Discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. To meet the complex field shaping requirements of state-of-the-art stellarator plasma equilibria, numerical optimization methods are typically necessary to find a viable design. Most stellarator magnet design approaches employed to date have used continuous optimization algorithms, and the magnet geometry has accordingly been defined with continuous parameters. However, discrete optimization methods could offer some advantages, particularly in finding designs that comply with arbitrary spatial restrictions. In this presentation, a possible approach for discrete coil design is introduced. The solution space is formulated as a "wireframe" consisting of a mesh of interconnected wire segments that encloses that plasma. The wireframe structure enables the use of a "greedy" optimization approach, in which loops of current are added to the mesh one-by-one to achieve the desired magnetic field on the plasma boundary. The greedy optimization developed here is inspired by the successful application of similar methods for designing arrays of permanent magnets for stellarators. This talk will describe the wireframe formulation and the greedy optimization algorithm and present some initial solutions obtained through this approach.