2021/12/09 by Yannick Privat, Privat, Yannick, Rémi Robin +3 · 1 citation
Materials Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Fusion materials and technologies #Laser-Plasma Interactions and Diagnostics #Magnetic confinement fusion research #Optimization and Control (math.OC) #Plasma Physics (physics.plasm-ph)
paper · doi:10.48550/arxiv.2112.05049
openalex publication_date 2021/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are interested in the design of stellarators, devices for the production of controlled nuclear fusion reactions alternative to tokamaks. The confinement of the plasma is entirely achieved by a helical magnetic field created by the complex arrangement of coils fed by high currents around a toroidal domain. Such coils describe a surface called "coil winding surface" (CWS). In this paper, we model the design of the CWS as a shape optimization problem, so that the cost functional reflects both optimal plasma confinement properties, through a least square discrepancy, and also manufacturability, thanks to geometrical terms involving the lateral surface or the curvature of the CWS. We completely analyze the resulting problem: on the one hand, we establish the existence of an optimal shape, prove the shape differentiability of the criterion, and provide the expression of the differential in a workable form. On the other hand, we propose a numerical method and perform simulations of optimal stellarator shapes. We discuss the efficiency of our approach with respect to the literature in this area.