutions, providing an opportunity to understand their properties and exhaust possibilities of quasisymmetric configurations. Finally, Part III, Quasisymmetry and magnetic islands, explores the concept of magnetic islands in quasisymmetric fields. This requires a study of current singularities in the fields, whose presence is the precursor of magnetic islands. A simple model for the interaction of these magnetic structures with flows, potentially significant in QS, is also presented.