Optimization of modular and helical coils applying genetic algorithm and fully-three-dimensional B-spline curves

A new numerical method for designing the external coils of a stellarator is presented. In this method, the shape of filamentary coils is expressed using fully three-dimensional B-spline curves that are not necessarily constrained on a winding surface. The control points of B-spline curves are optimized together with the coil position and current to minimize an objective function, which is defined using normal field components and engineering constraints. The genetic algorithm is employed to minimize the objective function for arbitrary combinations of modular, helical, and circular poloidal field coils without giving any specific initial guess of coil shapes. A new numerical code genetic optimizer using sequence of points for external coil is developed on the basis of this method, and successfully found optimized modular coils for the stellarators CFQS and Wendelstein 7-X. We also found a specific pattern of helical coil arrangement that can reproduce these optimized stellarators while creating divertor legs outside of the closed magnetic surfaces.