Flux-Surface Shaping in Stellarators and Tokamaks

This paper addresses the challenge of characterizing and shaping magnetic fields in stellarators, crucial for achieving quasi-symmetry and efficient plasma confinement. It introduces a novel method using Fourier mode analysis to define and analyze the shapes of flux surfaces, applicable to both axisymmetric and non-axisymmetric configurations. The findings reveal a spatial resonance between shape complexity and rotation, correlating with rotational transform and field periods, offering insights into optimizing stellarator designs.