Understanding and designing quasisymmetric stellarators: a topological approach

Designing viable stellarator configurations requires a search in a large space of parameters. Although optimization in such a space has proven useful and provided many designs, its complexity makes this approach seem like a `black box' that provides designs piecemeal. We present an alternative topology-mediated perspective on the space of configurations, focusing on quasisymmetric stellarators. The main change in perspective comes from considering configurations beginning from the axis and moving outward (the "inside-out" model) rather than the traditional approach that begins from the outermost flux surface and moves inward (the "outside-in" model). We characterize configurations in a highly reduced model, starting with the topological structure of a closed curve (the magnetic axis), along with a few additional shaping parameters. Doing so confers configuration space a topological structure (quasisymmetric phases and phase transitions) that organises it in a powerful way, in which the desirability of configurations as quasisymmetric designs can be simply assessed. This description can be used to understand the nature of typical quasisymmetric designs as well as explore the space of possibilities more exhaustively, leading to new design possibilities.