New high-order accurate free surface stellarator equilibria optimization and boundary integral methods in DESC

Abstract

DESC is the state-of-the-art code that solves the ideal magnetohydrodynamic partial differential equations subject to a fixed boundary condition. However, to simplify the problem a standard, yet potentially inconsistent, assumption is made: nested flux surfaces. Still, this assumption is commonly used because it simplifies the partial differential equation and most desirable equilibria approximately have this property. This work extends the DESC code so that this assumption does not need to be made in vacuum fields and improves free surface equilibrium optimization. We design and implement automatically differentiable algorithms to solve the vacuum field and free surface problems. This will lead to improved study of stellarator equilibria. The boundary integral methods implemented in this work also have utility for optimization objectives to be used in the future.