Numerical Methods for Stellarator Equilibrium and Optimization: Continuation Methods, Free Boundary Equilibrium, and Constrained Optimization

Abstract

The stellarator is a promising concept for a future nuclear fusion power plant, but hasgotten relatively little attention compared to the tokamak concept. One of the main reasons for this is the computational expense of modelling and designing them, and the fact that a stellarator power plant requires extensive numerical optimization to ensure good confinement of heat and particles. In this thesis a number of new developments towards the goal of designing and optimizing a future stellarator power plant are described, as encompassed in the DESC code for stellarator equilibrium and optimization. Novel use of continuation and perturbation methods allows for solving the complicated 3D MHD equilibrium problem orders of magnitude more quickly and accurately than legacy codes. New high order methods for singular integrals similarly improve the solution of the free boundary equilibrium problem. We also consider new optimization methods for both equilibrium constrained optimization and more general constraints that accelerate the problem of optimizing a stellarator for desirable physics properties.